Metrics for tanhf (example 3.4)

start0.0ms (0%)

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

analyze115.0ms (2.1%)

Memory

-0.3MiB live, 138.2MiB allocated; 30ms 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)

sample2.1s (39.9%)

Memory

89.1MiB live, 1 668.7MiB allocated; 963ms collecting garbage

Samples

713.0ms	2 312×	2	valid
418.0ms	4 143×	0	valid
400.0ms	1 189×	1	valid
309.0ms	609×	3	valid
3.0ms	3×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-cos: 798.0ms (59% of total)

adjust: 169.0ms (12.5% of total)

ival-sin: 168.0ms (12.4% of total)

ival-div: 115.0ms (8.5% of total)

ival-sub: 89.0ms (6.6% of total)

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

exact: 5.0ms (0.4% of total)

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

Bogosity

explain240.0ms (4.5%)

Memory

-10.2MiB live, 137.0MiB allocated; 21ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
62	0	-	1	(-9.561581879274004e-157)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
59	2	(-1.4473315214823506e+133)	0	-	`(-.f64 #s(literal 1 binary64) (cos.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	61	7
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	61	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	61

Confusion

	Predicted +	Predicted -
+	120	1
-	2	133

Precision

0.9836065573770492

Recall

0.9917355371900827

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	1	0
-	2	6	127

Precision?

0.937984496124031

Recall?

1.0

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

87.0ms	136×	2	valid
82.0ms	280×	0	valid
13.0ms	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: 174.0ms

ival-cos: 88.0ms (50.6% of total)

ival-sub: 58.0ms (33.4% of total)

ival-sin: 11.0ms (6.3% of total)

adjust: 9.0ms (5.2% of total)

ival-div: 6.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess235.0ms (4.4%)

Memory

-30.0MiB live, 171.0MiB 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

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify194.0ms (3.6%)

Memory

6.2MiB live, 193.0MiB allocated; 22ms 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)

localize54.0ms (1%)

Memory

7.7MiB live, 52.0MiB allocated; 5ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	13.292303953718926	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	14.48810532205564	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

23.0ms	68×	2	valid
14.0ms	140×	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: 40.0ms

ival-cos: 24.0ms (60.4% of total)

adjust: 5.0ms (12.6% of total)

ival-sin: 5.0ms (12.6% of total)

ival-div: 3.0ms (7.6% of total)

ival-sub: 2.0ms (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

3.0MiB live, 3.0MiB 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))

simplify194.0ms (3.6%)

Memory

12.8MiB live, 159.9MiB allocated; 19ms 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)

rewrite204.0ms (3.8%)

Memory

-24.1MiB live, 163.4MiB allocated; 27ms 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 (0.6%)

Memory: 24.8MiB live, 67.4MiB allocated; 5ms collecting garbage
Compiler: Compiled 4 121 to 798 computations (80.6% saved)

prune6.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Accuracy

100.0%

Counts

240 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
▶	46.9%	#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))
▶	47.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	47.3%	#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 138 to 106 computations (23.2% saved)

simplify147.0ms (2.7%)

Memory

-25.8MiB live, 84.8MiB allocated; 16ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(cos.f64 (/.f64 x #s(literal -2 binary64)))
cost-diff	0	(/.f64 x #s(literal 2 binary64))
cost-diff	0	(sin.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
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	28	157
0	44	145
1	81	145
2	192	145
3	590	145
4	1721	145
5	2927	145
6	3512	145
7	4309	145
8	5807	145
0	8158	145

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

localize162.0ms (3%)

Memory

-2.9MiB live, 181.9MiB allocated; 23ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 x #s(literal -2 binary64))
accuracy	0.0	(sin.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0.00390625	(cos.f64 (/.f64 x #s(literal -2 binary64)))
accuracy	0.2109375	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
accuracy	0.03515625	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.04296875	(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	0.0546875	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	33.950548683536034	#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	0.02734375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.078125	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	33.93965625740621	#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	33.70278039409116	#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	0.00390625	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

52.0ms	68×	2	valid
48.0ms	140×	0	valid
25.0ms	16×	3	valid
18.0ms	32×	1	valid

Compiler

Compiled 134 to 29 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

adjust: 37.0ms (31% of total)

ival-cos: 31.0ms (26% of total)

ival-mult: 13.0ms (10.9% of total)

ival-sin: 11.0ms (9.2% of total)

const: 8.0ms (6.7% of total)

ival-div: 7.0ms (5.9% of total)

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

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

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

exact: 1.0ms (0.8% of total)

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

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

series10.0ms (0.2%)

