Metrics for tanhf (example 3.4)

analyze181.0ms (2%)

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 7 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-sin: 30.0ms (37% of total)

ival-cos: 20.0ms (24.6% of total)

ival-sub: 18.0ms (22.2% of total)

ival-div: 8.0ms (9.9% of total)

const: 3.0ms (3.7% of total)

backward-pass: 1.0ms (1.2% of total)

sample1.9s (21.1%)

Results

807.0ms	1908×	2	valid
470.0ms	4263×	0	valid
309.0ms	2081×	1	valid
3.0ms	4×	3	valid

Precisions

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

ival-cos: 800.0ms (61.7% of total)

ival-sin: 204.0ms (15.7% of total)

ival-div: 100.0ms (7.7% of total)

ival-sub: 90.0ms (6.9% of total)

backward-pass: 88.0ms (6.8% of total)

const: 16.0ms (1.2% of total)

Bogosity

preprocess84.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

640×	`sum5-define`
524×	`sum3-define`
502×	`fnmadd-define`
430×	`fnmadd-define`
398×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	38	13
2	79	12
3	184	12
4	493	12
5	1160	12
6	2161	12
0	6	4
1	16	4
2	23	4
3	35	4
4	59	4
5	90	4
6	152	4
7	264	4
8	633	4
9	1210	4
10	1691	4
11	1714	4
12	1722	4
13	1728	4
14	1736	4
15	1749	4
16	1757	4
17	1766	4
18	1767	4
0	1767	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (- 1 (cos x)) (sin x))

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

Call 2

Inputs
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos (neg x))) (sin (neg x)))
(neg (/ (- 1 (cos (neg x))) (sin (neg x))))

Outputs
(/ (- 1 (cos x)) (sin x))
(tan (* x 1/2))
(/ (- 1 (cos (neg x))) (sin (neg x)))
(tan (* x -1/2))
(neg (/ (- 1 (cos (neg x))) (sin (neg x))))
(tan (* x 1/2))

Symmetry

(negabs x)

explain163.0ms (1.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
79	-	1	(1.5210048332210493e+65)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
64	-	4	(2.4931709653527886e-157)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	-	0	-	`x`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(cos.f64 x)`

Results

77.0ms	122×	2	valid
29.0ms	246×	0	valid
29.0ms	144×	1	valid

Compiler

Compiled 46 to 20 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-cos: 57.0ms (64.9% of total)

ival-sin: 12.0ms (13.7% of total)

ival-div: 6.0ms (6.8% of total)

backward-pass: 6.0ms (6.8% of total)

ival-sub: 5.0ms (5.7% of total)

const: 1.0ms (1.1% of total)

eval0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 6 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	6528	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Rules

430×	`fnmadd-define`
396×	`sum3-define`
332×	`fma-define`
290×	`fmsub-define`
272×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	16	23
2	23	23
3	35	23
4	59	23
5	90	23
6	152	23
7	264	23
8	633	23
9	1211	23
10	1692	23
11	1715	23
12	1723	23
13	1729	23
14	1737	23
15	1750	23
16	1758	23
17	1767	23
18	1768	23
0	1768	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(tan (/ x 2))
(/ x 2)
x
2
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
1
(cos x)
x
(sin x)

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

localize85.0ms (0.9%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	77.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	accuracy	73.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Results

31.0ms	61×	2	valid
24.0ms	123×	0	valid
18.0ms	72×	1	valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-cos: 24.0ms (46.6% of total)

ival-sin: 8.0ms (15.5% of total)

ival-div: 6.0ms (11.6% of total)

ival-tan: 6.0ms (11.6% of total)

backward-pass: 4.0ms (7.8% of total)

ival-sub: 3.0ms (5.8% of total)

const: 1.0ms (1.9% of total)

series5.0ms (0.1%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (tan (/ x 2))>
#<alt (/ x 2)>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (sin 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 (/ (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 (* 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

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- 1 (cos x)) (sin x))
1.0ms	x	@	inf	(/ x 2)
1.0ms	x	@	inf	(tan (/ x 2))
0.0ms	x	@	inf	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	-inf	(tan (/ x 2))

rewrite492.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4784×	`-lowering-.f32`
4784×	`-lowering-.f64`
2870×	`/-lowering-/.f32`
2870×	`/-lowering-/.f64`
2050×	`--lowering--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	47	19
2	275	19
3	2591	17
0	11834	17

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 1001

Calls

Call 1

Inputs
(tan (/ x 2))
(/ x 2)
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)

