Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze117.0ms (2.2%)

Memory

8.0MiB live, 140.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.1s (39.9%)

Memory

22.8MiB live, 1 610.1MiB allocated

Samples

907.0ms	2 259×	2	valid
487.0ms	4 162×	0	valid
263.0ms	582×	3	valid
137.0ms	1 252×	1	valid
1.0ms	1×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-cos: 792.0ms (49.6% of total)

ival-div: 387.0ms (24.3% of total)

ival-sin: 188.0ms (11.8% of total)

adjust: 114.0ms (7.1% of total)

ival-sub: 100.0ms (6.3% of total)

ival-true: 5.0ms (0.3% of total)

exact: 5.0ms (0.3% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain182.0ms (3.4%)

Memory

6.4MiB live, 139.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
71	1	(-4.501437748471027e+217)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
67	0	-	3	(2.612721615861705e-160)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	72	2
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	64	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	64

Confusion

	Predicted +	Predicted -
+	135	0
-	1	120

Precision

0.9926470588235294

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	135	0	0
-	1	2	118

Precision?

0.9782608695652174

Recall?

1.0

Freqs

test

number	freq
0	120
1	136

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms	128×	2	valid
26.0ms	254×	0	valid
17.0ms	50×	3	valid
9.0ms	80×	1	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-cos: 44.0ms (59.8% of total)

ival-sin: 11.0ms (14.9% of total)

adjust: 7.0ms (9.5% of total)

ival-div: 6.0ms (8.2% of total)

ival-sub: 5.0ms (6.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess196.0ms (3.7%)

Memory

33.2MiB live, 175.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	29	9
2	68	8
3	124	8
4	268	8
5	651	8
6	1657	8
7	3537	8
8	7497	8
0	6	7
0	10	4
1	24	4
2	34	4
3	43	4
4	54	4
5	80	4
6	133	4
7	276	4
8	689	4
9	1816	4
10	3921	4
11	7200	4
0	8327	4

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify156.0ms (3%)

Memory

-12.9MiB live, 143.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 x)
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	3	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	24	14
2	34	14
3	43	14
4	54	14
5	80	14
6	133	14
7	276	14
8	689	14
9	1816	14
10	3921	14
11	7200	14
0	8327	14

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize69.0ms (1.3%)

Memory

2.9MiB live, 49.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	15.037018958980703	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	15.469197777370486	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

37.0ms	64×	2	valid
13.0ms	127×	0	valid
8.0ms	25×	3	valid
4.0ms	40×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-cos: 40.0ms (73.4% of total)

ival-sin: 5.0ms (9.2% of total)

adjust: 4.0ms (7.3% of total)

ival-div: 3.0ms (5.5% of total)

ival-sub: 2.0ms (3.7% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

4 → 20

Calls

Call 1

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

Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 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 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)

Calls

3 calls:

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

simplify205.0ms (3.9%)

Memory

-4.8MiB live, 185.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	202
1	266	202
2	777	196
3	3247	196
4	7420	196
0	8622	178

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 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 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #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 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #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 (-.f64 (.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 (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/40320 binary64) (-.f64 (.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))
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 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)

rewrite201.0ms (3.8%)

Memory

-21.8MiB live, 121.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	41	12
2	277	12
3	2709	12
0	8299	12

