sqrt(1-sqrt(1-x^2))
Time bar (total: 5.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 0 |
| 100% | 25% | 0% | 75% | 0% | 0% | 0% | 1 |
Compiled 17 to 12 computations (29.4% saved)
| 1.4s | 4 568× | 2 | valid |
| 327.0ms | 2 429× | 1 | valid |
| 285.0ms | 1 078× | 3 | valid |
| 13.0ms | 181× | 0 | valid |
ival-sqrt: 545.0ms (33.6% of total)ival-sub: 491.0ms (30.3% of total)adjust: 326.0ms (20.1% of total)ival-pow2: 157.0ms (9.7% of total)ival-<=: 69.0ms (4.3% of total)ival-and: 15.0ms (0.9% of total)exact: 12.0ms (0.7% of total)ival-assert: 6.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 134 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
| 124 | 0 | - | 3 | (1.010186870570106e-159) | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
| 0 | 0 | - | 0 | - | (pow.f64 x #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) | cancellation | 134 | 0 |
sqrt.f64 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) | uflow-rescue | 121 | 0 |
| ↳ | (pow.f64 x #s(literal 2 binary64)) | underflow | 121 | |
| ↳ | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) | underflow | 121 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 255 | 0 |
| - | 0 | 1 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 255 | 0 | 0 |
| - | 0 | 0 | 1 |
| number | freq |
|---|---|
| 0 | 1 |
| 1 | 255 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 86.0ms | 158× | 1 | valid |
| 51.0ms | 272× | 2 | valid |
| 18.0ms | 70× | 3 | valid |
| 1.0ms | 12× | 0 | valid |
Compiled 81 to 28 computations (65.4% saved)
ival-sqrt: 86.0ms (68.3% of total)ival-sub: 15.0ms (11.9% of total)adjust: 14.0ms (11.1% of total)ival-pow2: 9.0ms (7.1% of total)exact: 1.0ms (0.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 21 |
| 1 | 22 | 19 |
| 2 | 47 | 19 |
| 3 | 100 | 19 |
| 4 | 142 | 19 |
| 5 | 199 | 19 |
| 6 | 329 | 19 |
| 7 | 601 | 19 |
| 8 | 1004 | 19 |
| 9 | 1584 | 19 |
| 10 | 3934 | 19 |
| 11 | 5632 | 19 |
| 12 | 6396 | 19 |
| 13 | 6694 | 19 |
| 14 | 6750 | 19 |
| 15 | 6770 | 19 |
| 16 | 7037 | 19 |
| 17 | 7631 | 19 |
| 0 | 8 | 9 |
| 0 | 13 | 9 |
| 1 | 20 | 9 |
| 2 | 31 | 9 |
| 3 | 42 | 9 |
| 4 | 61 | 9 |
| 5 | 88 | 9 |
| 6 | 138 | 9 |
| 7 | 311 | 9 |
| 8 | 642 | 9 |
| 9 | 1239 | 9 |
| 10 | 2151 | 9 |
| 11 | 3890 | 9 |
| 12 | 4877 | 9 |
| 13 | 5208 | 9 |
| 14 | 5492 | 9 |
| 15 | 5661 | 9 |
| 16 | 5738 | 9 |
| 17 | 6029 | 9 |
| 18 | 7025 | 9 |
| 0 | 8155 | 9 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
| Outputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) |
Compiled 9 to 8 computations (11.1% saved)
Compiled 0 to 1 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 7.1% | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
Compiled 9 to 8 computations (11.1% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 34 |
| 0 | 13 | 34 |
| 1 | 20 | 34 |
| 2 | 31 | 34 |
| 3 | 42 | 34 |
| 4 | 61 | 34 |
| 5 | 88 | 34 |
| 6 | 138 | 34 |
| 7 | 311 | 34 |
| 8 | 642 | 34 |
| 9 | 1239 | 34 |
| 10 | 2151 | 34 |
| 11 | 3890 | 34 |
| 12 | 4877 | 34 |
| 13 | 5208 | 34 |
| 14 | 5492 | 34 |
| 15 | 5661 | 34 |
| 16 | 5738 | 34 |
| 17 | 6029 | 34 |
| 18 | 7025 | 34 |
| 0 | 8155 | 34 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
(pow.f64 x #s(literal 2 binary64)) |
x |
#s(literal 2 binary64) |
| Outputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
#s(literal 1 binary64) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(pow.f64 x #s(literal 2 binary64)) |
(*.f64 x x) |
x |
#s(literal 2 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) | |
| accuracy | 0.00390625 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) | |
| accuracy | 28.47933286027541 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) | |
| accuracy | 30.276676547946387 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
| 24.0ms | 136× | 2 | valid |
| 10.0ms | 79× | 1 | valid |
| 8.0ms | 35× | 3 | valid |
| 0.0ms | 6× | 0 | valid |
Compiled 36 to 10 computations (72.2% saved)
ival-sqrt: 10.0ms (34.7% of total)adjust: 7.0ms (24.3% of total)ival-sub: 7.0ms (24.3% of total)ival-pow2: 4.0ms (13.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
| Outputs |
|---|
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/16 (/ (pow x 2) (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 5/128 (* 1/16 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* 1/8 (pow x 2)))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(+ 1 (* -1 (pow x 2))) |
(sqrt (* x (pow (sqrt -1) 3))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (* -1/8 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 9))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))))) |
(* -1 (* x (sqrt -1))) |
(* x (- (/ 1 x) (sqrt -1))) |
(* x (- (/ 1 x) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1)) |
(* -1 (sqrt (* x (pow (sqrt -1) 5)))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1)))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* 1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 3))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* -1 (/ (+ (* -1/4 (sqrt (/ x (pow (sqrt -1) 3)))) (* 1/8 (sqrt (/ x (pow (sqrt -1) 7))))) (pow x 3))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* x (+ (sqrt -1) (/ 1 x))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (sqrt -1)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (sqrt -1)))) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | inf | ((sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (- 1 (pow x 2))) |
| 1.0ms | x | @ | 0 | ((sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (- 1 (pow x 2))) |
| 1.0ms | x | @ | -inf | ((sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (- 1 (pow x 2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 211 | 710 |