Memory

16.7MiB live, 16.7MiB allocated; 0ms collecting garbage

Counts

17 → 36

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))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
(cos.f64 (/.f64 x #s(literal -2 binary64)))
(/.f64 x #s(literal -2 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)))
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(* -1/2 x)
(/ (- 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)))))
(/ (sin (* 1/2 x)) (cos (* -1/2 x)))
(sin (* 1/2 x))
(cos (* -1/2 x))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

Calls

3 calls:

Time	Variable		Point	Expression
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) (/ (sin (/ x 2)) (cos (/ x -2))) (sin (/ x 2)) (/ x 2) (cos (/ x -2)) (/ x -2))
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) (/ (sin (/ x 2)) (cos (/ x -2))) (sin (/ x 2)) (/ x 2) (cos (/ x -2)) (/ x -2))
3.0ms	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) (/ (sin (/ x 2)) (cos (/ x -2))) (sin (/ x 2)) (/ x 2) (cos (/ x -2)) (/ x -2))

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) (/ (sin (/ x 2)) (cos (/ x -2))) (sin (/ x 2)) (/ x 2) (cos (/ x -2)) (/ x -2))

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) (/ (sin (/ x 2)) (cos (/ x -2))) (sin (/ x 2)) (/ x 2) (cos (/ x -2)) (/ x -2))

3.0ms

((/ (- 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) (/ (sin (/ x 2)) (cos (/ x -2))) (sin (/ x 2)) (/ x 2) (cos (/ x -2)) (/ x -2))

simplify131.0ms (2.4%)

Memory

13.7MiB live, 148.1MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	321
1	336	321
2	961	320
3	3570	320
0	8202	299

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

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)))
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(* -1/2 x)
(/ (- 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)))))
(/ (sin (* 1/2 x)) (cos (* -1/2 x)))
(sin (* 1/2 x))
(cos (* -1/2 x))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

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))
(* x (+ 1/2 (* -1/48 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/3840 binary64) x) x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/645120 binary64)) #s(literal 1/48 binary64))) (*.f64 #s(literal 1/2 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/384 binary64) x) x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/46080 binary64)) #s(literal 1/8 binary64))) (*.f64 x x) #s(literal 1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(/ (- 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))
(/ (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)))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* -1/2 x))
(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (+.f64 (/.f64 #s(literal -1/24 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64))))

rewrite192.0ms (3.6%)

Memory

-22.4MiB live, 167.7MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	137
0	44	125
1	147	120
2	927	120
0	8552	120

Stop Event

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

Counts

17 → 321

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))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
(cos.f64 (/.f64 x #s(literal -2 binary64)))
(/.f64 x #s(literal -2 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 (*.f64 #s(literal -1/2 binary64) x))) (neg.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) x (PI.f64)))))
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(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))
(neg.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (fabs.f64 (*.f64 #s(literal -1/240 binary64) x)) x #s(literal 1/24 binary64))
(fma.f64 (fabs.f64 (*.f64 #s(literal 1/240 binary64) x)) x #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal -1/240 binary64) x) (neg.f64 x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (neg.f64 x) (*.f64 #s(literal -1/240 binary64) x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal -1/240 binary64) x)) #s(literal 1/24 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal 1/240 binary64) x)) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal 1/24 binary64))))
(-.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/240 binary64) (.f64 x x)))
(+.f64 (/.f64 #s(literal 1/13824 binary64) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(+.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) (/.f64 #s(literal 1/13824 binary64) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(+.f64 (/.f64 #s(literal 1/13824 binary64) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(+.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 #s(literal 1/13824 binary64) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 #s(literal -1/240 binary64) x)) x))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (*.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.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 (+.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (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 (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 (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 (neg.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 (-.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))) (neg.f64 (*.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (*.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (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 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (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 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(/.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)) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (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 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(neg.f64 (tan.f64 (/.f64 x #s(literal -2 binary64))))
(tan.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 2 binary64)) (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (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 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (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 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(neg.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))))
(sin.f64 (neg.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64))))
(sin.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64)))
(sin.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64)))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(cos.f64 (+.f64 (/.f64 (+.f64 x (PI.f64)) #s(literal 2 binary64)) (PI.f64)))
(cos.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (/.f64 (+.f64 (PI.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)))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64))) (.f64 (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))) (-.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (-.f64 (.f64 (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) (.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))))))
(neg.f64 (neg.f64 (cos.f64 (/.f64 x #s(literal -2 binary64)))))
(fma.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal -2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal -2 binary64)))))
(sin.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 x) (PI.f64)) #s(literal -2 binary64))))
(sin.f64 (neg.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (neg.f64 x)) #s(literal 2 binary64)) (PI.f64))))
(sin.f64 (+.f64 (/.f64 (+.f64 (neg.f64 x) (PI.f64)) #s(literal -2 binary64)) (PI.f64)))
(sin.f64 (+.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (neg.f64 x)) #s(literal 2 binary64)) (PI.f64)) (PI.f64)))
(sin.f64 (/.f64 (+.f64 x (PI.f64)) #s(literal 2 binary64)))
(sin.f64 (/.f64 (+.f64 (PI.f64) (neg.f64 x)) #s(literal 2 binary64)))
(-.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (neg.f64 (cos.f64 (/.f64 x #s(literal -2 binary64)))) #s(literal 1 binary64)))
(cos.f64 (+.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64)) (PI.f64)))
(cos.f64 (+.f64 (/.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (PI.f64)) #s(literal 2 binary64)) (PI.f64)))
(cos.f64 (+.f64 (/.f64 (+.f64 (neg.f64 x) (PI.f64)) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (neg.f64 x)) #s(literal 2 binary64)) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)) (PI.f64)))
(cos.f64 (-.f64 (/.f64 (+.f64 x (PI.f64)) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(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))) #s(literal 0 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal -2 binary64)))) (.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal -2 binary64)))))
(+.f64 (.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 x) #s(literal 2 binary64))
(/.f64 x #s(literal -2 binary64))
(neg.f64 (/.f64 x #s(literal 2 binary64)))