Outputs
(+.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)) (-.f64 #s(literal 0 binary64) (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 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (fma.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.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 (cos.f64 x) #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 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (*.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 #s(literal 2 binary64)))))) (.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)) (-.f64 #s(literal 0 binary64) (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 (cos.f64 x) #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 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (/.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 #s(literal 2 binary64))))) (/.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 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))))
(+.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))))
(+.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (cos.f64 x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (cos.f64 x))))
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(cos.f64 x)
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(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
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simplify453.0ms (5%)

Algorithm

1×	egg-herbie

Rules

2762×	`-lowering-.f32`
2762×	`-lowering-.f64`
2260×	`+-lowering-+.f64`
2260×	`+-lowering-+.f32`
1804×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	436
1	239	378
2	689	375
3	2205	375
4	3765	375
5	6141	375
6	6753	375
0	8098	375

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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

eval141.0ms (1.6%)

Compiler: Compiled 24513 to 1670 computations (93.2% saved)

prune94.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1068	5	1073
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	1068	7	1075

Accuracy

100.0%

Counts

1075 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.3%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	50.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
▶	54.0%	(/.f64 x #s(literal 2 binary64))
▶	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
▶	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
▶	53.8%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 125 to 86 computations (31.2% saved)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 14 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 x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64)))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
✓	cost-diff	0	(*.f64 x #s(literal 1/24 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))

Rules

1728×	`fma-define`
1312×	`fma-lowering-fma.f32`
1312×	`fma-lowering-fma.f64`
402×	`-lowering-.f32`
402×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	174
1	88	153
2	265	153
3	657	153
4	1328	153
5	1807	153
6	1972	153
7	1973	153
0	1973	153

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x 2)
x
2
(* x (+ 1/2 (* x (* x 1/24))))
x
(+ 1/2 (* x (* x 1/24)))
1/2
(* x (* x 1/24))
(* x 1/24)
1/24
(* x (+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240))))))
x
(+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240)))))
1/2
(* x (* x (+ 1/24 (* (* x x) 1/240))))
(* x (+ 1/24 (* (* x x) 1/240)))
(+ 1/24 (* (* x x) 1/240))
1/24
(* (* x x) 1/240)
(* x x)
1/240
(* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
x
(+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
1/2
(* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(* x x)
(+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
1/24
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(+ 1/240 (* (* x x) 17/40320))
1/240
(* (* x x) 17/40320)
17/40320
(pow 1 -1/2)
1
-1/2

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

localize138.0ms (1.5%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 17/40320 binary64))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/240 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64)))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	accuracy	99.7%	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))

Results

92.0ms

256×

valid

Compiler

Compiled 207 to 29 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 29.0ms (48.3% of total)

...c/correct-round.rkt:119:19: 18.0ms (30% of total)

ival-add: 7.0ms (11.7% of total)

ival-pow: 3.0ms (5% of total)

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

const: 1.0ms (1.7% of total)

backward-pass: 0.0ms (0% of total)

series10.0ms (0.1%)

Counts

17 → 192

Calls

Call 1

Inputs
#<alt (/ x 2)>
#<alt (* x (+ 1/2 (* x (* x 1/24))))>
#<alt (+ 1/2 (* x (* x 1/24)))>
#<alt (* x (* x 1/24))>
#<alt (* x 1/24)>
#<alt (* x (+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240))))))>
#<alt (+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240)))))>
#<alt (* x (* x (+ 1/24 (* (* x x) 1/240))))>
#<alt (* x (+ 1/24 (* (* x x) 1/240)))>
#<alt (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))>
#<alt (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))>
#<alt (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))>
#<alt (* x x)>
#<alt (pow 1 -1/2)>
#<alt (* (* x x) 1/240)>
#<alt (* (* x x) 17/40320)>
#<alt (* (* x x) (+ 1/240 (* (* x x) 17/40320)))>

Outputs
#<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 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (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 (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* (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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/240 (* 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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* x (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* x (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* 1/240 (pow x 3))>
#<alt (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 3))>
#<alt (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 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 (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 (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 (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))>
#<alt (* (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 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (* 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 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x (+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240))))))
1.0ms	x	@	inf	(* x (+ 1/2 (* x (* x 1/24))))
0.0ms	x	@	inf	(* x (+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240))))))
0.0ms	x	@	0	(* x (+ 1/2 (* x (* x 1/24))))
0.0ms	x	@	inf	(* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))

rewrite330.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4136×	`-lowering-.f32`
4136×	`-lowering-.f64`
2976×	`/-lowering-/.f32`
2976×	`/-lowering-/.f64`
2008×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	133
1	175	116
2	1483	116
0	8157	116

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 353

Calls

Call 1

Inputs
(/ x 2)
(* x (+ 1/2 (* x (* x 1/24))))
(+ 1/2 (* x (* x 1/24)))
(* x (* x 1/24))
(* x 1/24)
(* x (+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240))))))
(+ 1/2 (* x (* x (+ 1/24 (* (* x x) 1/240)))))
(* x (* x (+ 1/24 (* (* x x) 1/240))))
(* x (+ 1/24 (* (* x x) 1/240)))
(* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(+ 1/2 (* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(* (* x x) (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(* x x)
(pow 1 -1/2)
(* (* x x) 1/240)
(* (* x x) 17/40320)
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))

