cos(PI*x)

Time bar (total: 1.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample746.0ms (51.8%)

Memory
-18.3MiB live, 382.0MiB allocated
Samples
491.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 323.0ms
ival-cosu: 234.0ms (72.4% of total)
ival-<=: 57.0ms (17.6% of total)
ival-and: 15.0ms (4.6% of total)
exact: 13.0ms (4% of total)
ival-assert: 4.0ms (1.2% of total)
Bogosity

explain63.0ms (4.4%)

Memory
27.2MiB live, 27.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1290-0-(cos.f64 (*.f64 (PI.f64) x))
00-0-(*.f64 (PI.f64) x)
00-0-(PI.f64)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
cos.f64(cos.f64 (*.f64 (PI.f64) x))sensitivity1280
cos.f64(cos.f64 (*.f64 (PI.f64) x))oflow-rescue10
↳(*.f64 (PI.f64) x)overflow1
Confusion
Predicted +Predicted -
+1290
-0127
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+12900
-00127
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0127
1129
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
32.0ms512×0valid
Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-cosu: 12.0ms (59.7% of total)
ival-mult: 4.0ms (19.9% of total)
ival-pi: 3.0ms (14.9% of total)
ival-true: 1.0ms (5% of total)
ival-assert: 0.0ms (0% of total)

preprocess12.0ms (0.9%)

Memory
5.0MiB live, 5.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
1159
2299
3419
4499
5639
6829
7879
8939
9939
044
074
184
084
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(cos.f64 (*.f64 (PI.f64) x))
Outputs
(cos.f64 (*.f64 (PI.f64) x))
(cos.f64 (*.f64 x (PI.f64)))
Symmetry

(abs x)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶56.4%
(cos.f64 (*.f64 (PI.f64) x))
Compiler

Compiled 4 to 4 computations (0% saved)

simplify2.0ms (0.2%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) x)
cost-diff0
(cos.f64 (*.f64 (PI.f64) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
079
189
089
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(cos.f64 (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
x
Outputs
(cos.f64 (*.f64 (PI.f64) x))
(cos.f64 (*.f64 x (PI.f64)))
(*.f64 (PI.f64) x)
(*.f64 x (PI.f64))
(PI.f64)
x

localize19.0ms (1.4%)

Memory
6.3MiB live, 6.3MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(PI.f64)
accuracy0.28125
(*.f64 (PI.f64) x)
accuracy27.89586194158125
(cos.f64 (*.f64 (PI.f64) x))
Samples
15.0ms256×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-cosu: 6.0ms (66.2% of total)
ival-mult: 2.0ms (22.1% of total)
ival-pi: 1.0ms (11% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
0.7MiB live, 0.7MiB allocated
Counts
3 → 6
Calls
Call 1
Inputs
(cos.f64 (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
Outputs
1
(+ 1 (* -1/2 (* (pow x 2) (pow (PI) 2))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* 1/24 (* (pow x 2) (pow (PI) 4))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (PI) 6))) (* 1/24 (pow (PI) 4)))))))
(* x (PI))
(cos (* x (PI)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((cos (* (PI) x)) (* (PI) x) (PI))
0.0ms
x
@inf
((cos (* (PI) x)) (* (PI) x) (PI))
0.0ms
x
@-inf
((cos (* (PI) x)) (* (PI) x) (PI))

simplify20.0ms (1.4%)

Memory
3.9MiB live, 3.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03271
17671
223271
354571
484571
591671
691771
091765
Stop Event
1×iter limit
1×saturated
Counts
6 → 6
Calls
Call 1
Inputs
1
(+ 1 (* -1/2 (* (pow x 2) (pow (PI) 2))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* 1/24 (* (pow x 2) (pow (PI) 4))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (PI) 6))) (* 1/24 (pow (PI) 4)))))))
(* x (PI))
(cos (* x (PI)))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* (pow x 2) (pow (PI) 2))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* 1/24 (* (pow x 2) (pow (PI) 4))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (PI) 6))) (* 1/24 (pow (PI) 4)))))))
(fma.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64)) (pow.f64 (PI.f64) #s(literal 6 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))))
(* x (PI))
(*.f64 (PI.f64) x)
(cos (* x (PI)))
(cos.f64 (*.f64 (PI.f64) x))

rewrite79.0ms (5.5%)

Memory
-65.2MiB live, 12.8MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
048
078
1238
21218
38134
460114
560784
663644
777274
080564
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 6
Calls
Call 1
Inputs
(cos.f64 (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
Outputs
(cos.f64 x)
(*.f64 x (PI.f64))
(*.f64 (PI.f64) x)
x
(PI.f64)
#s(literal 1 binary64)

eval2.0ms (0.1%)

