Metrics for tanhf (example 3.4)

analyze325.0ms (2.4%)

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: 133.0ms

ival-sin: 50.0ms (37.7% of total)

ival-cos: 35.0ms (26.4% of total)

ival-sub: 26.0ms (19.6% of total)

ival-div: 16.0ms (12.1% of total)

const: 4.0ms (3% of total)

backward-pass: 1.0ms (0.8% of total)

sample3.3s (24.3%)

Results

1.3s	2020×	2	valid
946.0ms	4204×	0	valid
548.0ms	2027×	1	valid
6.0ms	5×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 2.3s

ival-cos: 1.2s (54.1% of total)

ival-sin: 448.0ms (19.9% of total)

ival-div: 231.0ms (10.2% of total)

ival-sub: 191.0ms (8.5% of total)

backward-pass: 140.0ms (6.2% of total)

const: 27.0ms (1.2% of total)

Bogosity

preprocess173.0ms (1.3%)

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)

explain308.0ms (2.3%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
76	4	(5.814228013462073e-162)	3	(14996467.76855129)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
64	0	-	3	(7.253667169366791e-159)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`

Results

99.0ms	126×	2	valid
70.0ms	260×	0	valid
59.0ms	126×	1	valid

Compiler

Compiled 46 to 20 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 156.0ms

ival-cos: 91.0ms (58.3% of total)

ival-sin: 26.0ms (16.6% of total)

ival-div: 14.0ms (9% of total)

backward-pass: 12.0ms (7.7% of total)

ival-sub: 11.0ms (7% of total)

const: 2.0ms (1.3% of total)

eval1.0ms (0%)

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

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Rules

2×	`/-lowering-/.f32`
2×	`tan-lowering-tan.f32`
2×	`/-lowering-/.f64`
2×	`tan-lowering-tan.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	4	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(tan (/ x 2))
(/ x 2)
x
2

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)

localize53.0ms (0.4%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Results

42.0ms

256×

valid

Compiler

Compiled 11 to 5 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-tan: 11.0ms (70.4% of total)

ival-div: 4.0ms (25.6% of total)

const: 1.0ms (6.4% of total)

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

series7.0ms (0.1%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (tan (/ x 2))>
#<alt (/ x 2)>

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)>

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ x 2)
2.0ms	x	@	inf	(tan (/ x 2))
1.0ms	x	@	-inf	(tan (/ x 2))
1.0ms	x	@	0	(tan (/ x 2))
1.0ms	x	@	-inf	(/ x 2)

rewrite508.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2784×	`-lowering-.f32`
2784×	`-lowering-.f64`
2350×	`/-lowering-/.f32`
2350×	`/-lowering-/.f64`
1558×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	17	7
2	50	7
3	192	7
4	905	7
0	8152	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 326

Calls

Call 1

Inputs
(tan (/ x 2))
(/ x 2)

Outputs
(+.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (+.f64 #s(literal 0 binary64) (sin.f64 x)) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (+.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))))
(/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))))
(/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (sin.f64 x) #s(literal 0 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (+.f64 (tan.f64 #s(literal 0 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 #s(literal 0 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) #s(literal -1 binary64)) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) #s(literal -1 binary64)) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (sin.f64 x))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (*.f64 (+.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))))
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(/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) x)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(.f64 x (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -1 binary64))
(.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (*.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -2 binary64)))
(.f64 (.f64 x x) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -2 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))
(*.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (/.f64 x #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)) (/.f64 #s(literal 4 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (/.f64 #s(literal 2 binary64) x))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(*.f64 (pow.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (pow.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))
(.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (pow.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) x)
(.f64 (.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (/.f64 x #s(literal 2 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) x))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x x)) x)

simplify146.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1708×	`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	26	156
1	73	150
2	232	150
3	651	150
4	1240	150
5	1665	150
6	1823	150
7	1824	150
0	1824	150

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

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)

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

eval106.0ms (0.8%)

Compiler: Compiled 4560 to 895 computations (80.4% saved)

prune97.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	346	4	350
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	346	5	351

