Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze105.0ms (1.7%)

Memory

-3.0MiB live, 133.6MiB allocated; 12ms collecting garbage

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)

sample2.2s (35.2%)

Memory

53.5MiB live, 1 681.1MiB allocated; 956ms collecting garbage

Samples

768.0ms	4 134×	0	valid
624.0ms	2 206×	2	valid
317.0ms	670×	3	valid
167.0ms	1 241×	1	valid
8.0ms	5×	4	valid

Precisions

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

ival-cos: 994.0ms (63.1% of total)

adjust: 201.0ms (12.8% of total)

ival-sin: 162.0ms (10.3% of total)

ival-div: 107.0ms (6.8% of total)

ival-sub: 97.0ms (6.2% of total)

ival-true: 6.0ms (0.4% of total)

exact: 5.0ms (0.3% of total)

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

Bogosity

explain185.0ms (3%)

Memory

-16.8MiB live, 128.3MiB allocated; 27ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
71	1	(1.1341258330745852e-161)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
64	0	-	6	(1.1341258330745852e-161)	`(/.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	5
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	58	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	58

Confusion

	Predicted +	Predicted -
+	130	0
-	0	126

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	0	0
-	0	5	121

Precision?

0.9629629629629629

Recall?

1.0

Freqs

test

number	freq
0	126
1	130

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

66.0ms	258×	0	valid
45.0ms	158×	2	valid
18.0ms	32×	3	valid
7.0ms	64×	1	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-sin: 49.0ms (41.5% of total)

ival-cos: 46.0ms (39% of total)

adjust: 10.0ms (8.5% of total)

ival-div: 6.0ms (5.1% of total)

ival-sub: 5.0ms (4.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess209.0ms (3.4%)

Memory

13.9MiB live, 214.5MiB allocated; 30ms collecting garbage

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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify153.0ms (2.5%)

Memory

21.4MiB live, 165.8MiB allocated; 20ms collecting garbage

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)

localize62.0ms (1%)

Memory

-12.3MiB live, 34.1MiB allocated; 3ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	14.39867253203259	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	15.475734138059382	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

31.0ms	79×	2	valid
13.0ms	129×	0	valid
7.0ms	16×	3	valid
4.0ms	32×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-cos: 31.0ms (66.8% of total)

adjust: 5.0ms (10.8% of total)

ival-sin: 5.0ms (10.8% of total)

ival-div: 3.0ms (6.5% of total)

ival-sub: 3.0ms (6.5% 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

2.1MiB live, 2.1MiB allocated; 0ms collecting garbage

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))

simplify230.0ms (3.7%)

Memory

-20.7MiB live, 166.0MiB allocated; 32ms collecting garbage

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)

rewrite152.0ms (2.5%)

Memory

-3.4MiB live, 145.9MiB allocated; 24ms collecting garbage

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)))

eval31.0ms (0.5%)

Memory: 10.9MiB live, 55.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 4 121 to 798 computations (80.6% saved)

prune7.0ms (0.1%)

Memory

17.4MiB live, 17.4MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	232	7	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	7	240

Accuracy

100.0%

Counts

240 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.5%	(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
	77.6%	(/.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))))
▶	50.7%	#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))
▶	50.7%	#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))
▶	50.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	51.1%	#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 226 to 150 computations (33.6% saved)

simplify253.0ms (4.1%)

Memory

3.0MiB live, 189.2MiB allocated; 42ms collecting garbage

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)

localize178.0ms (2.9%)

Memory

-19.8MiB live, 173.1MiB allocated; 25ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.03125	(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))
accuracy	0.0546875	(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	0.09765625	(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy	31.52203360533081	#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	0.0390625	(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	0.0390625	(.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	0.0859375	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	31.526431530006775	#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	0.05859375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.11328125	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	31.501347582740852	#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	31.31097530703006	#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	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
accuracy	0.0078125	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