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

simplify210.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2750×	`-lowering-.f32`
2750×	`-lowering-.f64`
1696×	`fnmadd-define`
1416×	`fma-lowering-fma.f32`
1416×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1508
1	311	1249
2	953	1244
3	2765	1208
4	6013	1208
0	8007	1208

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval82.0ms (0.9%)

Compiler: Compiled 18230 to 1485 computations (91.9% saved)

prune90.0ms (1%)

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	593	6	599
Fresh	0	0	0
Picked	1	4	5
Done	0	2	2
Total	594	12	606

Accuracy

100.0%

Counts

606 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	54.0%	(/.f64 x #s(literal 2 binary64))
▶	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
▶	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
▶	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
	53.2%	(.f64 x (/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) #s(literal 1/4 binary64)) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) #s(literal 1/2 binary64))))
▶	53.9%	(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
✓	53.8%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
▶	8.3%	#s(literal 1 binary64)

Compiler

Compiled 349 to 186 computations (46.7% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
✓	cost-diff	256	(+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))
✓	cost-diff	256	(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))
✓	cost-diff	0	(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))

Rules

2102×	`fma-define`
1652×	`fma-lowering-fma.f32`
1652×	`fma-lowering-fma.f64`
482×	`sum3-define`
402×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	281
1	96	248
2	300	242
3	844	242
4	1615	242
5	2193	242
6	2376	242
7	2377	242
0	2377	242

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (/ x 2) (* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))))
(/ x 2)
x
2
(* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
1/24
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(* x x)
(+ 1/240 (* (* x x) 17/40320))
1/240
(* (* x x) 17/40320)
17/40320
1
(+ (/ x 2) (* x (* x (* x 1/24))))
(/ x 2)
x
2
(* x (* x (* x 1/24)))
(* x (* x 1/24))
(* x 1/24)
1/24
(+ (/ x 2) (* (* x (* x x)) (+ 1/24 (* x (* x 1/240)))))
(/ x 2)
x
2
(* (* x (* x x)) (+ 1/24 (* x (* x 1/240))))
(* x (* x x))
(* x x)
(+ 1/24 (* x (* x 1/240)))
1/24
(* x (* x 1/240))
(* x 1/240)
1/240
(* x (+ (+ 1/2 (* x (* x 1/24))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
x
(+ (+ 1/2 (* x (* x 1/24))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(+ 1/2 (* x (* x 1/24)))
1/2
(* x (* x 1/24))
(* x 1/24)
1/24
(* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(* x x)
(+ 1/240 (* (* x x) 17/40320))
1/240
(* (* x x) 17/40320)
17/40320

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

localize169.0ms (1.9%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))
✓	accuracy	99.7%	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 17/40320 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/240 binary64)))
✓	accuracy	100.0%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
✓	accuracy	99.7%	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 17/40320 binary64))

Results

107.0ms

256×

valid

Compiler

Compiled 338 to 33 computations (90.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 27.0ms (54.6% of total)

...c/correct-round.rkt:119:19: 10.0ms (20.2% of total)

ival-add: 9.0ms (18.2% of total)

ival-div: 2.0ms (4% of total)

const: 1.0ms (2% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (+ (/ x 2) (* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))))>
#<alt (/ x 2)>
#<alt (* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))>
#<alt (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))>
#<alt (+ (/ x 2) (* x (* x (* x 1/24))))>
#<alt (* x (* x (* x 1/24)))>
#<alt (* x (* x 1/24))>
#<alt (+ (/ x 2) (* (* x (* x x)) (+ 1/24 (* x (* x 1/240)))))>
#<alt (* (* x (* x x)) (+ 1/24 (* x (* x 1/240))))>
#<alt (* x (* x x))>
#<alt (* x (+ (+ 1/2 (* x (* x 1/24))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))>
#<alt (+ (+ 1/2 (* x (* x 1/24))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))>
#<alt (+ 1/2 (* x (* x 1/24)))>
#<alt (* (* x x) 17/40320)>
#<alt (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))>
#<alt (* (* x x) (+ 1/240 (* (* x x) 17/40320)))>
#<alt (* x 1/24)>
#<alt (* x (* x 1/240))>
#<alt (* x 1/240)>