Memory
1.1MiB live, 1.1MiB allocated
Compiler

Compiled 115 to 37 computations (67.8% saved)

prune1.0ms (0.1%)

Memory
1.2MiB live, 1.2MiB allocated
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New9312
Fresh000
Picked011
Done000
Total9413
Accuracy
99.2%
Counts
13 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓56.4%
(cos.f64 (*.f64 (PI.f64) x))
▶54.1%
(cos.f64 x)
▶49.2%
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
▶97.7%
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify5.0ms (0.4%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
cost-diff0
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
cost-diff0
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
cost-diff0
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01450
02150
13350
25950
310550
411750
011750
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
(*.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(literal 1 binary64)
(cos.f64 x)
x
Outputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(fma.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(*.f64 x x)
x
#s(literal -1/2 binary64)
(*.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(literal 1 binary64)
(cos.f64 x)
x

localize38.0ms (2.7%)

Memory
13.3MiB live, 13.3MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(cos.f64 x)
accuracy0.0
(PI.f64)
accuracy0.015625
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
accuracy0.09765625
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
accuracy32.488454083040494
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
accuracy1.4993254312058366
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
Samples
30.0ms256×0valid
Compiler

Compiled 40 to 13 computations (67.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 6.0ms (28.7% of total)
ival-cosu: 6.0ms (28.7% of total)
ival-cos: 5.0ms (23.9% of total)
ival-pi: 1.0ms (4.8% of total)
ival-add: 1.0ms (4.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.3%)

Memory
1.9MiB live, 1.9MiB allocated
Counts
7 → 13
Calls
Call 1
Inputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
(cos.f64 x)
(PI.f64)
Outputs
1
(+ 1 (* -1/2 (* (pow x 2) (pow (PI) 2))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* 1/24 (* (pow x 2) (pow (PI) 4))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (PI) 6))) (* 1/24 (pow (PI) 4)))))))
(* -1/2 (pow x 2))
(pow x 2)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos (* x (PI)))
(* -1/2 (* (pow x 2) (pow (PI) 2)))
(* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (/ 1 (pow x 2))))
(cos x)
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((cos (* (PI) x)) (cos (* (PI) x)) (+ (* (* (* x x) -1/2) (* (PI) (PI))) 1) (* (* x x) -1/2) (* x x) (cos x) (PI))
1.0ms
x
@inf
((cos (* (PI) x)) (cos (* (PI) x)) (+ (* (* (* x x) -1/2) (* (PI) (PI))) 1) (* (* x x) -1/2) (* x x) (cos x) (PI))
1.0ms
x
@-inf
((cos (* (PI) x)) (cos (* (PI) x)) (+ (* (* (* x x) -1/2) (* (PI) (PI))) 1) (* (* x x) -1/2) (* x x) (cos x) (PI))

simplify145.0ms (10.1%)

Memory
32.3MiB live, 32.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049137
1114137
2313137
3748137
41479137
51821137
62218137
72756137
83510137
96092137
08156124
Stop Event
1×iter limit
1×node limit
Counts
13 → 13
Calls
Call 1
Inputs
1
(+ 1 (* -1/2 (* (pow x 2) (pow (PI) 2))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* 1/24 (* (pow x 2) (pow (PI) 4))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (PI) 6))) (* 1/24 (pow (PI) 4)))))))
(* -1/2 (pow x 2))
(pow x 2)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos (* x (PI)))
(* -1/2 (* (pow x 2) (pow (PI) 2)))
(* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (/ 1 (pow x 2))))
(cos x)
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* (pow x 2) (pow (PI) 2))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* 1/24 (* (pow x 2) (pow (PI) 4))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
(+ 1 (* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (PI) 6))) (* 1/24 (pow (PI) 4)))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 6 binary64)) #s(literal -1/720 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(cos (* x (PI)))
(cos.f64 (*.f64 x (PI.f64)))
(* -1/2 (* (pow x 2) (pow (PI) 2)))
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (PI.f64)) (*.f64 x (PI.f64)))
(* (pow x 2) (+ (* -1/2 (pow (PI) 2)) (/ 1 (pow x 2))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)

rewrite194.0ms (13.5%)