60.0ms	79×	2	valid
44.0ms	129×	0	valid
23.0ms	32×	1	valid
16.0ms	16×	3	valid

Compiler

Compiled 183 to 30 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-mult: 28.0ms (23.7% of total)

adjust: 25.0ms (21.1% of total)

ival-cos: 22.0ms (18.6% of total)

ival-tan: 12.0ms (10.1% of total)

const: 11.0ms (9.3% of total)

ival-add: 9.0ms (7.6% of total)

ival-sin: 5.0ms (4.2% of total)

ival-div: 3.0ms (2.5% of total)

ival-sub: 3.0ms (2.5% 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

20.8MiB live, 20.8MiB allocated; 0ms collecting garbage

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))

simplify186.0ms (3%)

Memory

-7.6MiB live, 176.3MiB allocated; 36ms collecting garbage

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))))

rewrite200.0ms (3.2%)

Memory

-3.5MiB live, 232.7MiB allocated; 30ms collecting garbage

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))))
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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)))

eval146.0ms (2.4%)

Memory: -11.8MiB live, 121.5MiB allocated; 40ms collecting garbage
Compiler: Compiled 22 012 to 2 482 computations (88.7% saved)

prune35.0ms (0.6%)

Memory

-13.9MiB live, 32.1MiB allocated; 4ms collecting garbage

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	513	1	514
Fresh	0	2	2
Picked	0	5	5
Done	0	0	0
Total	513	8	521

Accuracy

100.0%

Counts

521 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	24.5%	(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
▶	77.6%	(/.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))))
▶	50.8%	#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)))
✓	50.7%	#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))
✓	50.7%	#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))
✓	50.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.1%	#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 131 to 88 computations (32.8% saved)

simplify159.0ms (2.6%)

Memory

31.8MiB live, 121.1MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 (cos.f64 x))
cost-diff	0	(sqrt.f64 (neg.f64 (cos.f64 x)))
cost-diff	3	(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
cost-diff	6	(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64))
cost-diff	0	(/.f64 x #s(literal 2 binary64))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
cost-diff	10	(/.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))))
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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	110
0	40	81
1	91	81
2	249	81
3	728	80
4	3777	80
0	8323	78

Stop Event

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

Calls

Call 1

Inputs
#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)
(/.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 (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 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64))
(sqrt.f64 (neg.f64 (cos.f64 x)))
(neg.f64 (cos.f64 x))
(cos.f64 x)
x
#s(literal 1 binary64)
(sin.f64 x)

Outputs
#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 (.f64 x x) #s(literal 1/24 binary64) #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 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(/.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))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.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 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(sqrt.f64 (neg.f64 (cos.f64 x)))
(neg.f64 (cos.f64 x))
(cos.f64 x)
x
#s(literal 1 binary64)
(sin.f64 x)

localize120.0ms (1.9%)

Memory

-18.2MiB live, 119.2MiB allocated; 29ms collecting garbage

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	0.01953125	(sqrt.f64 (neg.f64 (cos.f64 x)))
accuracy	0.03515625	(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64))
accuracy	0.09375	(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
accuracy	0.0	(/.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0.12404252930532605	(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	0.127285009768442	(/.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))))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.02734375	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0703125	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	15.421013679043233	#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)))

Samples

74.0ms	193×	0	invalid
32.0ms	63×	0	valid

Compiler

Compiled 104 to 25 computations (76% saved)

Precisions

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

ival-mult: 25.0ms (33.8% of total)

ival-cos: 20.0ms (27.1% of total)

ival-tan: 9.0ms (12.2% of total)

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

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

const: 3.0ms (4.1% of total)

ival-add: 2.0ms (2.7% of total)

ival-sub: 1.0ms (1.4% of total)