| 1 | 591 | 651 |
| 2 | 1842 | 633 |
| 3 | 4839 | 611 |
| 0 | 8257 | 577 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/16 (/ (pow x 2) (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 5/128 (* 1/16 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* 1/8 (pow x 2)))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(+ 1 (* -1 (pow x 2))) |
(sqrt (* x (pow (sqrt -1) 3))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (* -1/8 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 9))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))))) |
(* -1 (* x (sqrt -1))) |
(* x (- (/ 1 x) (sqrt -1))) |
(* x (- (/ 1 x) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1)) |
(* -1 (sqrt (* x (pow (sqrt -1) 5)))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1)))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* 1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 3))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* -1 (/ (+ (* -1/4 (sqrt (/ x (pow (sqrt -1) 3)))) (* 1/8 (sqrt (/ x (pow (sqrt -1) 7))))) (pow x 3))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* x (+ (sqrt -1) (/ 1 x))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (sqrt -1)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (sqrt -1)))) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
| Outputs |
|---|
(* x (sqrt 1/2)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(* x (+ (sqrt 1/2) (* 1/16 (/ (pow x 2) (sqrt 1/2))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(*.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) x) (fma.f64 (*.f64 #s(literal 7/256 binary64) x) x #s(literal 1/16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 5/128 (* 1/16 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) x) (fma.f64 (*.f64 #s(literal 33/2048 binary64) x) x #s(literal 7/256 binary64)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(* 1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/2 binary64)) |
(* (pow x 2) (+ 1/2 (* 1/8 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* -1 (pow x 2))) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(sqrt (* x (pow (sqrt -1) 3))) |
(sqrt.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x)))) x) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x))))) x) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (* -1/8 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 9))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 9 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x)))))) x) |
(* -1 (* x (sqrt -1))) |
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) |
(* x (- (/ 1 x) (sqrt -1))) |
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) |
(* x (- (/ 1 x) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* x (- (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (fma.f64 x (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64))) |
(* x (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(fma.f64 (/.f64 x (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(fma.f64 (/.f64 x (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1)) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(* -1 (sqrt (* x (pow (sqrt -1) 5)))) |
(neg.f64 (sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1)))))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x)))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* 1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 3))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(*.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x)))) x) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* -1 (/ (+ (* -1/4 (sqrt (/ x (pow (sqrt -1) 3)))) (* 1/8 (sqrt (/ x (pow (sqrt -1) 7))))) (pow x 3))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(*.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 7 binary64)))) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x)))) x) |
(* x (+ (sqrt -1) (/ 1 x))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 1 binary64)) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (sqrt -1)))) |
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)) x)) x) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (sqrt -1)))) |
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x)) x) (sqrt.f64 #s(literal -1 binary64))) x) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (*.f64 x (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
(neg.f64 (fma.f64 (/.f64 x (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 28 |
| 0 | 13 | 28 |
| 1 | 52 | 28 |
| 2 | 333 | 28 |
| 3 | 3410 | 28 |
| 0 | 8967 | 24 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64)))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))) (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (-.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (-.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 0 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) (sqrt.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)))) |
(*.f64 (pow.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x))) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64)))) (pow.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) |
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 9/2 binary64))) (pow.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -2 binary64)) (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (-.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) |
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(exp.f64 (*.f64 (log.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 2 binary64))) |
(exp.f64 (log1p.f64 (*.f64 x x))) |
(+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))) |