Accuracy

100.0%

Counts

351 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(.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))))))))
▶	51.9%	(.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))))))
▶	51.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
▶	51.7%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 57 to 37 computations (35.1% saved)

simplify392.0ms (2.9%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

1744×	`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	22	191
1	80	171
2	277	171
3	704	171
4	1263	171
5	1689	171
6	1848	171
7	1849	171
0	1849	171

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize324.0ms (2.4%)

Localize:

Found 13 expressions of interest:

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

Results

234.0ms

256×

valid

Compiler

Compiled 193 to 23 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-mult: 106.0ms (73.7% of total)

...c/correct-round.rkt:119:19: 19.0ms (13.2% of total)

ival-add: 17.0ms (11.8% of total)

const: 1.0ms (0.7% of total)

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

series30.0ms (0.2%)

Counts

15 → 180

Calls

Call 1

Inputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (* x x))))>
#<alt (+ 1/2 (* 1/24 (* x x)))>
#<alt (* 1/24 (* x x))>
#<alt (* x x)>
#<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 (+ 1/2 (* (* 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) 1/240)>
#<alt (+ 1/24 (* (* 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 (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt 1/2>
#<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 (* 1/2 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 (* 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 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 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

45 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(* (* x x) (+ 1/240 (* (* x x) 17/40320)))
4.0ms	x	@	inf	(* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240)))))
2.0ms	x	@	-inf	(* x (+ 1/2 (* 1/24 (* x x))))
1.0ms	x	@	inf	(* x (+ 1/2 (* 1/24 (* x x))))
1.0ms	x	@	0	(* x (+ 1/2 (* 1/24 (* x x))))

rewrite863.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4102×	`-lowering-.f32`
4102×	`-lowering-.f64`
2910×	`/-lowering-/.f32`
2910×	`/-lowering-/.f64`
2156×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	151
1	155	134
2	1442	134
0	8142	134

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 338

Calls

Call 1

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

Outputs
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.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 #s(literal 1/2 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) x (.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 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (-.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 #s(literal 1/2 binary64) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.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 #s(literal 1/2 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 #s(literal -1/24 binary64) (*.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 #s(literal -1/24 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (-.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 #s(literal 1/2 binary64) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.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 #s(literal 1/2 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 #s(literal -1/24 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x 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 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) x)) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/13824 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.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 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (*.f64 #s(literal 1/2 binary64) x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))) x)
(+.f64 #s(literal 1/2 binary64) (.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 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/24 binary64)) x #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/48 binary64) (.f64 x x)))))
(/.f64 (-.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 #s(literal -1/24 binary64) (.f64 x x))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/48 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.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 #s(literal -1/24 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64)) (-.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/64 binary64) (-.f64 (.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 #s(literal 1/110592 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x 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 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/16 binary64) (+.f64 (.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x 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 #s(literal -1/24 binary64) (*.f64 x x)))))
(/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.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 #s(literal -1/24 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))) (neg.f64 (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 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
(pow.f64 (/.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 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.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 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 (.f64 x #s(literal 1/24 binary64)) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))))
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(-.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64))))) (-.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 17/40320 binary64)))))))
(fma.f64 x (.f64 x #s(literal 1/240 binary64)) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 17/40320 binary64)))))
(fma.f64 x (.f64 x (.f64 x (.f64 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 (.f64 x x) (.f64 x (*.f64 x #s(literal 17/40320 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 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 (.f64 x x) (.f64 x (*.f64 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 x (.f64 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 (.f64 x x) (.f64 x (*.f64 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))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))
(fma.f64 (.f64 (.f64 x (.f64 x #s(literal 17/40320 binary64))) x) x (.f64 x (*.f64 x #s(literal 1/240 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824000 binary64) (.f64 x (.f64 x x)))) (.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 x) (.f64 x x))))) (+.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64))))) (.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64))))))))
(/.f64 (-.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))))) (-.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 17/40320 binary64))))))
(/.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))))) (+.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x (.f64 x #s(literal 17/40320 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 17/40320 binary64))) #s(literal 1/240 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)))) (+.f64 #s(literal 1/240 binary64) (.f64 #s(literal -17/40320 binary64) (.f64 x x))))
(/.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 x (.f64 x #s(literal 17/40320 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 17/40320 binary64))) #s(literal 1/240 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64))) (.f64 x x)) (+.f64 #s(literal 1/240 binary64) (.f64 #s(literal -17/40320 binary64) (.f64 x x))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824000 binary64) (.f64 x (.f64 x x)))) (.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 x) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64))))) (.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64))))))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) (.f64 (.f64 x x) (.f64 x (*.f64 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 x (.f64 x #s(literal 17/40320 binary64))) (-.f64 (.f64 x (*.f64 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 x) (.f64 x x)) #s(literal 289/1625702400 binary64))))) (neg.f64 (+.f64 #s(literal 1/240 binary64) (.f64 #s(literal -17/40320 binary64) (.f64 x x)))))
(/.f64 (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 x (.f64 x #s(literal 17/40320 binary64))) (-.f64 (.f64 x (*.f64 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 x) (.f64 x x)) #s(literal 289/1625702400 binary64))) (.f64 x x))) (neg.f64 (+.f64 #s(literal 1/240 binary64) (.f64 #s(literal -17/40320 binary64) (.f64 x x)))))
(/.f64 (+.f64 (.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 x) (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/13824000 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64))))) (-.f64 (.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 x (.f64 x #s(literal 1/240 binary64)))))))
(.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64)))))
(.f64 (+.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64))))) x)