Stop Event

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

Counts

4 → 220

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(.f64 (neg.f64 (sin.f64 x)) (/.f64 (neg.f64 (sin.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (sin.f64 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (sin.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64))) (cos.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64))))
(/.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (sin.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (sin.f64 x)) (sin.f64 x))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal -2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x)) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (+.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 0 binary64))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
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(fma.f64 (sin.f64 x) #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) #s(literal 1 binary64))
(-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(+.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))))
(*.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))))
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (cos.f64 x)))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal 0 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x)))))
(/.f64 (-.f64 (cos.f64 x) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (sqrt.f64 (neg.f64 (neg.f64 (cos.f64 x)))) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 x x))))))
(fma.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64) (cos.f64 x))
(fma.f64 #s(literal 0 binary64) (sin.f64 x) (cos.f64 x))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(sin.f64 (+.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (acos.f64 (fabs.f64 (neg.f64 (sin.f64 x)))))
(sin.f64 (acos.f64 (fabs.f64 (sin.f64 x))))
(sin.f64 (acos.f64 (neg.f64 (sin.f64 x))))
(sin.f64 (acos.f64 (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(sqrt.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(-.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(fabs.f64 (neg.f64 (cos.f64 x)))
(fabs.f64 (cos.f64 x))
(cos.f64 (neg.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (asin.f64 (fabs.f64 (neg.f64 (sin.f64 x)))))
(cos.f64 (asin.f64 (fabs.f64 (sin.f64 x))))
(cos.f64 (asin.f64 (neg.f64 (sin.f64 x))))
(cos.f64 (asin.f64 (sin.f64 x)))
(cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x))))) (.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x))))))
(+.f64 (cosh.f64 (log.f64 (cos.f64 x))) (sinh.f64 (log.f64 (cos.f64 x))))
(+.f64 (.f64 (.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (cos.f64 x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (/.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(neg.f64 (neg.f64 (sin.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64) (*.f64 (neg.f64 (cos.f64 x)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(sin.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)))
(sin.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (neg.f64 (+.f64 (PI.f64) x)))
(sin.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)))
(sin.f64 (+.f64 (neg.f64 x) (PI.f64)))
(sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 x)
(-.f64 (.f64 (neg.f64 (cos.f64 x)) #s(literal 0 binary64)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(-.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (.f64 (cos.f64 x) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))))
(-.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(cos.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64))))
(cos.f64 (neg.f64 (+.f64 (+.f64 (PI.f64) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (PI.f64)))
(cos.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (PI.f64)))
(cos.f64 (+.f64 (+.f64 (PI.f64) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (.f64 (neg.f64 (cos.f64 x)) #s(literal 0 binary64)))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (.f64 (cos.f64 x) #s(literal 0 binary64)))

eval32.0ms (0.6%)

Memory: 11.9MiB live, 53.4MiB allocated
Compiler: Compiled 4 121 to 798 computations (80.6% saved)

prune6.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	234	5	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	235	5	240

Accuracy

100.0%

Counts

240 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
▶	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	52.1%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	100.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 172 to 122 computations (29.1% saved)

simplify214.0ms (4%)

Memory

-5.5MiB live, 187.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	216
0	45	201
1	92	201
2	270	201
3	1093	201
4	3980	201
5	7396	201
0	8255	201

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

localize211.0ms (4%)

Memory

-16.3MiB live, 219.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.0390625	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
accuracy	0.5109324865836249	(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy	30.85357301981528	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.02734375	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.03515625	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.46525791355980006	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	30.883650300317665	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0546875	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.4818063343331536	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	30.88048641524277	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	30.683000592384555	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Samples

83.0ms	64×	2	valid
69.0ms	127×	0	valid
19.0ms	25×	3	valid
17.0ms	40×	1	valid

Compiler

Compiled 183 to 30 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-mult: 58.0ms (35.9% of total)

const: 41.0ms (25.4% of total)

ival-cos: 21.0ms (13% of total)

adjust: 13.0ms (8.1% of total)

ival-add: 13.0ms (8.1% of total)

ival-tan: 5.0ms (3.1% of total)

ival-sin: 5.0ms (3.1% of total)

ival-div: 3.0ms (1.9% of total)

ival-sub: 3.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

17 → 44

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))

Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))
3.0ms	x	@	inf	((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))
2.0ms	x	@	0	((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

Time

Variable

Point

Expression

4.0ms

-inf

((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

3.0ms

inf

((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

2.0ms

((/ (- 1 (cos x)) (sin x)) (tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

simplify137.0ms (2.6%)

Memory

18.4MiB live, 159.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	457
1	359	457
2	1105	454
3	4199	450
0	8296	429

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
1/240
#s(literal 1/240 binary64)
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 1/240 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/240 binary64)))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 1/240 (pow x 2))
(.f64 #s(literal 1/240 binary64) (.f64 x x))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* 17/40320 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 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 17/40320 binary64)) (/.f64 (/.f64 (-.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) x) x)) (pow.f64 x #s(literal 7 binary64)))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal -17/40320 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 17/40320 (pow x 2))
(.f64 #s(literal 17/40320 binary64) (.f64 x x))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (+.f64 (/.f64 #s(literal -1/24 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (+.f64 (/.f64 #s(literal -1/240 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal 17/40320 binary64))))

rewrite205.0ms (3.9%)