ival-sqrt: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

adjust: 0.0ms (0% 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

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Counts

14 → 40

Calls

Call 1

Inputs
(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)
(/.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 (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 x #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64))
(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
(sqrt.f64 (neg.f64 (cos.f64 x)))
(neg.f64 (cos.f64 x))
(*.f64 #s(literal 1/2 binary64) x)
(cos.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))))))))
(* 1/24 (pow x 2))
(pow x 2)
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* 1/24 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* 17/2880 (pow x 2))))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 17/2880 (* 31/40320 (pow x 2))))))))
(+ 1 (pow (sqrt -1) 2))
(+ 1 (+ (* -1/2 (* (pow x 2) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))
(+ 1 (+ (* (pow x 2) (+ (* -1/2 (pow (sqrt -1) 2)) (* 1/24 (* (pow x 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))
(+ 1 (+ (* (pow x 2) (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (sqrt -1) 2))) (* 1/24 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))
(/ (+ 1 (pow (sqrt -1) 2)) x)
(/ (+ 1 (+ (* (pow x 2) (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (+ (* 1/24 (pow (sqrt -1) 2)) (* (pow x 2) (- (* -1/720 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2)))))) (+ (* -1/5040 (+ 1 (pow (sqrt -1) 2))) (* 1/120 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2)))))))))) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(sqrt -1)
(+ (sqrt -1) (* -1/4 (* (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/4 (sqrt -1)) (* -1/96 (* (pow x 2) (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/4 (sqrt -1)) (* (pow x 2) (+ (* -1/96 (sqrt -1)) (* -19/5760 (* (pow x 2) (sqrt -1))))))))
-1
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
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)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (pow (sin (* 1/2 x)) 2) (pow (cos (* 1/2 x)) 2))
(+ 1 (* (cos x) (pow (sqrt -1) 2)))
(/ (+ 1 (* (cos x) (pow (sqrt -1) 2))) (sin x))
(* (sqrt (cos x)) (sqrt -1))
(* -1 (cos x))
(cos x)

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

inf

((+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (/ (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2)) (/ x 2) (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (sqrt (neg (cos x))) (neg (cos x)) (* 1/2 x) (cos x))

3.0ms

-inf

((+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (/ (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2)) (/ x 2) (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (sqrt (neg (cos x))) (neg (cos x)) (* 1/2 x) (cos x))

3.0ms

((+ (* (* 1/24 (* x x)) x) (* 1/2 x)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (/ (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2)) (/ x 2) (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (sqrt (neg (cos x))) (neg (cos x)) (* 1/2 x) (cos x))

simplify128.0ms (2.1%)

Memory

-3.8MiB live, 95.7MiB allocated; 26ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	650
1	578	395
2	2368	381
3	6198	381
0	8040	347

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 40

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))))))))
(* 1/24 (pow x 2))
(pow x 2)
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* 1/24 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* 17/2880 (pow x 2))))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 17/2880 (* 31/40320 (pow x 2))))))))
(+ 1 (pow (sqrt -1) 2))
(+ 1 (+ (* -1/2 (* (pow x 2) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))
(+ 1 (+ (* (pow x 2) (+ (* -1/2 (pow (sqrt -1) 2)) (* 1/24 (* (pow x 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))
(+ 1 (+ (* (pow x 2) (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (sqrt -1) 2))) (* 1/24 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))
(/ (+ 1 (pow (sqrt -1) 2)) x)
(/ (+ 1 (+ (* (pow x 2) (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (+ (* 1/24 (pow (sqrt -1) 2)) (* (pow x 2) (- (* -1/720 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2)))))) (+ (* -1/5040 (+ 1 (pow (sqrt -1) 2))) (* 1/120 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2)))))))))) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(sqrt -1)
(+ (sqrt -1) (* -1/4 (* (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/4 (sqrt -1)) (* -1/96 (* (pow x 2) (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/4 (sqrt -1)) (* (pow x 2) (+ (* -1/96 (sqrt -1)) (* -19/5760 (* (pow x 2) (sqrt -1))))))))
-1
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
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)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (pow (sin (* 1/2 x)) 2) (pow (cos (* 1/2 x)) 2))
(+ 1 (* (cos x) (pow (sqrt -1) 2)))
(/ (+ 1 (* (cos x) (pow (sqrt -1) 2))) (sin x))
(* (sqrt (cos x)) (sqrt -1))
(* -1 (cos x))
(cos 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)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(pow x 2)
(*.f64 x x)
(* 1/4 (pow x 2))
(.f64 #s(literal 1/4 binary64) (.f64 x x))
(* (pow x 2) (+ 1/4 (* 1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* 17/2880 (pow x 2))))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 17/2880 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 17/2880 (* 31/40320 (pow x 2))))))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 31/40320 binary64) (.f64 x x) #s(literal 17/2880 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(+ 1 (pow (sqrt -1) 2))
#s(literal 0 binary64)
(+ 1 (+ (* -1/2 (* (pow x 2) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(+ 1 (+ (* (pow x 2) (+ (* -1/2 (pow (sqrt -1) 2)) (* 1/24 (* (pow x 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(+ 1 (+ (* (pow x 2) (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (sqrt -1) 2))) (* 1/24 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(/ (+ 1 (pow (sqrt -1) 2)) x)
#s(literal 0 binary64)
(/ (+ 1 (+ (* (pow x 2) (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (/.f64 x x))
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (+ (* 1/24 (pow (sqrt -1) 2)) (* (pow x 2) (- (* -1/720 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2)))))) (+ (* -1/5040 (+ 1 (pow (sqrt -1) 2))) (* 1/120 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2)))))))))) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(.f64 (.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 x x))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* -1/4 (* (pow x 2) (sqrt -1))))
(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/4 (sqrt -1)) (* -1/96 (* (pow x 2) (sqrt -1))))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/96 binary64) (.f64 x x) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/4 (sqrt -1)) (* (pow x 2) (+ (* -1/96 (sqrt -1)) (* -19/5760 (* (pow x 2) (sqrt -1))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 #s(literal -19/5760 binary64) (.f64 x x) #s(literal -1/96 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))))
-1
#s(literal -1 binary64)
(- (* 1/2 (pow x 2)) 1)
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(fma.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))
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))
(* 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 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 3 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)))
(/ (pow (sin (* 1/2 x)) 2) (pow (cos (* 1/2 x)) 2))
(/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)))
(+ 1 (* (cos x) (pow (sqrt -1) 2)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(/ (+ 1 (* (cos x) (pow (sqrt -1) 2))) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* (sqrt (cos x)) (sqrt -1))
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(cos x)
(cos.f64 x)