simplify488.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

2670×	`-lowering-.f32`
2670×	`-lowering-.f64`
1700×	`fnmadd-define`
1390×	`fma-lowering-fma.f32`
1390×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1452
1	300	1367
2	928	1362
3	2756	1338
4	5675	1338
0	8059	1338

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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

eval199.0ms (1.5%)

Compiler: Compiled 19043 to 1508 computations (92.1% saved)

prune140.0ms (1%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	606	2	608
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	606	7	613

Accuracy

100.0%

Counts

613 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.9%	(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 #s(literal 1/2 binary64) x))
▶	51.9%	(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
✓	52.0%	(.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))))))))
✓	51.9%	(.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))))))
✓	51.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
✓	51.7%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 87 to 57 computations (34.5% saved)

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
✓	cost-diff	128	(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 #s(literal 1/2 binary64) x))
✓	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 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
✓	cost-diff	128	(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))

Rules

296×	`fma-define`
232×	`fma-lowering-fma.f32`
232×	`fma-lowering-fma.f64`
144×	`-lowering-.f32`
144×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	94
1	41	88
2	113	82
3	241	82
4	340	82
5	366	82
6	367	82
0	367	82

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize183.0ms (1.3%)

Localize:

Found 8 expressions of interest:

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

Results

126.0ms

256×

valid

Compiler

Compiled 98 to 17 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 39.0ms (55.6% of total)

...c/correct-round.rkt:119:19: 22.0ms (31.4% of total)

ival-add: 9.0ms (12.8% of total)

const: 1.0ms (1.4% of total)

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

series13.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

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

30 calls:

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

rewrite639.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

5260×	`-lowering-.f32`
5260×	`-lowering-.f64`
1962×	`/-lowering-/.f32`
1962×	`/-lowering-/.f64`
1702×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	74
1	80	63
2	712	63
0	9105	63

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 203

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(+.f64 (/.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))) (/.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64)))))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8 binary64)))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8 binary64))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/576 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64))))))
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(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(+.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 x #s(literal 1/24 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)))) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))))
(fma.f64 x #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64))) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/240 binary64)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x #s(literal 1/240 binary64)) (.f64 x x) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) x (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/240 binary64) (*.f64 x #s(literal 1/24 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))) (.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64))))) (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 x (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/57600 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64))))) (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/57600 binary64))) x)))
(/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (*.f64 x #s(literal 1/24 binary64))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)))) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 x #s(literal 1/24 binary64))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64))) x) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))))) (neg.f64 (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64))) x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (*.f64 x #s(literal 1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)))) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 x #s(literal 1/24 binary64))))
(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))) x)
(.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))) x))
(.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))) x))
(.f64 (.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/240 binary64)))) (.f64 x #s(literal 1/24 binary64)))))))
(.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))))
(.f64 (.f64 x (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))))
(.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 #s(literal 1/13824000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))))
(.f64 (.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/57600 binary64))) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64))))))
(.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)

simplify452.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

2544×	`-lowering-.f32`
2544×	`-lowering-.f64`
1974×	`fma-define`
1784×	`fma-lowering-fma.f32`
1784×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	724
1	144	693
2	395	693
3	932	693
4	1917	682
5	4208	682
0	8206	682