eval71.0ms (1.3%)

Memory: 7.2MiB live, 65.6MiB allocated; 6ms collecting garbage
Compiler: Compiled 11 573 to 1 519 computations (86.9% saved)

prune23.0ms (0.4%)

Memory

-23.4MiB live, 21.8MiB allocated; 4ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	383	2	385
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	384	6	390

Accuracy

100.0%

Counts

390 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
▶	99.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x))))
✓	46.9%	#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))
✓	47.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	47.3%	#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 100 to 74 computations (26% saved)

simplify127.0ms (2.4%)

Memory

26.9MiB live, 116.1MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	105
0	32	99
1	68	97
2	170	97
3	557	97
4	1721	97
5	3588	97
6	3959	97
7	4471	97
8	5558	97
9	7613	97
0	8137	95

Stop Event

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

Calls

Call 1

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

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

localize169.0ms (3.1%)

Memory

-50.0MiB live, 167.2MiB allocated; 48ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x))
accuracy	0.0546875	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.1640625	(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
accuracy	33.950548683536034	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
accuracy	0.0	(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x))))
accuracy	0.00390625	(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
accuracy	0.2109375	(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x)))

Samples

61.0ms	68×	2	valid
47.0ms	140×	0	valid
11.0ms	16×	3	valid
9.0ms	32×	1	valid

Compiler

Compiled 85 to 23 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-cos: 38.0ms (33.7% of total)

ival-add: 23.0ms (20.4% of total)

adjust: 17.0ms (15.1% of total)

ival-mult: 10.0ms (8.9% of total)

ival-sin: 10.0ms (8.9% of total)

const: 8.0ms (7.1% of total)

ival-div: 4.0ms (3.5% of total)

ival-sub: 3.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Counts

9 → 27

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(cos.f64 (*.f64 #s(literal -1/2 binary64) 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))))))))
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(* 1/24 x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* -1/2 x)))
(sin (* 1/2 x))
(* 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 3))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(cos (* -1/2 x))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify143.0ms (2.7%)

Memory

19.1MiB live, 119.8MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	252
1	316	252
2	882	251
3	3167	251
0	8354	233

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

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))))))))
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(* 1/24 x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(/ (- 1 (cos x)) (sin x))
(/ (sin (* 1/2 x)) (cos (* -1/2 x)))
(sin (* 1/2 x))
(* 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 3))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(cos (* -1/2 x))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

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)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/645120 binary64) (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 x x)) #s(literal 1/48 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
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
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/46080 binary64) (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 x x)) #s(literal 1/8 binary64))) (*.f64 x x) #s(literal 1 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)))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64))) (pow.f64 x #s(literal 5 binary64)))
(* 1/240 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(* 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))
(cos (* -1/2 x))
(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x) x) #s(literal 1/240 binary64)))

rewrite200.0ms (3.7%)

Memory

18.5MiB live, 283.8MiB allocated; 43ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	89
0	32	83
1	115	81
2	800	71
0	8458	69