(+.f64 (pow.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))) |
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64)) |
(+.f64 (*.f64 x x) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) x)) |
(+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 x) x))) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)) |
(+.f64 #s(literal 1 binary64) (*.f64 x x)) |
Compiled 10 814 to 2 037 computations (81.2% saved)
8 alts after pruning (8 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 469 | 8 | 477 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 470 | 8 | 478 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 7.1% | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
| ▶ | 6.5% | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
| ▶ | 5.3% | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
| ▶ | 55.3% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
| 55.2% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) | |
| 55.0% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) | |
| 54.5% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) | |
| ▶ | 98.4% | #s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
Compiled 280 to 210 computations (25% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) | |
| cost-diff | 0 | (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) | |
| cost-diff | 0 | #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) | |
| cost-diff | 0 | (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) | |
| cost-diff | 0 | (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) | |
| cost-diff | 0 | #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) | |
| cost-diff | 0 | #s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 278 |
| 0 | 60 | 278 |
| 1 | 100 | 278 |
| 2 | 151 | 278 |
| 3 | 335 | 278 |
| 4 | 787 | 278 |
| 5 | 1610 | 278 |
| 6 | 2331 | 278 |
| 7 | 2861 | 278 |
| 8 | 3044 | 278 |
| 9 | 3669 | 278 |
| 10 | 7022 | 278 |
| 0 | 8382 | 278 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
#s(literal -1/2 binary64) |
(*.f64 x x) |
x |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(neg.f64 x) |
x |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
#s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) |
(fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) |
#s(literal 5/128 binary64) |
(*.f64 x x) |
x |
#s(literal 1/16 binary64) |
#s(literal 1/8 binary64) |
#s(literal 1/2 binary64) |
| Outputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
#s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (sqrt (- 1 (pow x 2))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
#s(literal -1/2 binary64) |
(*.f64 x x) |
x |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(neg.f64 x) |
x |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
#s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) |
(fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) |
(fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) |
#s(literal 5/128 binary64) |
(*.f64 x x) |
x |
#s(literal 1/16 binary64) |
#s(literal 1/8 binary64) |
#s(literal 1/2 binary64) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) | |
| accuracy | 0.01953125 | (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) | |
| accuracy | 0.15232092680874962 | #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) | |
| accuracy | 28.47933286027541 | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) | |
| accuracy | 0.0 | (neg.f64 x) | |
| accuracy | 0.00390625 | (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) | |
| accuracy | 28.47933286027541 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) | |
| accuracy | 30.276676547946387 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) | |
| accuracy | 0.00390625 | (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) | |
| accuracy | 0.3643557379566187 | #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) | |
| accuracy | 28.47933286027541 | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) | |
| accuracy | 30.276676547946387 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) | |
| accuracy | 0.7327753657688801 | #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) | |
| accuracy | 28.47933286027541 | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) | |
| accuracy | 30.276676547946387 | (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) | |
| accuracy | 0.0 | (sqrt.f64 #s(literal 1/2 binary64)) | |
| accuracy | 0.40234375 | (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) | |
| accuracy | 0.6607474855742861 | #s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
| 76.0ms | 136× | 2 | valid |
| 29.0ms | 79× | 1 | valid |
| 22.0ms | 35× | 3 | valid |
| 1.0ms | 6× | 0 | valid |
Compiled 223 to 33 computations (85.2% saved)
adjust: 25.0ms (28.6% of total)ival-sqrt: 21.0ms (24% of total)ival-mult: 15.0ms (17.2% of total)ival-sub: 11.0ms (12.6% of total)ival-add: 8.0ms (9.2% of total)ival-pow2: 6.0ms (6.9% of total)exact: 1.0ms (1.1% of total)ival-neg: 1.0ms (1.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) |
#s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
#s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(neg.f64 x) |
| Outputs |
|---|
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/16 (/ (pow x 2) (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 5/128 (* 1/16 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* 1/8 (pow x 2)))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(+ 1 (* -1 (pow x 2))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/8 (pow x 2)))) |
(* x (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(* x (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
(* -1 x) |