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 (* 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 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 (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))>
#<alt (* (pow x 3) (+ 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))))))>
#<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 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))>
#<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 (* 1/2 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 (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 3))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (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 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))>
#<alt (* (pow x 3) (+ 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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (* 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 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 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 (* 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 1/2>
#<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 (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* 17/40320 (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 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))>
#<alt (* (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 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (* 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 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 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 (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (pow x 2))>
#<alt (* 1/240 (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)>

Calls

57 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (/ x 2) (* x (* x (* x 1/24))))
0.0ms	x	@	inf	(+ (/ x 2) (* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(* x 1/240)
0.0ms	x	@	-inf	(+ (/ x 2) (* (* x (* x x)) (+ 1/24 (* x (* x 1/240)))))

rewrite370.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3938×	`-lowering-.f32`
3938×	`-lowering-.f64`
2578×	`/-lowering-/.f32`
2578×	`/-lowering-/.f64`
2256×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	180
1	199	152
2	2003	148
0	8146	148

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 526

Calls

Call 1

Inputs
(+ (/ x 2) (* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))))
(/ x 2)
(* x (* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(* x (* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(+ (/ x 2) (* x (* x (* x 1/24))))
(* x (* x (* x 1/24)))
(* x (* x 1/24))
(+ (/ x 2) (* (* x (* x x)) (+ 1/24 (* x (* x 1/240)))))
(* (* x (* x x)) (+ 1/24 (* x (* x 1/240))))
(* x (* x x))
(* x (+ (+ 1/2 (* x (* x 1/24))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(+ (+ 1/2 (* x (* x 1/24))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(+ 1/2 (* x (* x 1/24)))
(* (* x x) 17/40320)
(* x (+ 1/24 (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(* x 1/24)
(* x (* x 1/240))
(* x 1/240)

Outputs
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))) (/.f64 x #s(literal 2 binary64)))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(+.f64 (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))))
(-.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))) (/.f64 x #s(literal -2 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))))) (/.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))))))
(fma.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (/.f64 x #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(fma.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(fma.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (/.f64 x #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (.f64 x x) (/.f64 x #s(literal 2 binary64)))
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(/.f64 (.f64 (+.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/40320 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))
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(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (neg.f64 (+.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x (.f64 x x)) x)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 17/40320 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x (.f64 x x)) x)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 17/40320 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/40320 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 289/1625702400 binary64))))) (neg.f64 (-.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)))) (.f64 x x))) (neg.f64 (+.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/40320 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 289/1625702400 binary64))) (.f64 x x))) (neg.f64 (-.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))
(.f64 (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) x)
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(.f64 x (.f64 x #s(literal 1/240 binary64)))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(.f64 #s(literal 1/240 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/240 binary64)) x)
(*.f64 x #s(literal 1/240 binary64))
(*.f64 #s(literal 1/240 binary64) x)

simplify264.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

3092×	`-lowering-.f32`
3092×	`-lowering-.f64`
1920×	`fnmadd-define`
1630×	`fma-lowering-fma.f32`
1630×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1856
1	331	1588
2	1006	1576
3	2822	1560
4	5782	1560
0	8474	1560

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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

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

eval118.0ms (1.3%)

Compiler: Compiled 34089 to 1847 computations (94.6% saved)

prune83.0ms (0.9%)

Pruning

13 alts after pruning (2 fresh and 11 done)

	Pruned	Kept	Total
New	900	2	902
Fresh	1	0	1
Picked	0	5	5
Done	0	6	6
Total	901	13	914

Accuracy

100.0%

Counts

914 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	54.0%	(/.f64 x #s(literal 2 binary64))
✓	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
✓	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
✓	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
▶	53.2%	(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
✓	53.9%	(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
▶	53.3%	(.f64 x (+.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
✓	53.8%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	8.3%	#s(literal 1 binary64)

Compiler

Compiled 273 to 144 computations (47.3% saved)

simplify195.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	256	(-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
✓	cost-diff	512	(-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
✓	cost-diff	3200	(/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
✓	cost-diff	3200	(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
✓	cost-diff	256	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))))
✓	cost-diff	256	(+.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))
✓	cost-diff	256	(.f64 x (+.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))

Rules

3612×	`-lowering-.f32`
3612×	`-lowering-.f64`
2694×	`+-lowering-+.f64`
2694×	`+-lowering-+.f32`
1480×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	484
1	125	385
2	464	354
3	2156	322
0	8349	322

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* x (+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
x
(+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))))
(+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824)))
1/8
(* (* x (* x x)) (* (* x (* x x)) 1/13824))
(* x (* x x))
(* x x)
(* (* x (* x x)) 1/13824)
1/13824
(/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))
1
(+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))
1/4
(* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))
(* 1/24 (* x x))
1/24
(- (* 1/24 (* x x)) 1/2)
1/2
(* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(+ 1/240 (* (* x x) 17/40320))
1/240
(* (* x x) 17/40320)
17/40320
(* x (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))))
x
(/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2)))
(- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2)))
(* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(* x x)
(+ 1/240 (* (* x x) 17/40320))
1/240
(* (* x x) 17/40320)
17/40320
(* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))
(+ (* 1/24 (* x x)) 1/2)
(* 1/24 (* x x))
1/24
1/2
(- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))