Memory
-51.9MiB live, 44.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01442
02142
16242
234440
3322740
0830838
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 201
Calls
Call 1
Inputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
(cos.f64 x)
(PI.f64)
Outputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(approx (cos (* (PI) x)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 6 binary64)) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal -1 binary64))) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
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(fma.f64 x (exp.f64 (log.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (PI.f64)) (PI.f64)))) #s(literal 1 binary64))
(fma.f64 x (*.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (PI.f64)) (PI.f64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (PI.f64)) (PI.f64)) #s(literal 1 binary64))
(-.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1 binary64))) (pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) x) x)
(*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 x (*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(*.f64 x (*.f64 #s(literal -1/2 binary64) x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(cos.f64 x)
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 11/4 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 17/6 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 8 binary64)) (sqrt.f64 (PI.f64))))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 8 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8 binary64)) #s(literal 1 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (E.f64) (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))) (cbrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 7 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (cbrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 5/6 binary64)))
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8 binary64))))))
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 7 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (exp.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (E.f64) (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (PI.f64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 (cbrt.f64 (PI.f64))))
(pow.f64 (exp.f64 #s(literal 1/3 binary64)) (*.f64 #s(literal 3 binary64) (log.f64 (PI.f64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/3 binary64)) (*.f64 #s(literal 3 binary64) (log.f64 (PI.f64))))
(pow.f64 (pow.f64 (E.f64) #s(literal 3 binary64)) (log.f64 (cbrt.f64 (PI.f64))))
(pow.f64 (pow.f64 (E.f64) #s(literal 2 binary64)) (log.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 6 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (pow.f64 (PI.f64) #s(literal 6 binary64)) #s(literal 1/6 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 3/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(fabs.f64 (PI.f64))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(+.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(+.f64 (log.f64 (pow.f64 (E.f64) (/.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (pow.f64 (E.f64) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)

eval32.0ms (2.2%)

Memory
24.4MiB live, 24.4MiB allocated
Compiler

Compiled 6 298 to 1 006 computations (84% saved)

prune8.0ms (0.6%)

Memory
11.3MiB live, 11.3MiB allocated
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New2662268
Fresh000
Picked033
Done011
Total2666272
Accuracy
99.2%
Counts
272 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓56.4%
(cos.f64 (*.f64 (PI.f64) x))
✓54.1%
(cos.f64 x)
49.2%
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) (PI.f64)) #s(literal 1 binary64)))
✓49.2%
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
✓97.7%
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
49.0%
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
Compiler

Compiled 110 to 69 computations (37.3% saved)

regimes6.0ms (0.4%)

Memory
5.8MiB live, 5.8MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) (PI.f64)) #s(literal 1 binary64)))
(cos.f64 x)
(cos.f64 (*.f64 (PI.f64) x))
Outputs
(cos.f64 (*.f64 (PI.f64) x))
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
Calls

3 calls:

2.0ms
(*.f64 (PI.f64) x)
2.0ms
x
2.0ms
(cos.f64 (*.f64 (PI.f64) x))
Results
AccuracySegmentsBranch
99.2%2x
97.7%1(cos.f64 (*.f64 (PI.f64) x))
99.2%2(*.f64 (PI.f64) x)
Compiler

Compiled 8 to 8 computations (0% saved)

regimes5.0ms (0.4%)

Memory
5.5MiB live, 5.5MiB allocated
Accuracy

Total -31.2b remaining (-2078.6%)

Threshold costs -31.2b (-2078.6%)

Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) (PI.f64)) #s(literal 1 binary64)))
(cos.f64 x)
Outputs
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
Calls

3 calls:

2.0ms
(*.f64 (PI.f64) x)
2.0ms
x
2.0ms
(cos.f64 (*.f64 (PI.f64) x))
Results
AccuracySegmentsBranch
97.7%1(cos.f64 (*.f64 (PI.f64) x))
97.7%1x
97.7%1(*.f64 (PI.f64) x)
Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
36361622034430.53
1.603884060531438e+20
Compiler

Compiled 7 to 8 computations (-14.3% saved)

simplify9.0ms (0.6%)

Memory
5.1MiB live, 5.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11522
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (*.f64 (PI.f64) x) #s(literal 50000000000000 binary64)) (cos.f64 (*.f64 (PI.f64) x)) #s(approx (cos (* (PI) x)) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))
Outputs
(if (<=.f64 (*.f64 (PI.f64) x) #s(literal 50000000000000 binary64)) (cos.f64 (*.f64 (PI.f64) x)) #s(approx (cos (* (PI) x)) #s(literal 1 binary64)))
#s(approx (cos (* (PI) x)) #s(literal 1 binary64))

soundness21.0ms (1.5%)

Memory
0.7MiB live, 0.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03271
17671
223271
354571
484571
591671
691771
091765
Stop Event
1×fuel
1×iter limit
1×saturated
Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess24.0ms (1.7%)

Memory
-69.8MiB live, 11.7MiB allocated
Compiler

Compiled 84 to 56 computations (33.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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