rewrite167.0ms (2.7%)

Memory

12.0MiB live, 201.7MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	101
0	40	69
1	144	68
2	1059	68
0	8929	66

Stop Event

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

Counts

14 → 886

Calls

Call 1

Inputs
(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)
(/.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 (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 x #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64))
(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (sin.f64 x))
(sqrt.f64 (neg.f64 (cos.f64 x)))
(neg.f64 (cos.f64 x))
(*.f64 #s(literal 1/2 binary64) x)
(cos.f64 x)

Outputs
(.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) x) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 x (-.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))))) (fma.f64 (/.f64 #s(literal 1/576 binary64) x) (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))))) (-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) x)))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (-.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))) (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))) (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))
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(cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (PI.f64) x))
(+.f64 (.f64 #s(literal -1 binary64) (.f64 (sin.f64 x) #s(literal 0 binary64))) (neg.f64 (cos.f64 x)))
(+.f64 (neg.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64))) (neg.f64 (cos.f64 x)))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (neg.f64 (cos.f64 x)))
(+.f64 (cosh.f64 (log.f64 (neg.f64 (cos.f64 x)))) (sinh.f64 (log.f64 (neg.f64 (cos.f64 x)))))
(+.f64 (neg.f64 (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (neg.f64 (cos.f64 x))))
(*.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))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (sin.f64 x) #s(literal 0 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (sin.f64 x) #s(literal 0 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x)))))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(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) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (*.f64 (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (neg.f64 (cos.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) #s(literal 0 binary64))) (cos.f64 x))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))

eval115.0ms (1.9%)

Memory: -28.2MiB live, 160.9MiB allocated; 45ms collecting garbage
Compiler: Compiled 16 125 to 2 440 computations (84.9% saved)

prune64.0ms (1%)

Memory

-13.2MiB live, 34.8MiB allocated; 3ms collecting garbage

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	762	4	766
Fresh	0	0	0
Picked	2	1	3
Done	0	5	5
Total	764	10	774

Accuracy

100.0%

Counts

774 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.6%	(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	65.7%	(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
✓	50.8%	#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)))
✓	50.7%	#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))
✓	50.7%	#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))
✓	50.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.1%	#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)))
▶	28.7%	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
▶	4.3%	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Compiler