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 (* 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))
(* 1/24 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)))
(* 1/24 (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 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 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)))))
(* 1/240 (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 (* 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 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 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))
(* 1/24 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 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 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 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))))
(* 1/240 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.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 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 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 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))))
(* 1/240 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.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 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 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 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* 1/240 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* 1/240 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/24 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)))))
(* 1/240 (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)))
(* 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))

eval96.0ms (0.7%)

Compiler: Compiled 10144 to 660 computations (93.5% saved)

prune82.0ms (0.6%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	322	8	330

Accuracy

100.0%

Counts

330 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
✓	51.9%	(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 #s(literal 1/2 binary64) x))
✓	51.9%	(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
✓	52.0%	(.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))))))))
✓	51.9%	(.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))))))
✓	51.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
✓	51.7%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 101 to 67 computations (33.7% saved)

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

104×	`-lowering-.f32`
104×	`-lowering-.f64`
82×	`/-lowering-/.f32`
82×	`/-lowering-/.f64`
52×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	30	43
2	76	43
3	134	43
4	172	43
5	218	43
6	229	43
7	231	43
0	231	43

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (/ 1 (* x (+ (* 1/24 (* x x)) 1/2))))
1
(/ 1 (* x (+ (* 1/24 (* x x)) 1/2)))
(* x (+ (* 1/24 (* x x)) 1/2))
x
(+ (* 1/24 (* x x)) 1/2)
(* 1/24 (* x x))
1/24
(* x x)
1/2

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

localize98.0ms (0.7%)

Localize:

Found 4 expressions of interest:

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

Results

65.0ms

256×

valid

Compiler

Compiled 54 to 11 computations (79.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 15.0ms (44.4% of total)

ival-div: 8.0ms (23.7% of total)

...c/correct-round.rkt:119:19: 7.0ms (20.7% of total)

ival-add: 3.0ms (8.9% of total)

const: 1.0ms (3% of total)

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

series4.0ms (0%)

Counts

5 → 60

Calls

Call 1

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

Outputs
#<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 (/ 2 x)>
#<alt (/ (+ 2 (* -1/6 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* 1/72 (pow x 2)) 1/6))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/72 (* -1/864 (pow x 2)))) 1/6))) x)>
#<alt (/ 24 (pow x 3))>
#<alt (/ (- 24 (* 288 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 24 (/ 3456 (pow x 4))) (* 288 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 24 (/ 3456 (pow x 4))) (+ (* 288 (/ 1 (pow x 2))) (* 41472 (/ 1 (pow x 6))))) (pow x 3))>
#<alt (/ 24 (pow x 3))>
#<alt (* -1 (/ (- (* 288 (/ 1 (pow x 2))) 24) (pow x 3)))>
#<alt (* -1 (/ (- (* 288 (/ 1 (pow x 2))) (+ 24 (/ 3456 (pow x 4)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* 288 (/ 1 (pow x 2))) (* 41472 (/ 1 (pow x 6)))) (+ 24 (/ 3456 (pow x 4)))) (pow x 3)))>
#<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))>

Calls

15 calls:

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

rewrite801.0ms (5.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3080×	`-lowering-.f32`
3080×	`-lowering-.f64`
2346×	`/-lowering-/.f32`
2346×	`/-lowering-/.f64`
1326×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	61	36
2	380	36
3	3046	36
0	8456	36

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 621

Calls

Call 1

Inputs
(/ 1 (/ 1 (* x (+ (* 1/24 (* x x)) 1/2))))
(/ 1 (* x (+ (* 1/24 (* x x)) 1/2)))
(* x (+ (* 1/24 (* x x)) 1/2))
(+ (* 1/24 (* x x)) 1/2)
(* 1/24 (* x x))