(sqrt (* x (pow (sqrt -1) 3))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (* -1/8 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 9))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))))) |
(* -1 (* x (sqrt -1))) |
(* x (- (/ 1 x) (sqrt -1))) |
(* x (- (/ 1 x) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1)) |
(* 5/128 (pow x 8)) |
(* (pow x 8) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))) |
(* (pow x 8) (+ 5/128 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 2)))))) |
(* (pow x 8) (+ 5/128 (+ (/ 1/8 (pow x 4)) (+ (* 1/16 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) |
(* 5/128 (pow x 7)) |
(* (pow x 7) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))) |
(* (pow x 7) (+ 5/128 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 2)))))) |
(* (pow x 7) (+ 5/128 (+ (/ 1/8 (pow x 4)) (+ (* 1/16 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) |
(* -1 (sqrt (* x (pow (sqrt -1) 5)))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1)))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* 1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 3))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* -1 (/ (+ (* -1/4 (sqrt (/ x (pow (sqrt -1) 3)))) (* 1/8 (sqrt (/ x (pow (sqrt -1) 7))))) (pow x 3))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* x (+ (sqrt -1) (/ 1 x))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (sqrt -1)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (sqrt -1)))) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/16 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 5/128))) |
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | inf | ((sqrt (- 1 (sqrt (- 1 (pow x 2))))) (* (sqrt 1/2) x) (sqrt 1/2) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (+ (* -1/2 (* x x)) 1) (sqrt (- 1 (sqrt (+ (* (neg x) x) 1)))) (- 1 (sqrt (+ (* (neg x) x) 1))) (sqrt (+ (* (neg x) x) 1)) (+ (* (neg x) x) 1) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (* (* (+ (* (+ (* (+ (* 5/128 (* x x)) 1/16) (* x x)) 1/8) (* x x)) 1/2) x) x) (* (+ (* (+ (* (+ (* 5/128 (* x x)) 1/16) (* x x)) 1/8) (* x x)) 1/2) x) (neg x)) |
| 2.0ms | x | @ | 0 | ((sqrt (- 1 (sqrt (- 1 (pow x 2))))) (* (sqrt 1/2) x) (sqrt 1/2) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (+ (* -1/2 (* x x)) 1) (sqrt (- 1 (sqrt (+ (* (neg x) x) 1)))) (- 1 (sqrt (+ (* (neg x) x) 1))) (sqrt (+ (* (neg x) x) 1)) (+ (* (neg x) x) 1) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (* (* (+ (* (+ (* (+ (* 5/128 (* x x)) 1/16) (* x x)) 1/8) (* x x)) 1/2) x) x) (* (+ (* (+ (* (+ (* 5/128 (* x x)) 1/16) (* x x)) 1/8) (* x x)) 1/2) x) (neg x)) |
| 2.0ms | x | @ | -inf | ((sqrt (- 1 (sqrt (- 1 (pow x 2))))) (* (sqrt 1/2) x) (sqrt 1/2) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (sqrt (- 1 (pow x 2))) (+ (* -1/2 (* x x)) 1) (sqrt (- 1 (sqrt (+ (* (neg x) x) 1)))) (- 1 (sqrt (+ (* (neg x) x) 1))) (sqrt (+ (* (neg x) x) 1)) (+ (* (neg x) x) 1) (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (- 1 (sqrt (- 1 (pow x 2)))) (* (* (+ (* (+ (* (+ (* 5/128 (* x x)) 1/16) (* x x)) 1/8) (* x x)) 1/2) x) x) (* (+ (* (+ (* (+ (* 5/128 (* x x)) 1/16) (* x x)) 1/8) (* x x)) 1/2) x) (neg x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 253 | 928 |
| 1 | 733 | 869 |
| 2 | 2229 | 848 |
| 3 | 5807 | 828 |
| 0 | 8167 | 786 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/16 (/ (pow x 2) (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 5/128 (* 1/16 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* 1/8 (pow x 2)))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(+ 1 (* -1 (pow x 2))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/8 (pow x 2)))) |
(* x (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(* x (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
(* -1 x) |
(sqrt (* x (pow (sqrt -1) 3))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (* -1/8 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 9))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))))) |
(* -1 (* x (sqrt -1))) |
(* x (- (/ 1 x) (sqrt -1))) |
(* x (- (/ 1 x) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1)) |
(* 5/128 (pow x 8)) |
(* (pow x 8) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))) |
(* (pow x 8) (+ 5/128 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 2)))))) |
(* (pow x 8) (+ 5/128 (+ (/ 1/8 (pow x 4)) (+ (* 1/16 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) |
(* 5/128 (pow x 7)) |
(* (pow x 7) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))) |
(* (pow x 7) (+ 5/128 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 2)))))) |
(* (pow x 7) (+ 5/128 (+ (/ 1/8 (pow x 4)) (+ (* 1/16 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) |
(* -1 (sqrt (* x (pow (sqrt -1) 5)))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1)))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* 1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 3))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* -1 (/ (+ (* -1/4 (sqrt (/ x (pow (sqrt -1) 3)))) (* 1/8 (sqrt (/ x (pow (sqrt -1) 7))))) (pow x 3))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(* x (+ (sqrt -1) (/ 1 x))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (sqrt -1)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (sqrt -1)))) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/16 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 5/128))) |
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))))) |
| Outputs |
|---|
(* x (sqrt 1/2)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(* x (+ (sqrt 1/2) (* 1/16 (/ (pow x 2) (sqrt 1/2))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(*.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) x) (fma.f64 (*.f64 #s(literal 7/256 binary64) x) x #s(literal 1/16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x) |
