Metrics for 1-cos(x) + 1/x-1/tan(x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	24.2%	75.8%	0%	0%	0%	0
0%	0%	24.2%	75.8%	0%	0%	0%	1
50%	12.1%	12.1%	75.8%	0%	0%	0%	2
75%	18.2%	6.1%	75.8%	0%	0%	0%	3
87.5%	21.2%	3%	75.8%	0%	0%	0%	4
93.8%	22.7%	1.5%	75.8%	0%	0%	0%	5
96.9%	23.5%	0.8%	75.8%	0%	0%	0%	6
98.4%	23.9%	0.4%	75.8%	0%	0%	0%	7
99.2%	24.1%	0.2%	75.8%	0%	0%	0%	8
99.6%	24.2%	0.1%	75.8%	0%	0%	0%	9
99.8%	24.2%	0%	75.8%	0%	0%	0%	10
99.9%	24.2%	0%	75.8%	0%	0%	0%	11
100%	24.2%	0%	75.8%	0%	0%	0%	12

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample13.9s (80.7%)

Memory

165.4MiB live, 3 177.2MiB allocated

Samples

10.8s	4 070×	2	valid
2.3s	4 186×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 12.5s

ival-tan: 8.5s (67.8% of total)

ival-cos: 2.1s (17.2% of total)

adjust: 656.0ms (5.3% of total)

ival-div: 598.0ms (4.8% of total)

ival-sub: 361.0ms (2.9% of total)

ival-add: 129.0ms (1% of total)

ival-<=: 89.0ms (0.7% of total)

exact: 18.0ms (0.1% of total)

ival-and: 16.0ms (0.1% of total)

ival-assert: 5.0ms (0% of total)

Bogosity

explain1.0s (6%)

Memory

-19.7MiB live, 293.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`
116	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	-	`(tan.f64 x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	-	`(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))`
0	-	-	`(cos.f64 x)`
0	-	-	`x`
0	-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`	cancellation	255	0
`-.f64`	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`	nan-rescue	1	0
↳	`(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))`	overflow	1
↳	`(/.f64 #s(literal 1 binary64) x)`	overflow	1
↳	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`	overflow	1

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

837.0ms	276×	2	valid
92.0ms	236×	1	valid

Compiler

Compiled 93 to 31 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 895.0ms

ival-tan: 713.0ms (79.7% of total)

ival-cos: 113.0ms (12.6% of total)

ival-div: 23.0ms (2.6% of total)

adjust: 23.0ms (2.6% of total)

ival-sub: 13.0ms (1.5% of total)

ival-add: 7.0ms (0.8% of total)

ival-true: 1.0ms (0.1% of total)

ival-assert: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess62.0ms (0.4%)

Memory

7.9MiB live, 7.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	32	29
2	101	26
3	335	26
4	847	26
5	1244	26
6	1351	26
7	1357	26
0	9	13
0	16	13
1	27	13
2	61	13
3	162	13
4	378	13
5	744	13
6	1037	13
7	1252	13
8	1265	13
0	1265	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs

(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

(-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (cos.f64 x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 13 to 9 computations (30.8% 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

Status	Accuracy	Program
▶	5.7%	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify31.0ms (0.2%)

Memory

3.4MiB live, 3.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	0	(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
0	16	38
1	27	38
2	61	38
3	162	38
4	378	38
5	744	38
6	1037	38
7	1252	38
8	1265	38
0	1265	38

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

Outputs
(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (cos.f64 x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
(-.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

localize342.0ms (2%)

Memory

20.6MiB live, 20.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(tan.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	26.776630456970185	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	60.33741834446585	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

286.0ms	138×	2	valid
44.0ms	118×	1	valid

Compiler

Compiled 40 to 11 computations (72.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 314.0ms

ival-tan: 225.0ms (71.7% of total)

ival-cos: 57.0ms (18.2% of total)

adjust: 11.0ms (3.5% of total)

ival-div: 10.0ms (3.2% of total)

ival-sub: 7.0ms (2.2% of total)

ival-add: 3.0ms (1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Counts

5 → 26

Calls

Call 1

Inputs
(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(tan.f64 x)

Outputs
(* 1/3 x)
(* x (+ 1/3 (* 1/2 x)))
(* x (+ 1/3 (* x (+ 1/2 (* 1/45 x)))))
(* x (+ 1/3 (* x (+ 1/2 (* x (+ 1/45 (* -1/24 x)))))))
(/ 1 x)
(/ (+ 1 (* 1/2 (pow x 3))) x)
(/ (+ 1 (* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))) x)
(/ (+ 1 (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))) x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 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)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(- 1 (+ (cos x) (/ (cos x) (sin x))))
(- (+ 1 (/ 1 x)) (+ (cos x) (/ (cos x) (sin x))))
(- 1 (cos x))
(- (+ 1 (/ 1 x)) (cos x))
(cos x)
(/ (sin x) (cos x))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (+ (- 1 (cos x)) (/ 1 x)) (- 1 (cos x)) (cos x) (tan x))
1.0ms	x	@	-inf	((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (+ (- 1 (cos x)) (/ 1 x)) (- 1 (cos x)) (cos x) (tan x))
1.0ms	x	@	inf	((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (+ (- 1 (cos x)) (/ 1 x)) (- 1 (cos x)) (cos x) (tan x))

