Metrics for tanhf (example 3.4)

analyze114.0ms (1.6%)

Memory

24.0MiB live, 140.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.8s (24.9%)

Memory

26.9MiB live, 1 743.6MiB allocated

Samples

676.0ms	2 235×	2	valid
487.0ms	4 283×	0	valid
211.0ms	523×	3	valid
134.0ms	1 213×	1	valid
2.0ms	2×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-cos: 784.0ms (61% of total)

ival-sin: 195.0ms (15.2% of total)

adjust: 106.0ms (8.3% of total)

ival-div: 104.0ms (8.1% of total)

ival-sub: 81.0ms (6.3% of total)

ival-true: 7.0ms (0.5% of total)

exact: 5.0ms (0.4% of total)

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

Bogosity

preprocess48.0ms (0.7%)

Memory

7.6MiB live, 46.0MiB allocated

Algorithm

1×	egg-herbie

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
98×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Stop Event

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

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))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))

Symmetry

(negabs x)

explain170.0ms (2.4%)

Memory

3.9MiB live, 132.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
78	2	(1.1230818321180297e+216)	1	(7.24136798541894e+219)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
66	0	-	6	(1.0638290099235998e-159)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	79	6
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	60	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	60

Confusion

	Predicted +	Predicted -
+	138	0
-	1	117

Precision

0.9928057553956835

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	138	0	0
-	1	6	111

Precision?

0.9517241379310345

Recall?

1.0

Freqs

test

number	freq
0	117
1	139

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms	248×	0	valid
44.0ms	148×	2	valid
11.0ms	32×	3	valid
9.0ms	82×	1	valid
2.0ms	2×	4	valid

Compiler

Compiled 54 to 28 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-cos: 43.0ms (40.7% of total)

ival-sub: 29.0ms (27.4% of total)

ival-sin: 19.0ms (18% of total)

adjust: 7.0ms (6.6% of total)

ival-div: 6.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify29.0ms (0.4%)

Memory

-12.6MiB live, 23.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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	6848	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
82×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Stop Event

1×	iter limit
1×	saturated
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))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize64.0ms (0.9%)

Memory

21.8MiB live, 60.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	76.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	accuracy	74.3%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

21.0ms	74×	2	valid
15.0ms	16×	3	valid
13.0ms	124×	0	valid
4.0ms	41×	1	valid
1.0ms	1×	4	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

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

ival-cos: 31.0ms (67.5% of total)

ival-sin: 5.0ms (10.9% of total)

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

adjust: 3.0ms (6.5% of total)

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

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	inf	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	0	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	0	(cos x)
0.0ms	x	@	0	(- 1 (cos x))

rewrite358.0ms (5%)

Memory

-25.2MiB live, 368.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 606×	`lower-*.f64`
4 606×	`lower-*.f32`
3 722×	`lower-/.f32`
3 720×	`lower-/.f64`
2 028×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Counts

4 → 615

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
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (cos.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (cos.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (/.f64 (+.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x x))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (sin.f64 x)) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(fma.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
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(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1 binary64))) (sin.f64 x))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))) (neg.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)))
(.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))

simplify436.0ms (6.1%)

Memory

28.6MiB live, 694.3MiB allocated

Algorithm

1×	egg-herbie

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
3 796×	`lower-*.f64`
3 796×	`lower-*.f32`
3 232×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
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))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

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

eval193.0ms (2.7%)

Memory: -10.4MiB live, 127.8MiB allocated
Compiler: Compiled 14 403 to 1 633 computations (88.7% saved)

prune97.0ms (1.4%)

Memory

-13.5MiB live, 142.1MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	655	7	662
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	655	8	663

Accuracy

100.0%

Counts

663 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	8.1%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	50.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
	99.8%	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
▶	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
▶	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
▶	54.0%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
▶	54.0%	(*.f64 #s(literal 1/2 binary64) x)
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 138 to 92 computations (33.3% saved)

simplify35.0ms (0.5%)

Memory

25.7MiB live, 63.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

1 312×	`lower-fma.f32`
1 300×	`lower-fma.f64`
402×	`lower-*.f32`
384×	`lower-*.f64`
256×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	136
0	43	136
1	102	136
2	250	136
3	503	136
4	704	136
5	770	136
6	774	136
0	774	136