(* x (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (- 5/128 (* 1/16 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/16 (* 1/256 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/16 (/ 1 (sqrt 1/2))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) x) (fma.f64 (*.f64 #s(literal 33/2048 binary64) x) x #s(literal 7/256 binary64)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (* 1/8 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* -1 (pow x 2))) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/8 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(* x (+ 1/2 (* (pow x 2) (+ 1/8 (* 1/16 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(* x (+ 1/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/16 (* 5/128 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(* -1 x) |
(neg.f64 x) |
(sqrt (* x (pow (sqrt -1) 3))) |
(sqrt.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x))) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)))) x) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x))))) x) |
(* x (+ (sqrt (/ (pow (sqrt -1) 3) x)) (+ (* -1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (* -1/8 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 9))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 9 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)))))) x) |
(* -1 (* x (sqrt -1))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x)) |
(* x (- (/ 1 x) (sqrt -1))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x) #s(literal 1 binary64)) |
(* x (- (/ 1 x) (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))))) |
(-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* x (- (+ (/ 1 x) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) x (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))) |
(* x (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x) |
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)) |
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) |
(fma.f64 (/.f64 x (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(fma.f64 (/.f64 x (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64) (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* -1/2 (pow x 2)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1)) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(* 5/128 (pow x 8)) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 5/128 binary64)) |
(* (pow x 8) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 5/128 binary64)) (pow.f64 x #s(literal 8 binary64))) |
(* (pow x 8) (+ 5/128 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 5/128 binary64)) (/.f64 #s(literal 1/16 binary64) (*.f64 x x))) (pow.f64 x #s(literal 8 binary64))) |
(* (pow x 8) (+ 5/128 (+ (/ 1/8 (pow x 4)) (+ (* 1/16 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) |
(*.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 5/128 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 8 binary64))) |
(* 5/128 (pow x 7)) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 5/128 binary64)) |
(* (pow x 7) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 5/128 binary64))) |
(* (pow x 7) (+ 5/128 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 2)))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 5/128 binary64)) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) |
(* (pow x 7) (+ 5/128 (+ (/ 1/8 (pow x 4)) (+ (* 1/16 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 5/128 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x x))))) |
(* -1 (sqrt (* x (pow (sqrt -1) 5)))) |
(neg.f64 (sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x))) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1)))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x))) (neg.f64 x)) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* 1/4 (sqrt (/ 1 (* (pow x 5) (pow (sqrt -1) 3))))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x)))) (neg.f64 x)) |
(* -1 (* x (+ (sqrt (/ (pow (sqrt -1) 5) x)) (+ (* -1 (/ (+ (* -1/4 (sqrt (/ x (pow (sqrt -1) 3)))) (* 1/8 (sqrt (/ x (pow (sqrt -1) 7))))) (pow x 3))) (* 1/2 (sqrt (/ 1 (* (pow x 3) (sqrt -1))))))))) |
(*.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (neg.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 7 binary64)))) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) x)))) x) |
(* x (+ (sqrt -1) (/ 1 x))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 1 binary64)) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (sqrt -1)))) |
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)) x)) x) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x))) x)) (sqrt -1)))) |
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x) (sqrt.f64 #s(literal -1 binary64))) x) |
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) |
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))) |
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) |
(neg.f64 (fma.f64 (/.f64 x (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))) |
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) |
(neg.f64 (fma.f64 (/.f64 x (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64) (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))) |
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/16 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 5/128))) |
(*.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/16 binary64)) x) x) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 5/128 (* 1/16 (/ 1 (pow x 2))))))) |
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -5/128 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 226 |