Outputs
(* x (+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(.f64 x (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
x
(+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))
(* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))
(+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824)))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x (.f64 x x)))))))
1/8
#s(literal 1/8 binary64)
(* (* x (* x x)) (* (* x (* x x)) 1/13824))
(.f64 x (.f64 x (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(* (* x (* x x)) 1/13824)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824 binary64))
1/13824
#s(literal 1/13824 binary64)
(/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))
1
#s(literal 1 binary64)
(+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))
1/4
#s(literal 1/4 binary64)
(* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))
(* 1/24 (* x x))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
1/24
#s(literal 1/24 binary64)
(- (* 1/24 (* x x)) 1/2)
(+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))
(* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))
(+ 1/240 (* (* x x) 17/40320))
(+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))
1/240
#s(literal 1/240 binary64)
(* (* x x) 17/40320)
(.f64 (.f64 x x) #s(literal 17/40320 binary64))
17/40320
#s(literal 17/40320 binary64)
(* x (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) #s(literal 1/24 binary64))))) #s(literal 1 binary64))
x
(/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2)))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))) #s(literal 1/24 binary64)))))
(- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2)))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) #s(literal -1/24 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))) #s(literal 1/24 binary64)))))
(* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
(* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(.f64 x (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))))
(* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))
(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
(.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))
(* x x)
(*.f64 x x)
(+ 1/240 (* (* x x) 17/40320))
(+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))
1/240
#s(literal 1/240 binary64)
(* (* x x) 17/40320)
(.f64 (.f64 x x) #s(literal 17/40320 binary64))
17/40320
#s(literal 17/40320 binary64)
(* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))
(.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))
(* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))
(.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(+ (* 1/24 (* x x)) 1/2)
(+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
(* 1/24 (* x x))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
1/24
#s(literal 1/24 binary64)
1/2
#s(literal 1/2 binary64)
(- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) #s(literal -1/24 binary64))))

localize184.0ms (2%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 #s(literal 1/24 binary64) (.f64 x x))
✓	accuracy	81.6%	(-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
✓	accuracy	72.6%	(-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
✓	accuracy	66.1%	(/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(.f64 #s(literal 1/24 binary64) (.f64 x x))
✓	accuracy	99.5%	(.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824 binary64))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
✓	accuracy	67.3%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))))

Results

108.0ms

256×

valid

Compiler

Compiled 655 to 36 computations (94.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 41.0ms (59.1% of total)

...c/correct-round.rkt:119:19: 15.0ms (21.6% of total)

ival-add: 6.0ms (8.7% of total)

ival-sub: 3.0ms (4.3% of total)

ival-div: 3.0ms (4.3% of total)

const: 1.0ms (1.4% of total)

backward-pass: 0.0ms (0% of total)

series10.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (* x (+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))>
#<alt (+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))>
#<alt (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))))>
#<alt (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))>
#<alt (* x (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))))>
#<alt (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2)))>
#<alt (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2)))>
#<alt (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))>
#<alt (* (* x (* x x)) 1/13824)>
#<alt (* 1/24 (* x 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 (* 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 1/2>
#<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 4>
#<alt (+ 4 (* 1/3 (pow x 2)))>
#<alt (+ 4 (* (pow x 2) (+ 1/3 (* -1/432 (pow x 4)))))>
#<alt (+ 4 (* (pow x 2) (+ 1/3 (* (pow x 4) (- (* -1/5184 (pow x 2)) 1/432)))))>
#<alt (/ 576 (pow x 4))>
#<alt (/ (+ 576 (* 6912 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 576 (* 6912 (/ 1 (pow x 2)))) (/ 995328 (pow x 6))) (pow x 4))>
#<alt (/ (+ 576 (+ (* -1 (/ (+ 995328 (* 11943936 (/ 1 (pow x 2)))) (pow x 6))) (* 6912 (/ 1 (pow x 2))))) (pow x 4))>
#<alt (/ 576 (pow x 4))>
#<alt (/ (+ 576 (* 6912 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 576 (* 6912 (/ 1 (pow x 2)))) (/ 995328 (pow x 6))) (pow x 4))>
#<alt (/ (+ 576 (+ (* -1 (/ (+ 995328 (* 11943936 (/ 1 (pow x 2)))) (pow x 6))) (* 6912 (/ 1 (pow x 2))))) (pow x 4))>
#<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 -1/4>
#<alt (- (* -1/24 (pow x 2)) 1/4)>
#<alt (- (* (pow x 2) (- (* -1/576 (pow x 2)) 1/24)) 1/4)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* 1/57600 (pow x 4)) 1/576)) 1/24)) 1/4)>
#<alt (* 289/1625702400 (pow x 12))>
#<alt (* (pow x 12) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))>
#<alt (* (pow x 12) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))>
#<alt (* (pow x 12) (- (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))) (* 1/576 (/ 1 (pow x 8)))))>
#<alt (* 289/1625702400 (pow x 12))>
#<alt (* (pow x 12) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))>
#<alt (* (pow x 12) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))>
#<alt (* (pow x 12) (- (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))) (* 1/576 (/ 1 (pow x 8)))))>
#<alt -1/2>
#<alt (- (* -1/24 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (- (* 1/240 (pow x 2)) 1/24)) 1/2)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))) 1/24)) 1/2)>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))) (/ 1/24 (pow x 4))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (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 (* 1/240 (/ 1 (pow x 2)))) (/ 1/24 (pow x 4))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/13824 (pow x 3))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>