Outputs
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (neg.f64 (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64)) #s(literal -1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (log.f64 (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))))) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1/576 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/576 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
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(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal 1/2641807540224 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64)) (/.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))))))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal -1/110592 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64))) #s(literal -1/64 binary64)) (/.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))))))) (neg.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64))) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (neg.f64 (+.f64 (.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2304 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/576 binary64)))) #s(literal 1/4 binary64))))
(pow.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/576 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.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)) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (/.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))))))
(.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (/.f64 (/.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))))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 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)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 (/.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))))) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/576 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))) (/.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))))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64))) (+.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/191102976 binary64))) (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64))))))) (+.f64 (.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (-.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (.f64 (+.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 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)) (.f64 x (.f64 x #s(literal 1/48 binary64)))))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)) (.f64 x (.f64 x #s(literal 1/48 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal -1/4 binary64)) (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64))))))
(exp.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64)))) #s(literal 1 binary64)))
(pow.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(.f64 x (exp.f64 (log.f64 (.f64 x #s(literal 1/24 binary64)))))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/24 binary64))))
(.f64 (.f64 x #s(literal 1/24 binary64)) x)
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal 1/24 binary64)))) x)
(.f64 (exp.f64 (log.f64 #s(literal 1/24 binary64))) (.f64 x x))

simplify489.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

2024×	`fma-lowering-fma.f32`
2024×	`fma-lowering-fma.f64`
1656×	`-lowering-.f32`
1656×	`-lowering-.f64`
1606×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	480
1	184	445
2	546	443
3	1615	443
4	4796	443
0	8379	443

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 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)))))
(/ 2 x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* 1/72 (pow x 2)) 1/6))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/72 (* -1/864 (pow x 2)))) 1/6))) x)
(/ 24 (pow x 3))
(/ (- 24 (* 288 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 24 (/ 3456 (pow x 4))) (* 288 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 24 (/ 3456 (pow x 4))) (+ (* 288 (/ 1 (pow x 2))) (* 41472 (/ 1 (pow x 6))))) (pow x 3))
(/ 24 (pow x 3))
(* -1 (/ (- (* 288 (/ 1 (pow x 2))) 24) (pow x 3)))
(* -1 (/ (- (* 288 (/ 1 (pow x 2))) (+ 24 (/ 3456 (pow x 4)))) (pow x 3)))
(* -1 (/ (- (+ (* 288 (/ 1 (pow x 2))) (* 41472 (/ 1 (pow x 6)))) (+ 24 (/ 3456 (pow x 4)))) (pow x 3)))
(* 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))

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 (* 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 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x)
(/ (+ 2 (* (pow x 2) (- (* 1/72 (pow x 2)) 1/6))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/72 binary64))))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/72 (* -1/864 (pow x 2)))) 1/6))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/72 binary64) (.f64 x (.f64 x #s(literal -1/864 binary64)))))))) x)
(/ 24 (pow x 3))
(/.f64 #s(literal 24 binary64) (.f64 x (.f64 x x)))
(/ (- 24 (* 288 (/ 1 (pow x 2)))) (pow x 3))
(/.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal -288 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(/ (- (+ 24 (/ 3456 (pow x 4))) (* 288 (/ 1 (pow x 2)))) (pow x 3))
(/.f64 (+.f64 #s(literal 24 binary64) (+.f64 (/.f64 (/.f64 #s(literal 3456 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal -288 binary64) (.f64 x x)))) (.f64 x (*.f64 x x)))
(/ (- (+ 24 (/ 3456 (pow x 4))) (+ (* 288 (/ 1 (pow x 2))) (* 41472 (/ 1 (pow x 6))))) (pow x 3))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 3456 binary64) x) (.f64 x (.f64 x x))) (-.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal -288 binary64) (.f64 x x))) (/.f64 #s(literal 41472 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x (*.f64 x x)))
(/ 24 (pow x 3))
(/.f64 #s(literal 24 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (- (* 288 (/ 1 (pow x 2))) 24) (pow x 3)))
(/.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal -288 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(* -1 (/ (- (* 288 (/ 1 (pow x 2))) (+ 24 (/ 3456 (pow x 4)))) (pow x 3)))
(/.f64 (+.f64 #s(literal 24 binary64) (+.f64 (/.f64 (/.f64 #s(literal 3456 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal -288 binary64) (.f64 x x)))) (.f64 x (*.f64 x x)))
(* -1 (/ (- (+ (* 288 (/ 1 (pow x 2))) (* 41472 (/ 1 (pow x 6)))) (+ 24 (/ 3456 (pow x 4)))) (pow x 3)))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 3456 binary64) x) (.f64 x (.f64 x x))) (-.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal -288 binary64) (.f64 x x))) (/.f64 #s(literal 41472 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x (*.f64 x 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 x (*.f64 x #s(literal 1/24 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 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(+ 1/2 (* 1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(+ 1/2 (* 1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))