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize94.0ms (1.3%)

Memory

7.1MiB live, 165.3MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/40320 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	99.9%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

63.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 154 to 29 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 23.0ms (47.6% of total)

const: 13.0ms (26.9% of total)

ival-add: 6.0ms (12.4% of total)

ival-tan: 5.0ms (10.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-21.6MiB live, 16.4MiB allocated

Counts

16 → 192

Calls

Call 1

Inputs
#<alt (tan.f64 (*.f64 x #s(literal 1/2 binary64)))>
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/24 binary64))>
#<alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x x)>
#<alt (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>
#<alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>
#<alt (*.f64 x #s(literal 1/240 binary64))>
#<alt (*.f64 x #s(literal 17/40320 binary64))>
#<alt (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))>

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

Calls

48 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* x 1/2)
1.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2)
1.0ms	x	@	inf	(* x (+ (* x (* x 1/24)) 1/2))
0.0ms	x	@	inf	(tan (* x 1/2))
0.0ms	x	@	inf	(* x (+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2))

rewrite416.0ms (5.8%)

Memory

-12.7MiB live, 516.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 286×	`lower-fma.f32`
8 274×	`lower-fma.f64`
5 180×	`lower-*.f32`
5 162×	`lower-*.f64`
4 214×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	117
0	43	117
1	180	117
2	1326	117
0	8495	117

Stop Event

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

Counts

16 → 448

Calls

Call 1

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

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

simplify538.0ms (7.5%)

Memory

16.5MiB live, 501.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14 486×	`lower-fma.f64`
14 486×	`lower-fma.f32`
4 500×	`lower-*.f64`
4 500×	`lower-*.f32`
2 872×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	1340
1	314	1340
2	826	1336
3	2138	1334
4	4717	1334
0	8194	1229

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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

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

eval90.0ms (1.3%)

Memory: 17.0MiB live, 169.7MiB allocated
Compiler: Compiled 22 880 to 1 768 computations (92.3% saved)

prune78.0ms (1.1%)

Memory

4.4MiB live, 119.3MiB allocated

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	673	3	676
Fresh	0	2	2
Picked	0	5	5
Done	0	1	1
Total	673	11	684

Accuracy

100.0%

Counts

684 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.2%	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
▶	54.0%	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
▶	8.1%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	50.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
▶	99.8%	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
✓	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.0%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
▶	54.2%	(.f64 x (+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64)))
✓	54.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 181 to 117 computations (35.4% saved)

simplify57.0ms (0.8%)

Memory

-20.6MiB live, 63.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
✓	cost-diff	0	(.f64 x (+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64)))
✓	cost-diff	128	(+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(*.f64 x #s(literal 1/240 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	cost-diff	320	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	320	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(cos.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))

Rules

1 312×	`lower-fma.f32`
1 302×	`lower-fma.f64`
402×	`lower-*.f32`
388×	`lower-*.f64`
256×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	179
0	46	169
1	94	169
2	202	169
3	426	169
4	757	169
5	854	169
6	862	169
0	862	167

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize120.0ms (1.7%)

Memory

2.1MiB live, 198.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
✓	accuracy	99.7%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
✓	accuracy	99.9%	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(cos.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))

Samples

75.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 196 to 31 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 27.0ms (44.5% of total)

const: 9.0ms (14.8% of total)

ival-sin: 9.0ms (14.8% of total)

ival-add: 6.0ms (9.9% of total)

ival-cos: 5.0ms (8.2% of total)

ival-div: 2.0ms (3.3% of total)