Calls

30 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* x (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))))
1.0ms	x	@	inf	(* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))))
0.0ms	x	@	0	(* x (+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
0.0ms	x	@	0	(* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))))
0.0ms	x	@	0	(* x (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))))

rewrite447.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3130×	`-lowering-.f32`
3130×	`-lowering-.f64`
2872×	`/-lowering-/.f32`
2872×	`/-lowering-/.f64`
2356×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	270
1	240	167
2	2259	155
0	8497	155

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 388

Calls

Call 1

Inputs
(* x (+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))))))
(+ (* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))
(* (+ 1/8 (* (* x (* x x)) (* (* x (* x x)) 1/13824))) (/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2)))))
(/ 1 (+ 1/4 (* (* 1/24 (* x x)) (- (* 1/24 (* x x)) 1/2))))
(* x (/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))))
(/ (- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2))) (- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2)))
(- (* x (* (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320)))) (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))))) (* (+ (* 1/24 (* x x)) 1/2) (+ (* 1/24 (* x x)) 1/2)))
(- (* x (* x (* (* x x) (+ 1/240 (* (* x x) 17/40320))))) (+ (* 1/24 (* x x)) 1/2))
(* (* x (* x x)) 1/13824)
(* 1/24 (* x x))

Outputs
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(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))))) (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))))) #s(literal 1/8 binary64))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64))) (neg.f64 (+.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) (.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) (+.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))) (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))))) #s(literal -1 binary64))
(.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) (+.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))))
(.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))) (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/24 binary64))) #s(literal 3 binary64)))
(pow.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 3 binary64))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/13824 binary64)))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/13824 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824 binary64))
(.f64 #s(literal 1/13824 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/24 binary64))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/13824 binary64)) x)
(.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (*.f64 x #s(literal 1/24 binary64)))
(.f64 (.f64 #s(literal 1/13824 binary64) x) (*.f64 x x))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/24 binary64)) x)

simplify222.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2918×	`-lowering-.f32`
2918×	`-lowering-.f64`
2086×	`sum3-define`
1862×	`+-lowering-+.f64`
1862×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1274
1	443	1093
2	1285	1081
3	3549	1065
4	6935	1065
0	8393	1065

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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))))))))
(* 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)))))))
1/2
(+ 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)))))
4
(+ 4 (* 1/3 (pow x 2)))
(+ 4 (* (pow x 2) (+ 1/3 (* -1/432 (pow x 4)))))
(+ 4 (* (pow x 2) (+ 1/3 (* (pow x 4) (- (* -1/5184 (pow x 2)) 1/432)))))
(/ 576 (pow x 4))
(/ (+ 576 (* 6912 (/ 1 (pow x 2)))) (pow x 4))
(/ (- (+ 576 (* 6912 (/ 1 (pow x 2)))) (/ 995328 (pow x 6))) (pow x 4))
(/ (+ 576 (+ (* -1 (/ (+ 995328 (* 11943936 (/ 1 (pow x 2)))) (pow x 6))) (* 6912 (/ 1 (pow x 2))))) (pow x 4))
(/ 576 (pow x 4))
(/ (+ 576 (* 6912 (/ 1 (pow x 2)))) (pow x 4))
(/ (- (+ 576 (* 6912 (/ 1 (pow x 2)))) (/ 995328 (pow x 6))) (pow x 4))
(/ (+ 576 (+ (* -1 (/ (+ 995328 (* 11943936 (/ 1 (pow x 2)))) (pow x 6))) (* 6912 (/ 1 (pow x 2))))) (pow x 4))
(* 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)))))))
-1/4
(- (* -1/24 (pow x 2)) 1/4)
(- (* (pow x 2) (- (* -1/576 (pow x 2)) 1/24)) 1/4)
(- (* (pow x 2) (- (* (pow x 2) (- (* 1/57600 (pow x 4)) 1/576)) 1/24)) 1/4)
(* 289/1625702400 (pow x 12))
(* (pow x 12) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))
(* (pow x 12) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(* (pow x 12) (- (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))) (* 1/576 (/ 1 (pow x 8)))))
(* 289/1625702400 (pow x 12))
(* (pow x 12) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))
(* (pow x 12) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(* (pow x 12) (- (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))) (* 1/576 (/ 1 (pow x 8)))))
-1/2
(- (* -1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* 1/240 (pow x 2)) 1/24)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))) 1/24)) 1/2)
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))) (/ 1/24 (pow x 4))))
(* (pow x 6) (+ 17/40320 (+ (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (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 (* 1/240 (/ 1 (pow x 2)))) (/ 1/24 (pow x 4))))
(* (pow x 6) (+ 17/40320 (+ (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (* 1/240 (/ 1 (pow x 2))))))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/13824 (pow x 3))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
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(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 17/40320 binary64) (-.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 6) (+ 17/40320 (+ (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 17/40320 binary64) (/.f64 #s(literal 1/240 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/13824 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/13824 binary64))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))