Memory

-36.9MiB live, 153.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	191
0	45	176
1	185	176
2	1341	176
0	8252	176

Stop Event

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

Counts

17 → 369

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (+.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))) (neg.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64))) (cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64))))
(/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
(/.f64 (+.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64))))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (+.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)))
(tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x)))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x)) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) x)) (neg.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(/.f64 (.f64 x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(+.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (.f64 #s(literal -1/24 binary64) (.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (neg.f64 (.f64 x x)) #s(literal 1/24 binary64)) (.f64 (neg.f64 (.f64 x x)) #s(literal 1/24 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 x x)) #s(literal 1/24 binary64))))
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(+.f64 (/.f64 (.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) #s(literal 17/9676800 binary64))))) (/.f64 #s(literal 1/13824000 binary64) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(+.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) #s(literal 1/240 binary64))
(+.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (.f64 x x)))

eval75.0ms (1.4%)

Memory: 15.8MiB live, 113.6MiB allocated
Compiler: Compiled 22 012 to 2 482 computations (88.7% saved)

prune13.0ms (0.2%)

Memory

-12.5MiB live, 34.2MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	512	2	514
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	512	7	519

Accuracy

100.0%

Counts

519 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
▶	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
✓	51.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	52.1%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 127 to 90 computations (29.1% saved)

simplify167.0ms (3.2%)

Memory

-27.1MiB live, 152.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/24 binary64) (.f64 x x))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
cost-diff	2	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
cost-diff	2	(.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	123
0	32	115
1	78	113
2	204	109
3	613	109
4	1582	109
5	2921	109
6	3789	109
7	4177	109
8	4704	109
9	5757	109
10	7369	109
0	8032	107

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
x
#s(literal 1/2 binary64)
(.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) x)
x
#s(literal 1/2 binary64)
(.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x)
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize134.0ms (2.5%)

Memory

-2.7MiB live, 131.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.05078125	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.5989938343331536	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	30.88048641524277	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
accuracy	0.10546875	(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
accuracy	0.21875	(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
accuracy	0.46525791355980006	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	30.883650300317665	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))

Samples

41.0ms	40×	1	valid
31.0ms	64×	2	valid
26.0ms	127×	0	valid
19.0ms	25×	3	valid

Compiler

Compiled 105 to 23 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

ival-mult: 45.0ms (44.5% of total)

ival-cos: 20.0ms (19.8% of total)

adjust: 13.0ms (12.9% of total)

const: 8.0ms (7.9% of total)

ival-add: 5.0ms (4.9% of total)

ival-sin: 5.0ms (4.9% of total)

ival-div: 3.0ms (3% of total)

ival-sub: 3.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

11 → 25

Calls

Call 1

Inputs
(.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(*.f64 x x)
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(*.f64 #s(literal 1/2 binary64) x)

Outputs
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))
(pow x 2)
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/24 x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 3))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (/ (- 1 (cos x)) (sin x)) (+ (* x 1/2) (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x)) (* (* (+ (* 1/240 (* x x)) 1/24) x) x) (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (+ (* 1/240 (* x x)) 1/24) (* (+ (* 1/240 (* x x)) 1/24) x) (* 1/2 x))

2.0ms

-inf

((* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (/ (- 1 (cos x)) (sin x)) (+ (* x 1/2) (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x)) (* (* (+ (* 1/240 (* x x)) 1/24) x) x) (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (+ (* 1/240 (* x x)) 1/24) (* (+ (* 1/240 (* x x)) 1/24) x) (* 1/2 x))

1.0ms

((* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (/ (- 1 (cos x)) (sin x)) (+ (* x 1/2) (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x)) (* (* (+ (* 1/240 (* x x)) 1/24) x) x) (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (+ (* 1/240 (* x x)) 1/24) (* (+ (* 1/240 (* x x)) 1/24) x) (* 1/2 x))

simplify153.0ms (2.9%)

Memory

15.0MiB live, 69.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	210
1	227	210
2	670	209
3	2577	209
0	8400	196

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 25

Calls

Call 1

Inputs
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))
(pow x 2)
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/24 x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 3))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