Compiled 161 to 113 computations (29.8% saved)

simplify117.0ms (1.9%)

Memory

51.2MiB live, 134.8MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 x #s(literal 2 binary64))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff	7	(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
cost-diff	2	(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
cost-diff	2	(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	4	(/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	112
0	34	87
1	77	87
2	187	87
3	520	71
4	1850	71
0	8557	71

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)

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

localize81.0ms (1.3%)

Memory

-39.7MiB live, 65.8MiB allocated; 8ms collecting garbage

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0.0390625	(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	0.04363251953688403	(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	0.0	(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
accuracy	0.00390625	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0.033535009768442016	(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
accuracy	0.09312438862423138	(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	0.0	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	2.366664482772906	(/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	5.644050364915708	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	5.812571513901652	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Samples

60.0ms	232×	0	invalid
6.0ms	24×	0	valid

Compiler

Compiled 104 to 24 computations (76.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-sin: 17.0ms (31.5% of total)

ival-exp: 6.0ms (11.1% of total)

ival-mult: 6.0ms (11.1% of total)

ival-cos: 6.0ms (11.1% of total)

ival-div: 5.0ms (9.3% of total)

ival-tan: 5.0ms (9.3% of total)

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

ival-pow2: 2.0ms (3.7% of total)

ival-add: 1.0ms (1.9% of total)

ival-sqrt: 1.0ms (1.9% of total)

exact: 1.0ms (1.9% of total)

ival-neg: 1.0ms (1.9% of total)

adjust: 0.0ms (0% of total)

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

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

series58.0ms (0.9%)

Memory

12.4MiB live, 56.8MiB allocated; 6ms collecting garbage

Counts

12 → 22

Calls

Call 1

Inputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x)
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 x #s(literal 2 binary64))

Outputs
(/ (+ 1 (pow (sqrt -1) 2)) x)
(/ (+ 1 (+ (* (pow x 2) (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (+ (* 1/24 (pow (sqrt -1) 2)) (* (pow x 2) (- (* -1/720 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2)))))) (+ (* -1/5040 (+ 1 (pow (sqrt -1) 2))) (* 1/120 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2)))))))))) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(* 1/2 x)
(* 1/2 (pow x 2))
(pow x 2)
(* 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))))))))
(+ (log 1/2) (log x))
(+ (log 1/2) (+ (log x) (* 1/12 (pow x 2))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/12 (* 7/1440 (pow x 2))))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 7/1440 (* 31/90720 (pow x 2))))))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* 1/24 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* 17/2880 (pow x 2))))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 17/2880 (* 31/40320 (pow x 2))))))))
(/ (+ 1 (* (cos x) (pow (sqrt -1) 2))) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(log (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (pow (sin (* 1/2 x)) 2) (pow (cos (* 1/2 x)) 2))

Calls

3 calls:

Time

Variable

Point

Expression

29.0ms

inf

((/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/ (* (* x x) 1/2) x) (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (* (* x x) 1/2) (* x x) (exp (* (log (tan (/ x 2))) 1)) (* (log (tan (/ x 2))) 1) (log (tan (/ x 2))) (tan (/ x 2)) (/ (pow (tan (/ x 2)) 2) (tan (/ x 2))) (pow (tan (/ x 2)) 2) (/ x 2))

27.0ms

-inf

((/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/ (* (* x x) 1/2) x) (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (* (* x x) 1/2) (* x x) (exp (* (log (tan (/ x 2))) 1)) (* (log (tan (/ x 2))) 1) (log (tan (/ x 2))) (tan (/ x 2)) (/ (pow (tan (/ x 2)) 2) (tan (/ x 2))) (pow (tan (/ x 2)) 2) (/ x 2))

2.0ms

((/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/ (* (* x x) 1/2) x) (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (* (* x x) 1/2) (* x x) (exp (* (log (tan (/ x 2))) 1)) (* (log (tan (/ x 2))) 1) (log (tan (/ x 2))) (tan (/ x 2)) (/ (pow (tan (/ x 2)) 2) (tan (/ x 2))) (pow (tan (/ x 2)) 2) (/ x 2))

simplify132.0ms (2.1%)