Time

Variable

Point

Expression

1.0ms

((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (+ (- 1 (cos x)) (/ 1 x)) (- 1 (cos x)) (cos x) (tan x))

1.0ms

-inf

((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (+ (- 1 (cos x)) (/ 1 x)) (- 1 (cos x)) (cos x) (tan x))

1.0ms

inf

((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (+ (- 1 (cos x)) (/ 1 x)) (- 1 (cos x)) (cos x) (tan x))

simplify184.0ms (1.1%)

Memory

36.5MiB live, 36.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	269
1	276	263
2	681	263
3	1822	263
4	3226	263
5	3743	263
6	4298	263
7	5129	263
8	6629	263
9	7800	263
0	8284	233

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 25

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/2 x)))
(* x (+ 1/3 (* x (+ 1/2 (* 1/45 x)))))
(* x (+ 1/3 (* x (+ 1/2 (* x (+ 1/45 (* -1/24 x)))))))
(/ 1 x)
(/ (+ 1 (* 1/2 (pow x 3))) x)
(/ (+ 1 (* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))) x)
(/ (+ 1 (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))) x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 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)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(- 1 (+ (cos x) (/ (cos x) (sin x))))
(- (+ 1 (/ 1 x)) (+ (cos x) (/ (cos x) (sin x))))
(- 1 (cos x))
(- (+ 1 (/ 1 x)) (cos x))
(cos x)
(/ (sin x) (cos x))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* x (+ 1/2 (* 1/45 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/45 binary64) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* x (+ 1/2 (* x (+ 1/45 (* -1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/24 binary64) x #s(literal 1/45 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 (pow x 3))) x)
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))) x)
(/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))) x)
(/.f64 (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)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.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)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 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) (- (* 1/24 (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))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(- 1 (+ (cos x) (/ (cos x) (sin x))))
(fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64))
(- (+ 1 (/ 1 x)) (+ (cos x) (/ (cos x) (sin x))))
(fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal 1 binary64)) (cos.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- (+ 1 (/ 1 x)) (cos x))
(-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) x))
(cos x)
(cos.f64 x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite263.0ms (1.5%)

Memory

-77.4MiB live, 66.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	16	29
1	80	29
2	899	29
0	8374	29

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

5 → 482

Calls

Call 1

Inputs
(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(tan.f64 x)

Outputs
(*.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (pow.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) #s(literal -1 binary64))
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(-.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64))))))) (/.f64 (pow.f64 (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64))) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64))))))))
(-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 x #s(literal -1 binary64)))))
(-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64))))
(+.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (neg.f64 (cos.f64 x)))
(+.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (cos.f64 x) (pow.f64 x #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (cos.f64 x) (pow.f64 x #s(literal -1 binary64)))))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))))
(-.f64 (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 (tan.f64 x))) #s(literal 1 binary64))
(/.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(tan.f64 x)
(-.f64 #s(literal 0 binary64) (/.f64 (tan.f64 x) #s(literal -1 binary64)))
(exp.f64 (log.f64 (tan.f64 x)))

eval68.0ms (0.4%)

Memory: -36.6MiB live, 49.4MiB allocated
Compiler: Compiled 20 265 to 1 947 computations (90.4% saved)

prune9.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	505	2	507
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	506	2	508

Accuracy

99.5%

Counts

508 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
▶	99.0%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Status

Accuracy

Program

▶

99.5%

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))

▶

99.0%

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 37 to 26 computations (29.7% saved)

simplify46.0ms (0.3%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
cost-diff	0	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
cost-diff	0	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	55
0	20	55
1	35	55
2	75	55
3	179	55
4	395	55
5	769	55
6	1104	55
7	1549	55
8	1705	55
9	1722	55
0	1722	55

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1/3 binary64)

Outputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1/3 binary64)

localize379.0ms (2.2%)

Memory

-37.9MiB live, 39.4MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
accuracy	0.00390625	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))
accuracy	0.296875	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
accuracy	0.3125	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.32432812217567275	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Samples

311.0ms	138×	2	valid
55.0ms	118×	1	valid

Compiler

Compiled 48 to 17 computations (64.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 342.0ms

ival-tan: 226.0ms (66.1% of total)

ival-cos: 57.0ms (16.7% of total)

adjust: 14.0ms (4.1% of total)

ival-div: 11.0ms (3.2% of total)

ival-sub: 11.0ms (3.2% of total)

const: 8.0ms (2.3% of total)

ival-mult: 8.0ms (2.3% of total)

ival-add: 6.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Counts

5 → 12

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))