eval91.0ms (1%)

Compiler: Compiled 59213 to 1812 computations (96.9% saved)

prune89.0ms (1%)

Pruning

15 alts after pruning (4 fresh and 11 done)

	Pruned	Kept	Total
New	568	4	572
Fresh	0	0	0
Picked	2	0	2
Done	0	11	11
Total	570	15	585

Accuracy

100.0%

Counts

585 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	54.0%	(/.f64 x #s(literal 2 binary64))
✓	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
✓	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
✓	53.9%	(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
	52.5%	(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
	53.4%	(.f64 x (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
	53.4%	(.f64 x (/.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
	53.0%	(.f64 x (/.f64 #s(literal -1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
✓	53.9%	(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
✓	53.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
✓	53.8%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	8.3%	#s(literal 1 binary64)

Compiler

Compiled 774 to 272 computations (64.9% saved)

regimes35.0ms (0.4%)

Counts

19 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 x #s(literal 2 binary64))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(.f64 x (/.f64 #s(literal -1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (/.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (+.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(.f64 x (/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) #s(literal 1/4 binary64)) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) #s(literal 1/2 binary64))))
(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

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

Calls

2 calls:

26.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
6.0ms	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%)

Counts

17 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 x #s(literal 2 binary64))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(.f64 x (/.f64 #s(literal -1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (/.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (+.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(.f64 x (/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) #s(literal 1/4 binary64)) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))))) #s(literal 1/2 binary64))))
(.f64 x (/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))))) (.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs

(*.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x (+.f64 #s(literal -1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/240 binary64) (*.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))

#s(literal 1 binary64)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
58.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Counts

11 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 x #s(literal 2 binary64))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
(.f64 x (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(.f64 x (/.f64 #s(literal -1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))

Outputs

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

#s(literal 1 binary64)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
58.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

7 → 2

Calls

Call 1

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

Outputs

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

regimes21.0ms (0.2%)

Counts

6 → 2

Calls

Call 1

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

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

regimes9.0ms (0.1%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
58.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 2

Calls

Call 1

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

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

regimes2.0ms (0%)

Counts

3 → 2

Calls

Call 1

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

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

regimes2.0ms (0%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
57.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

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

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
8.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.6772715680681682	44102.630972932144

Results

14.0ms

128×

valid

Compiler

Compiled 364 to 233 computations (36% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-cos: 5.0ms (45.8% of total)

ival-sin: 4.0ms (36.6% of total)

ival-sub: 1.0ms (9.2% of total)

ival-div: 1.0ms (9.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.6772715680681682	44102.630972932144

Results

15.0ms

128×

valid

Compiler

Compiled 236 to 161 computations (31.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-cos: 6.0ms (50.9% of total)

ival-sin: 4.0ms (33.9% of total)

ival-sub: 1.0ms (8.5% of total)

ival-div: 1.0ms (8.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch18.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	0.6772715680681682	44102.630972932144

Results

13.0ms

128×

valid

Compiler

Compiled 220 to 145 computations (34.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-cos: 4.0ms (41.4% of total)

ival-sin: 4.0ms (41.4% of total)

ival-sub: 1.0ms (10.4% of total)

ival-div: 1.0ms (10.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.6772715680681682	44102.630972932144

Results

15.0ms

128×

valid

Compiler

Compiled 188 to 137 computations (27.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-cos: 6.0ms (51.1% of total)

ival-sin: 4.0ms (34% of total)

ival-sub: 1.0ms (8.5% of total)

ival-div: 1.0ms (8.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch40.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
39.0ms	0.6772715680681682	44102.630972932144