Stop Event

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

Counts

9 → 216

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) x (PI.f64))))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x)))
(neg.f64 (tan.f64 (*.f64 #s(literal -1/2 binary64) x)))
(tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) x)))
(sin.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
(sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)))
(sin.f64 (fma.f64 #s(literal -1/2 binary64) x (PI.f64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)))
(cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(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 (/.f64 (.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64))) x) (/.f64 (.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64))) (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))))
(.f64 (neg.f64 x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) x) x) #s(literal 1/2 binary64)))
(.f64 (neg.f64 x) (fma.f64 (.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64)) x) x #s(literal -1/2 binary64)))
(.f64 (neg.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) x) x)))
(.f64 x (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal -1/2 binary64)))
(.f64 x (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64)))) (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64))))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64)))))) (fma.f64 (/.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 2 binary64)) x) (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64))))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))))))
(/.f64 (-.f64 #s(literal 1/13824 binary64) (pow.f64 (.f64 #s(literal -1/240 binary64) (.f64 x x)) #s(literal 3 binary64))) (+.f64 #s(literal 1/576 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/240 binary64) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (-.f64 (.f64 (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))) (.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) #s(literal 1/13824 binary64))) (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64))) (neg.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))
(neg.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (fabs.f64 (*.f64 #s(literal -1/240 binary64) x)) x #s(literal 1/24 binary64))
(fma.f64 (fabs.f64 (*.f64 #s(literal 1/240 binary64) x)) x #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal -1/240 binary64) x) (neg.f64 x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (neg.f64 x) (*.f64 #s(literal -1/240 binary64) x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal -1/240 binary64) x)) #s(literal 1/24 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal 1/240 binary64) x)) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(-.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/240 binary64) (.f64 x x)))
(+.f64 (/.f64 #s(literal 1/13824 binary64) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(+.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))) (/.f64 #s(literal 1/13824 binary64) (-.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64))) (.f64 #s(literal 1/5760 binary64) (*.f64 x x)))))
(+.f64 (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(+.f64 (/.f64 (.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))) (/.f64 #s(literal 1/13824 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (*.f64 x x))))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 #s(literal -1/240 binary64) x)) x))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64))) (.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (-.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))))
(neg.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) x (PI.f64))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64) (.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64) (.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal -1/2 binary64) x)) (.f64 #s(literal 0 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) x))))
(sin.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))))
(sin.f64 (neg.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64))))
(sin.f64 (+.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) (PI.f64)))
(sin.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)) (PI.f64)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) x (PI.f64))) #s(literal 1 binary64)))
(cos.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (PI.f64)) (PI.f64)))
(cos.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)))
(cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)))
(cos.f64 (+.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal -1/2 binary64) x))) (.f64 #s(literal 0 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))

eval75.0ms (1.4%)

Memory: -25.4MiB live, 36.3MiB allocated; 15ms collecting garbage
Compiler: Compiled 9 511 to 1 078 computations (88.7% saved)

prune7.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	249	6	255

Accuracy

100.0%

Counts

255 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
✓	99.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal -1/2 binary64) x))))
✓	46.9%	#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))
✓	47.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	47.3%	#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 216 to 116 computations (46.3% saved)

regimes5.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Accuracy

Total -0.4b remaining (-1.1%)

Threshold costs -0.4b (-1.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
47.3%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
47.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify208.0ms (3.9%)

Memory

-24.3MiB live, 66.2MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations213.0ms (4%)

Memory

-0.9MiB live, 99.5MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 23 to 11 computations (52.2% saved)

preprocess56.0ms (1%)

Memory: -13.2MiB live, 32.6MiB allocated; 6ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 92 to 62 computations (32.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze115.0ms (2.1%)

sample2.1s (39.9%)

explain240.0ms (4.5%)

preprocess235.0ms (4.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify194.0ms (3.6%)

localize54.0ms (1%)

series2.0ms (0%)

simplify194.0ms (3.6%)

rewrite204.0ms (3.8%)

eval31.0ms (0.6%)

prune6.0ms (0.1%)

simplify147.0ms (2.7%)

localize162.0ms (3%)

series10.0ms (0.2%)

simplify131.0ms (2.4%)

rewrite192.0ms (3.6%)

eval71.0ms (1.3%)

prune23.0ms (0.4%)

simplify127.0ms (2.4%)

localize169.0ms (3.1%)

series4.0ms (0.1%)

simplify143.0ms (2.7%)

rewrite200.0ms (3.7%)

eval75.0ms (1.4%)

prune7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify208.0ms (3.9%)

derivations213.0ms (4%)

preprocess56.0ms (1%)

end0.0ms (0%)

Profiling