Memory

17.8MiB live, 110.3MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	454
1	418	257
2	1683	247
3	5373	244
0	8146	223

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 22

Calls

Call 1

Inputs
(/ (+ 1 (pow (sqrt -1) 2)) x)
(/ (+ 1 (+ (* (pow x 2) (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (+ (* 1/24 (pow (sqrt -1) 2)) (* (pow x 2) (- (* -1/720 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2)))))) (+ (* -1/5040 (+ 1 (pow (sqrt -1) 2))) (* 1/120 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2)))))))))) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(* 1/2 x)
(* 1/2 (pow x 2))
(pow x 2)
(* 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))))))))
(+ (log 1/2) (log x))
(+ (log 1/2) (+ (log x) (* 1/12 (pow x 2))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/12 (* 7/1440 (pow x 2))))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 7/1440 (* 31/90720 (pow x 2))))))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* 1/24 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* 17/2880 (pow x 2))))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 17/2880 (* 31/40320 (pow x 2))))))))
(/ (+ 1 (* (cos x) (pow (sqrt -1) 2))) (sin x))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(log (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (pow (sin (* 1/2 x)) 2) (pow (cos (* 1/2 x)) 2))

Outputs
(/ (+ 1 (pow (sqrt -1) 2)) x)
#s(literal 0 binary64)
(/ (+ 1 (+ (* (pow x 2) (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) (/.f64 x x))
(/ (+ 1 (+ (* (pow x 2) (- (+ (* -1/2 (pow (sqrt -1) 2)) (* (pow x 2) (- (+ (* 1/24 (pow (sqrt -1) 2)) (* (pow x 2) (- (* -1/720 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* 1/24 (pow (sqrt -1) 2)) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2)))))) (+ (* -1/5040 (+ 1 (pow (sqrt -1) 2))) (* 1/120 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2)))))))))) (+ (* -1/6 (- (* -1/2 (pow (sqrt -1) 2)) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (* 1/120 (+ 1 (pow (sqrt -1) 2))))))) (* -1/6 (+ 1 (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x)
(.f64 (.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 x x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #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)
(+ (log 1/2) (log x))
(+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (+ (log x) (* 1/12 (pow x 2))))
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) x (+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/12 (* 7/1440 (pow x 2))))))
(fma.f64 (.f64 (fma.f64 #s(literal 7/1440 binary64) (.f64 x x) #s(literal 1/12 binary64)) x) x (+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 7/1440 (* 31/90720 (pow x 2))))))))
(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 31/90720 binary64) (.f64 x x) #s(literal 7/1440 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) x) x (+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))))
(* 1/4 (pow x 2))
(.f64 #s(literal 1/4 binary64) (.f64 x x))
(* (pow x 2) (+ 1/4 (* 1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* 17/2880 (pow x 2))))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 17/2880 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 17/2880 (* 31/40320 (pow x 2))))))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 31/40320 binary64) (.f64 x x) #s(literal 17/2880 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(/ (+ 1 (* (cos x) (pow (sqrt -1) 2))) (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)))
(log (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(log.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x))))
(/ (pow (sin (* 1/2 x)) 2) (pow (cos (* 1/2 x)) 2))
(/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)))

rewrite74.0ms (1.2%)

Memory

-20.2MiB live, 25.7MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	97
0	34	79
1	117	79
0	654	79

Stop Event

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

Counts

12 → 128

Calls

Call 1

Inputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x)
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 x #s(literal 2 binary64))

Outputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) x))
(.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) x))
(.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) x) x))
(.f64 x (.f64 x (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))) (neg.f64 (neg.f64 x)))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (neg.f64 x))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(neg.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x))
(neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (neg.f64 x)))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x))
(.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1/2 binary64)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 x (.f64 #s(literal 1/2 binary64) x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))) (-.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 (.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (+.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (PI.f64)))))
(/.f64 (sin.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64)))) (cos.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(tan.f64 (+.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(+.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(exp.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (log.f64 (sin.f64 x)))
(-.f64 (log.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (log.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(-.f64 (log.f64 (sin.f64 x)) (log1p.f64 (cos.f64 x)))
(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (log.f64 (sin.f64 x)))
(-.f64 (log.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (log.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(-.f64 (log.f64 (sin.f64 x)) (log1p.f64 (cos.f64 x)))
(log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))) (-.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 (.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (+.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (PI.f64)))))
(/.f64 (sin.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64)))) (cos.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(tan.f64 (+.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(+.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(exp.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(*.f64 (/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(neg.f64 (/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(*.f64 (fabs.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) (fabs.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(pow.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 x))
(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(/.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(fma.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(fma.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(+.f64 (.f64 (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(+.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (cosh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sinh.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(+.f64 (cosh.f64 (.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))))
(exp.f64 (+.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (/.f64 x #s(literal -2 binary64)))

eval15.0ms (0.2%)

Memory: 26.3MiB live, 26.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 409 to 444 computations (81.6% saved)

prune13.0ms (0.2%)

Memory

-27.5MiB live, 16.7MiB allocated; 5ms collecting garbage

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	0	0
Picked	1	3	4
Done	0	6	6
Total	129	11	140

Accuracy

100.0%

Counts

140 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.6%	(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	65.7%	(exp.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
✓	50.8%	#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)))
✓	50.7%	#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))
✓	50.7%	#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))
✓	50.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.1%	#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)))
✓	28.7%	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) x))
	51.0%	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (.f64 x (.f64 x (/.f64 #s(literal 1/2 binary64) x))))
✓	4.3%	#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Compiler

Compiled 404 to 189 computations (53.2% saved)

regimes9.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 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 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (.f64 x (.f64 x (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #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)) (.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))
(exp.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) #s(literal 1 binary64)) (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))))

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

Calls

2 calls:

4.0ms	x
4.0ms	(/.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)

regimes6.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 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 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (.f64 x (.f64 x (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (/.f64 (.f64 (.f64 x x) #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)) (.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:

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

Results

Accuracy	Segments	Branch
51.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
51.1%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Outputs
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
4.3%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
4.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify45.0ms (0.7%)

Memory

-11.2MiB live, 32.5MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	41	27
2	86	27
3	167	23
4	310	23
5	713	23
6	1918	23
7	5267	23

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))

#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (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))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (+ (* (sqrt (neg (cos x))) (sqrt (neg (cos x)))) 1) (sin x)) #s(literal 0 binary64))

derivations488.0ms (7.9%)

Memory

-9.4MiB live, 323.0MiB allocated; 57ms collecting garbage

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
0	170	650
1	578	395
2	2368	381
3	6198	381
0	8040	347
0	79	202
1	266	202
2	777	196
3	3247	196
4	7420	196
0	8622	178

Stop Event

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

Compiler

Compiled 53 to 16 computations (69.8% saved)

preprocess37.0ms (0.6%)

Memory: 3.6MiB live, 48.8MiB allocated; 4ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 242 to 130 computations (46.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze105.0ms (1.7%)

sample2.2s (35.2%)

explain185.0ms (3%)

preprocess209.0ms (3.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify153.0ms (2.5%)

localize62.0ms (1%)

series2.0ms (0%)

simplify230.0ms (3.7%)

rewrite152.0ms (2.5%)

eval31.0ms (0.5%)

prune7.0ms (0.1%)

simplify253.0ms (4.1%)

localize178.0ms (2.9%)

series10.0ms (0.2%)

simplify186.0ms (3%)

rewrite200.0ms (3.2%)

eval146.0ms (2.4%)

prune35.0ms (0.6%)

simplify159.0ms (2.6%)

localize120.0ms (1.9%)

series10.0ms (0.2%)

simplify128.0ms (2.1%)

rewrite167.0ms (2.7%)

eval115.0ms (1.9%)

prune64.0ms (1%)

simplify117.0ms (1.9%)

localize81.0ms (1.3%)

series58.0ms (0.9%)

simplify132.0ms (2.1%)

rewrite74.0ms (1.2%)

eval15.0ms (0.2%)

prune13.0ms (0.2%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

simplify45.0ms (0.7%)

derivations488.0ms (7.9%)

preprocess37.0ms (0.6%)

end0.0ms (0%)

Profiling