Results

35.0ms

128×

valid

Compiler

Compiled 172 to 129 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-cos: 4.0ms (41% of total)

ival-sin: 4.0ms (41% of total)

ival-sub: 1.0ms (10.3% of total)

ival-div: 1.0ms (10.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch18.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	0.6772715680681682	44102.630972932144

Results

13.0ms

128×

valid

Compiler

Compiled 140 to 105 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-cos: 4.0ms (41.5% of total)

ival-sin: 4.0ms (41.5% of total)

ival-sub: 1.0ms (10.4% of total)

ival-div: 1.0ms (10.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch26.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
25.0ms	0.6772715680681682	44102.630972932144

Results

21.0ms

128×

valid

Compiler

Compiled 124 to 97 computations (21.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-cos: 12.0ms (67.1% of total)

ival-sin: 4.0ms (22.4% of total)

ival-sub: 1.0ms (5.6% of total)

ival-div: 1.0ms (5.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.6772715680681682	44102.630972932144

Results

15.0ms

128×

valid

Compiler

Compiled 76 to 65 computations (14.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-cos: 4.0ms (41.2% of total)

ival-sin: 4.0ms (41.2% of total)

ival-sub: 1.0ms (10.3% of total)

ival-div: 1.0ms (10.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

64×	`*-commutative_binary64`
40×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	183
1	110	183
2	118	183
3	132	183
4	144	183
5	152	183
6	156	183
7	157	183

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(if (<=.f64 x #s(literal 1800 binary64)) (.f64 x (/.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(if (<=.f64 x #s(literal 1800 binary64)) (.f64 x (/.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 1800 binary64)) (.f64 x (/.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/576 binary64))))) #s(literal -1/4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) #s(literal 17/40320 binary64)))))) (+.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64)))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))) #s(literal 1/24 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.8s (19.8%)

Rules

4784×	`-lowering-.f32`
4784×	`-lowering-.f64`
4136×	`-lowering-.f32`
4136×	`-lowering-.f64`
3938×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	180
1	199	152
2	2003	148
0	8146	148
0	82	436
1	239	378
2	689	375
3	2205	375
4	3765	375
5	6141	375
6	6753	375
0	8098	375
0	9	19
1	47	19
2	275	19
3	2591	17
0	11834	17
0	28	133
1	175	116
2	1483	116
0	8157	116
0	6	4
1	16	4
2	23	4
3	35	4
4	59	4
5	90	4
6	152	4
7	264	4
8	633	4
9	1210	4
10	1691	4
11	1714	4
12	1722	4
13	1728	4
14	1736	4
15	1749	4
16	1757	4
17	1766	4
18	1767	4
0	1767	4
0	152	1274
1	443	1093
2	1285	1081
3	3549	1065
4	6935	1065
0	8393	1065

Stop Event

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

Compiler

Compiled 535 to 310 computations (42.1% saved)

preprocess93.0ms (1%)

Remove: (negabs x)
Compiler: Compiled 414 to 168 computations (59.4% saved)

analyze181.0ms (2%)

sample1.9s (21.1%)

preprocess84.0ms (0.9%)

explain163.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify51.0ms (0.6%)

localize85.0ms (0.9%)

series5.0ms (0.1%)

rewrite492.0ms (5.4%)

simplify453.0ms (5%)

eval141.0ms (1.6%)

prune94.0ms (1%)

simplify58.0ms (0.6%)

localize138.0ms (1.5%)

series10.0ms (0.1%)

rewrite330.0ms (3.6%)

simplify210.0ms (2.3%)

eval82.0ms (0.9%)

prune90.0ms (1%)

simplify90.0ms (1%)

localize169.0ms (1.9%)

series8.0ms (0.1%)

rewrite370.0ms (4.1%)

simplify264.0ms (2.9%)

eval118.0ms (1.3%)

prune83.0ms (0.9%)

simplify195.0ms (2.1%)

localize184.0ms (2%)

series10.0ms (0.1%)

rewrite447.0ms (4.9%)

simplify222.0ms (2.4%)

eval91.0ms (1%)

prune89.0ms (1%)

regimes35.0ms (0.4%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes21.0ms (0.2%)

regimes9.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch20.0ms (0.2%)

bsearch20.0ms (0.2%)

bsearch18.0ms (0.2%)

bsearch20.0ms (0.2%)

bsearch40.0ms (0.4%)

bsearch18.0ms (0.2%)

bsearch26.0ms (0.3%)

bsearch20.0ms (0.2%)

simplify13.0ms (0.1%)

soundness1.8s (19.8%)

preprocess93.0ms (1%)

end0.0ms (0%)

Profiling