ival-pow: 2.0ms (3.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

17 → 192

Calls

Call 1

Inputs
#<alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))>
#<alt (sin.f64 (*.f64 x #s(literal 1/2 binary64)))>
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt (cos.f64 (*.f64 x #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))>
#<alt (.f64 x (.f64 x x))>
#<alt (*.f64 x x)>
#<alt (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>
#<alt (*.f64 x #s(literal 1/240 binary64))>
#<alt (+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64))>
#<alt (.f64 x (+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64)))>
#<alt (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))>
#<alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))>
#<alt (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))>
#<alt (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))>
#<alt (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/48 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (cos (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (* 17/40320 (pow x 7))>
#<alt (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt (* 17/40320 (pow x 7))>
#<alt (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* x (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))>
#<alt (* x (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))>
#<alt (* 17/40320 (pow x 5))>
#<alt (* (pow x 5) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* 17/40320 (pow x 5))>
#<alt (* (pow x 5) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))>
#<alt 1/240>
#<alt (+ 1/240 (* 17/40320 (pow x 2)))>
#<alt (+ 1/240 (* 17/40320 (pow x 2)))>
#<alt (+ 1/240 (* 17/40320 (pow x 2)))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))>
#<alt (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))>
#<alt (* 17/40320 (pow x 4))>
#<alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* 17/40320 (pow x 4))>
#<alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>

Calls

48 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (* x (* x x)) 1/24) (* x 1/2))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(+ (* (+ (* x (* x 1/240)) 1/24) (* x (* x x))) (* x 1/2))
0.0ms	x	@	0	(+ (* (* x (* x x)) 1/24) (* x 1/2))
0.0ms	x	@	0	(sin (* x 1/2))

rewrite685.0ms (9.6%)

Memory

-23.2MiB live, 654.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

10 062×	`lower-fma.f32`
10 052×	`lower-fma.f64`
5 204×	`lower-*.f32`
5 190×	`lower-*.f64`
4 006×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	146
0	46	133
1	184	133
2	1253	133
0	8314	131

Stop Event

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

Counts

17 → 459

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (neg.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(cos.f64 (*.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(neg.f64 (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal 1/24 binary64))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 x x) (*.f64 x #s(literal 1/24 binary64))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x x) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) x) (/.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) x) (/.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/576 binary64) x) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) x) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) x) x) (/.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x))) x) (/.f64 #s(literal 1/24 binary64) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) #s(literal 1/24 binary64)) x) (/.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x)))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 #s(literal -1/576 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/576 binary64))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/576 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))))))
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(.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal 1/576 binary64)) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))))
(.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))))
(.f64 (fma.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal 1/576 binary64)) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))))
(.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))

simplify376.0ms (5.3%)

Memory

8.5MiB live, 544.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 758×	`lower-fma.f64`
13 758×	`lower-fma.f32`
3 814×	`lower-*.f64`
3 814×	`lower-*.f32`
2 772×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	1528
1	414	1528
2	1071	1524
3	2681	1514
4	5345	1514
0	8156	1425

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 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)) (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)) (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)) (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)) (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)) (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)) (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)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
(cos (* 1/2 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) x))
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(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 17/40320 (pow x 4))
(.f64 x (.f64 #s(literal 17/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))

eval135.0ms (1.9%)

Memory: 12.1MiB live, 165.5MiB allocated
Compiler: Compiled 26 238 to 2 142 computations (91.8% saved)

prune94.0ms (1.3%)

Memory

-30.1MiB live, 127.8MiB allocated

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	766	1	767
Fresh	0	0	0
Picked	1	4	5
Done	0	6	6
Total	767	11	778

Accuracy

100.0%

Counts

778 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
✓	54.0%	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	50.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	99.8%	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
✓	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.0%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.2%	(.f64 x (+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64)))
✓	54.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	8.1%	#s(literal 1 binary64)

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify3.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1
1	3	1
0	3	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

localize6.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated

Samples

3.0ms

256×

valid

Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.1MiB live, 0.0MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite7.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify2.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune6.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Pruning

11 alts after pruning (0 fresh and 11 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	10	10
Total	11	11

Accuracy

100.0%

Counts

11 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
✓	54.0%	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	50.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	99.8%	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
✓	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.2%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.0%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.2%	(.f64 x (+.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))) #s(literal 1/2 binary64)))
✓	54.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	8.1%	#s(literal 1 binary64)

Compiler

Compiled 229 to 116 computations (49.3% saved)

regimes12.0ms (0.2%)

Memory

-21.0MiB live, 17.5MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Calls

2 calls:

5.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
4.0ms	x

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

9 → 2

Calls

Call 1

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

Outputs

(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))

#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
58.3%	2	`x`
58.0%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
58.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
58.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes13.0ms (0.2%)