Outputs
(* 1/3 x)
(* x (+ 1/3 (* 1/2 x)))
(* x (+ 1/3 (* x (+ 1/2 (* 1/45 x)))))
(* x (+ 1/3 (* x (+ 1/2 (* x (+ 1/45 (* -1/24 x)))))))
1/3
(+ 1/3 (* 1/2 x))
(- 1 (+ (cos x) (/ (cos x) (sin x))))
(- (+ 1 (/ 1 x)) (+ (cos x) (/ (cos x) (sin x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/3 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/3 (/ 1 x))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* 1/3 x) (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* (+ (* 1/2 x) 1/3) x) (+ (* 1/2 x) 1/3))
1.0ms	x	@	-inf	((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* 1/3 x) (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* (+ (* 1/2 x) 1/3) x) (+ (* 1/2 x) 1/3))
1.0ms	x	@	inf	((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* 1/3 x) (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* (+ (* 1/2 x) 1/3) x) (+ (* 1/2 x) 1/3))

Time

Variable

Point

Expression

1.0ms

((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* 1/3 x) (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* (+ (* 1/2 x) 1/3) x) (+ (* 1/2 x) 1/3))

1.0ms

-inf

((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* 1/3 x) (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* (+ (* 1/2 x) 1/3) x) (+ (* 1/2 x) 1/3))

1.0ms

inf

((- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* 1/3 x) (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (* (+ (* 1/2 x) 1/3) x) (+ (* 1/2 x) 1/3))

simplify132.0ms (0.8%)

Memory

29.4MiB live, 29.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	86
1	114	86
2	239	86
3	425	86
4	741	86
5	1670	86
6	5721	86
7	6659	86
0	8338	77

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/2 x)))
(* x (+ 1/3 (* x (+ 1/2 (* 1/45 x)))))
(* x (+ 1/3 (* x (+ 1/2 (* x (+ 1/45 (* -1/24 x)))))))
1/3
(+ 1/3 (* 1/2 x))
(- 1 (+ (cos x) (/ (cos x) (sin x))))
(- (+ 1 (/ 1 x)) (+ (cos x) (/ (cos x) (sin x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/3 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/3 (/ 1 x))))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* x (+ 1/2 (* 1/45 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/45 binary64) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* x (+ 1/2 (* x (+ 1/45 (* -1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/24 binary64) x #s(literal 1/45 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))
(- 1 (+ (cos x) (/ (cos x) (sin x))))
(fma.f64 (cos.f64 x) (-.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(- (+ 1 (/ 1 x)) (+ (cos x) (/ (cos x) (sin x))))
(fma.f64 (cos.f64 x) (-.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* 1/3 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/3 (/ 1 x))))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))

rewrite174.0ms (1%)

Memory

-31.0MiB live, 45.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	50
0	20	50
1	102	50
2	1049	50
0	8425	50

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

5 → 53

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))

Outputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x)
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x) (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 #s(literal 1/3 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/3 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x)) (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 #s(literal 1/2 binary64) x) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x) (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64))) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/3 binary64) x (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(fma.f64 x (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (*.f64 #s(literal 1/3 binary64) x))
(+.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (*.f64 #s(literal 1/3 binary64) x))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (*.f64 #s(literal 1/2 binary64) x) x))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (*.f64 #s(literal 1/2 binary64) x)))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/9 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64))) (neg.f64 (+.f64 #s(literal 1/9 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/6 binary64))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/6 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64))))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1/3 binary64))
(-.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/2 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/2 binary64) x))

eval7.0ms (0%)

Memory: 5.9MiB live, 5.9MiB allocated
Compiler: Compiled 1 810 to 258 computations (85.7% saved)

prune5.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	59	5	64

Accuracy

100.0%

Counts

64 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1/3 binary64) x)))
	99.6%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
	99.6%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	99.5%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
✓	99.0%	#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 251 to 133 computations (47% saved)

regimes4.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes3.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))

Outputs

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes3.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))

#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal 1/3 binary64) x)))

Outputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Outputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify95.0ms (0.6%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	97
1	54	97
2	96	97
3	207	97
4	462	97
5	1086	97
6	2107	97
7	4858	97
8	6947	97

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Outputs
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/6 binary64))))))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/3 binary64))))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/3 binary64)) x))
#s(approx (- (+ (- 1 (cos x)) (/ 1 x)) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

soundness454.0ms (2.6%)

Memory

5.1MiB live, 5.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	269
1	276	263
2	681	263
3	1822	263
4	3226	263
5	3743	263
6	4298	263
7	5129	263
8	6629	263
9	7800	263
0	8284	233
0	16	50
0	20	50
1	102	50
2	1049	50
0	8425	50

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 158 to 84 computations (46.8% saved)

preprocess30.0ms (0.2%)

Memory: 18.2MiB live, 18.2MiB allocated
Compiler: Compiled 220 to 94 computations (57.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample13.9s (80.7%)

explain1.0s (6%)

preprocess62.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify31.0ms (0.2%)

localize342.0ms (2%)

series4.0ms (0%)

simplify184.0ms (1.1%)

rewrite263.0ms (1.5%)

eval68.0ms (0.4%)

prune9.0ms (0.1%)

simplify46.0ms (0.3%)

localize379.0ms (2.2%)

series4.0ms (0%)

simplify132.0ms (0.8%)

rewrite174.0ms (1%)

eval7.0ms (0%)

prune5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify95.0ms (0.6%)

soundness454.0ms (2.6%)

preprocess30.0ms (0.2%)

end0.0ms (0%)

Profiling