| 0 | 60 | 226 |
| 1 | 231 | 226 |
| 2 | 1434 | 226 |
| 0 | 8539 | 213 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) |
#s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) |
(fma.f64 (neg.f64 x) x #s(literal 1 binary64)) |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
#s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) |
(neg.f64 x) |
| Outputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (log.f64 x))) |
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) |
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) |
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(pow.f64 (exp.f64 (log1p.f64 (neg.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
(exp.f64 (*.f64 (log1p.f64 (neg.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) #s(literal 1/2 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) #s(literal -1 binary64)) |
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(fma.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x (*.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x)) |
(fma.f64 x (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))) |
(+.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x) (*.f64 #s(literal 1/2 binary64) x)) |
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x)) |
(+.f64 (*.f64 x (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (*.f64 x #s(literal 1/2 binary64))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))) |
(*.f64 #s(literal -1 binary64) x) |
(*.f64 x #s(literal -1 binary64)) |
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 0 binary64) (neg.f64 x))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (+.f64 #s(literal 0 binary64) x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))) |
(/.f64 (*.f64 (neg.f64 x) x) (+.f64 #s(literal 0 binary64) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) x) (*.f64 (neg.f64 x) x))) |
(neg.f64 x) |
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x))) |
(-.f64 #s(literal 0 binary64) x) |
(+.f64 #s(literal 0 binary64) (neg.f64 x)) |
Compiled 14 453 to 2 142 computations (85.2% saved)
10 alts after pruning (5 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 467 | 2 | 469 |
| Fresh | 0 | 3 | 3 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 0 | 0 |
| Total | 467 | 10 | 477 |
| Status | Accuracy | Program |
|---|---|---|
| 32.9% | (pow.f64 (*.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) #s(literal 1/4 binary64)) | |
| ✓ | 7.1% | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
| ✓ | 6.5% | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
| ✓ | 5.3% | (sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
| ✓ | 55.3% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
| 55.2% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) | |
| 55.0% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) | |
| 54.5% | (sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) | |
| 98.1% | #s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)) | |
| ✓ | 98.4% | #s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
Compiled 445 to 205 computations (53.9% saved)
| Inputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))) |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
(sqrt.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
(pow.f64 (*.f64 #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)) #s(approx (- 1 (sqrt (- 1 (pow x 2)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) (*.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))) #s(literal 1/4 binary64)) |
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)) |
| Outputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
6 calls:
| 3.0ms | x |
| 2.0ms | (pow.f64 x #s(literal 2 binary64)) |
| 2.0ms | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
| 2.0ms | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
| 2.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
| 98.4% | 1 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
| 98.4% | 1 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
| 98.4% | 1 | (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
| 98.4% | 1 | (pow.f64 x #s(literal 2 binary64)) |
Compiled 32 to 30 computations (6.3% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
| Outputs |
|---|
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
6 calls:
| 1.0ms | x |
| 1.0ms | (pow.f64 x #s(literal 2 binary64)) |
| 1.0ms | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
| 1.0ms | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
| 1.0ms | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.3% | 1 | x |
| 5.3% | 1 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
| 5.3% | 1 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) |
| 5.3% | 1 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) |
| 5.3% | 1 | (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) |
| 5.3% | 1 | (pow.f64 x #s(literal 2 binary64)) |
Compiled 32 to 30 computations (6.3% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 15 | 25 |
| 1 | 24 | 25 |
| 2 | 38 | 25 |
| 3 | 54 | 25 |
| 4 | 82 | 25 |
| 5 | 114 | 25 |
| 6 | 238 | 25 |
| 7 | 785 | 25 |
| 8 | 1779 | 25 |
| 9 | 3195 | 25 |
| 10 | 5220 | 25 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (sqrt (- 1 (sqrt (- 1 (pow x 2))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1 (pow x 2))) #s(literal 1 binary64)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 211 | 710 |
| 1 | 591 | 651 |
| 2 | 1842 | 633 |
| 3 | 4839 | 611 |
| 0 | 8257 | 577 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
Compiled 33 to 24 computations (27.3% saved)
Compiled 68 to 48 computations (29.4% saved)
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