Outputs
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x)
(pow x 2)
(*.f64 x x)
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x)
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 (-.f64 (-.f64 #s(literal 1/240 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 1/240 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/240 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(* 1/240 (pow x 3))
(*.f64 #s(literal 1/240 binary64) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x)
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (-.f64 (/.f64 #s(literal -1/24 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64))))

rewrite278.0ms (5.3%)

Memory

-5.1MiB live, 229.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	113
0	32	105
1	139	99
2	938	99
0	9202	97

Stop Event

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

Counts

11 → 324

Calls

Call 1

Inputs
(.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(*.f64 x x)
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(*.f64 #s(literal 1/2 binary64) x)

Outputs
(.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (neg.f64 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) x) (.f64 (neg.f64 x) x))
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(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 #s(literal 1/24 binary64) x) (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)) x)) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) x)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)) x) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(/.f64 (.f64 x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(fma.f64 (.f64 #s(literal -1/240 binary64) x) (.f64 (neg.f64 x) x) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal -1/240 binary64) x) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) x (.f64 (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) x))
(fma.f64 (.f64 #s(literal -1/240 binary64) (.f64 x x)) (neg.f64 x) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 (.f64 x #s(literal 1/240 binary64)) (.f64 x x) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 (neg.f64 x) (.f64 #s(literal -1/240 binary64) (.f64 x x)) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) x (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 #s(literal 1/24 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/240 binary64)) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 x (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (.f64 x (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/240 binary64)) (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 x #s(literal 1/24 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)))
(fma.f64 #s(literal 1/240 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/24 binary64) x))
(-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) (.f64 #s(literal -1/24 binary64) x))
(-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) (.f64 (neg.f64 x) #s(literal 1/24 binary64)))
(-.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (.f64 #s(literal -1/240 binary64) (.f64 x x)) x))
(-.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal 1/240 binary64))))
(+.f64 (.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) x) (.f64 (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))) x))
(+.f64 (.f64 x (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))) (.f64 x (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))))
(+.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) (.f64 #s(literal 1/24 binary64) x))
(+.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)))
(fabs.f64 (*.f64 #s(literal -1/2 binary64) x))
(fabs.f64 (*.f64 #s(literal 1/2 binary64) x))

eval62.0ms (1.2%)

Memory: 0.9MiB live, 46.2MiB allocated
Compiler: Compiled 12 969 to 1 638 computations (87.4% saved)

prune11.0ms (0.2%)

Memory

-21.5MiB live, 25.0MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	362	0	362
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	362	7	369

Accuracy

100.0%

Counts

369 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
✓	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
✓	51.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	52.1%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 261 to 130 computations (50.2% saved)

regimes5.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

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

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
100.0%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Accuracy

Total -0.3b remaining (-1.1%)

Threshold costs -0.3b (-1.1%)

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
52.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
52.1%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify58.0ms (1.1%)

Memory

-24.2MiB live, 30.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	25	17
2	35	17
3	45	17
4	61	17
5	99	17
6	180	17
7	381	17
8	1027	17
9	3190	17
10	6949	17

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness190.0ms (3.6%)

Memory

-0.0MiB live, 140.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	202
1	266	202
2	777	196
3	3247	196
4	7420	196
0	8622	178

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 30 to 18 computations (40% saved)

preprocess72.0ms (1.4%)

Memory: 36.9MiB live, 86.7MiB allocated
Remove: (negabs x)
Compiler: Compiled 92 to 62 computations (32.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze117.0ms (2.2%)

sample2.1s (39.9%)

explain182.0ms (3.4%)

preprocess196.0ms (3.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify156.0ms (3%)

localize69.0ms (1.3%)

series2.0ms (0%)

simplify205.0ms (3.9%)

rewrite201.0ms (3.8%)

eval32.0ms (0.6%)

prune6.0ms (0.1%)

simplify214.0ms (4%)

localize211.0ms (4%)

series10.0ms (0.2%)

simplify137.0ms (2.6%)

rewrite205.0ms (3.9%)

eval75.0ms (1.4%)

prune13.0ms (0.2%)

simplify167.0ms (3.2%)

localize134.0ms (2.5%)

series6.0ms (0.1%)

simplify153.0ms (2.9%)

rewrite278.0ms (5.3%)

eval62.0ms (1.2%)

prune11.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify58.0ms (1.1%)

soundness190.0ms (3.6%)

preprocess72.0ms (1.4%)

end0.0ms (0%)

Profiling