Memory

-28.8MiB live, 8.2MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))

Outputs
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
#s(literal 1 binary64)

Calls

2 calls:

10.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
57.8%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
58.0%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))

Outputs
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(literal 1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
58.0%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) x)

Outputs
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
57.4%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
57.5%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
8.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
8.1%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch30.0ms (0.4%)

Memory

-13.2MiB live, 26.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
28.0ms	2.159677971969701	296524.5817834894

Samples

23.0ms

144×

valid

Compiler

Compiled 218 to 145 computations (33.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-cos: 13.0ms (65.3% of total)

ival-sin: 5.0ms (25.1% of total)

ival-sub: 1.0ms (5% of total)

ival-div: 1.0ms (5% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.159677971969701	296524.5817834894

Compiler

Compiled 191 to 136 computations (28.8% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.159677971969701	296524.5817834894

Compiler

Compiled 173 to 127 computations (26.6% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.159677971969701	296524.5817834894

Compiler

Compiled 146 to 109 computations (25.3% saved)

bsearch1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.159677971969701	296524.5817834894

Compiler

Compiled 128 to 100 computations (21.9% saved)

bsearch1.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.159677971969701	296524.5817834894

Compiler

Compiled 83 to 73 computations (12% saved)

simplify6.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	102
1	44	102

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness916.0ms (12.8%)

Memory

-3.1MiB live, 590.2MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
10 062×	`lower-fma.f32`
10 052×	`lower-fma.f64`
8 286×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	117
0	43	117
1	180	117
2	1326	117
0	8495	117
0	24	146
0	46	133
1	184	133
2	1253	133
0	8314	131
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Compiler

Compiled 218 to 111 computations (49.1% saved)

preprocess75.0ms (1.1%)

Memory: 11.9MiB live, 172.9MiB allocated
Remove: (negabs x)
Compiler: Compiled 242 to 92 computations (62% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	21	136
0	43	136
1	102	136
2	250	136
3	503	136
4	704	136
5	770	136
6	774	136
0	774	136

Iter	Nodes	Cost
0	24	179
0	46	169
1	94	169
2	202	169
3	426	169
4	757	169
5	854	169
6	862	169
0	862	167

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	21	136
0	43	136
1	102	136
2	250	136
3	503	136
4	704	136
5	770	136
6	774	136
0	774	136

Iter	Nodes	Cost
0	24	179
0	46	169
1	94	169
2	202	169
3	426	169
4	757	169
5	854	169
6	862	169
0	862	167

analyze114.0ms (1.6%)

sample1.8s (24.9%)

preprocess48.0ms (0.7%)

explain170.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (0.4%)

localize64.0ms (0.9%)

series3.0ms (0%)

rewrite358.0ms (5%)

simplify436.0ms (6.1%)

eval193.0ms (2.7%)

prune97.0ms (1.4%)

simplify35.0ms (0.5%)

localize94.0ms (1.3%)

series14.0ms (0.2%)

rewrite416.0ms (5.8%)

simplify538.0ms (7.5%)

eval90.0ms (1.3%)

prune78.0ms (1.1%)

simplify57.0ms (0.8%)

localize120.0ms (1.7%)

series6.0ms (0.1%)

rewrite685.0ms (9.6%)

simplify376.0ms (5.3%)

eval135.0ms (1.9%)

prune94.0ms (1.3%)

simplify3.0ms (0%)

localize6.0ms (0.1%)

series0.0ms (0%)

rewrite7.0ms (0.1%)

simplify2.0ms (0%)

eval0.0ms (0%)

prune6.0ms (0.1%)

regimes12.0ms (0.2%)

regimes7.0ms (0.1%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes13.0ms (0.2%)

regimes2.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

bsearch30.0ms (0.4%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify6.0ms (0.1%)

soundness916.0ms (12.8%)

preprocess75.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	21	136
0	43	136
1	102	136
2	250	136
3	503	136
4	704	136
5	770	136
6	774	136
0	774	136

Iter	Nodes	Cost
0	24	179
0	46	169
1	94	169
2	202	169
3	426	169
4	757	169
5	854	169
6	862	169
0	862	167