eval247.0ms (1.8%)

Compiler: Compiled 20913 to 1936 computations (90.7% saved)

prune204.0ms (1.5%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	679	2	681
Fresh	0	0	0
Picked	1	0	1
Done	1	6	7
Total	681	8	689

Accuracy

100.0%

Counts

689 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x))
	51.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	51.9%	(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 #s(literal 1/2 binary64) x))
✓	52.0%	(.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))))))))
✓	51.9%	(.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))))))
✓	51.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
✓	51.7%	(*.f64 #s(literal 1/2 binary64) x)
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 210 to 114 computations (45.7% saved)

regimes14.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.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))))))
(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 #s(literal 1/2 binary64) x))
(.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))))))))
(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:

6.0ms	(/.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)

regimes15.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(.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))))))
(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal 1/240 binary64)))))) (.f64 #s(literal 1/2 binary64) x))
(.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
52.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
51.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
51.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
51.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	34	38

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(*.f64 #s(literal 1/2 binary64) x)

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x #s(literal 1/2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))

soundness2.5s (18.5%)

Rules

5260×	`-lowering-.f32`
5260×	`-lowering-.f64`
4102×	`-lowering-.f32`
4102×	`-lowering-.f64`
2910×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	151
1	155	134
2	1442	134
0	8142	134
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	16	74
1	80	63
2	712	63
0	9105	63
0	26	156
1	73	150
2	232	150
3	651	150
4	1240	150
5	1665	150
6	1823	150
7	1824	150
0	1824	150
0	69	480
1	184	445
2	546	443
3	1615	443
4	4796	443
0	8379	443

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×	saturated
1×	iter limit
1×	node limit

Compiler

Compiled 135 to 91 computations (32.6% saved)

preprocess157.0ms (1.2%)

Remove: (negabs x)
Compiler: Compiled 154 to 102 computations (33.8% saved)

analyze325.0ms (2.4%)

sample3.3s (24.3%)

preprocess173.0ms (1.3%)

explain308.0ms (2.3%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify6.0ms (0%)

localize53.0ms (0.4%)

series7.0ms (0.1%)

rewrite508.0ms (3.8%)

simplify146.0ms (1.1%)

eval106.0ms (0.8%)

prune97.0ms (0.7%)

simplify392.0ms (2.9%)

localize324.0ms (2.4%)

series30.0ms (0.2%)

rewrite863.0ms (6.4%)

simplify488.0ms (3.6%)

eval199.0ms (1.5%)

prune140.0ms (1%)

simplify36.0ms (0.3%)

localize183.0ms (1.3%)

series13.0ms (0.1%)

rewrite639.0ms (4.7%)

simplify452.0ms (3.3%)

eval96.0ms (0.7%)

prune82.0ms (0.6%)

simplify25.0ms (0.2%)

localize98.0ms (0.7%)

series4.0ms (0%)

rewrite801.0ms (5.9%)

simplify489.0ms (3.6%)

eval247.0ms (1.8%)

prune204.0ms (1.5%)

regimes14.0ms (0.1%)

regimes15.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify16.0ms (0.1%)

soundness2.5s (18.5%)

preprocess157.0ms (1.2%)

end0.0ms (0%)

Profiling