Metrics for expm1 (example 3.7)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

Precisions

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

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

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

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

const: 0.0ms (0% of total)

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

ival-<=: 0.0ms (0% of total)

sample1.7s (26.7%)

Results

1.5s	8058×	1	valid
10.0ms	198×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-exp: 643.0ms (62.1% of total)

ival-<=: 133.0ms (12.8% of total)

ival-sub: 108.0ms (10.4% of total)

backward-pass: 81.0ms (7.8% of total)

ival-fabs: 61.0ms (5.9% of total)

const: 12.0ms (1.2% of total)

Bogosity

preprocess17.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

60×	`sum3-define`
58×	`fmsub-define`
30×	`fmm-def`
28×	`fma-define`
28×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (exp x) 1)

Outputs
(- (exp x) 1)
(expm1.f64 x)

Call 2

Inputs
(- (exp x) 1)
(- (exp (neg x)) 1)
(neg (- (exp (neg x)) 1))

Outputs
(- (exp x) 1)
(expm1 x)
(- (exp (neg x)) 1)
(expm1 (neg x))
(neg (- (exp (neg x)) 1))
(neg (expm1 (neg x)))

explain123.0ms (1.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
255	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`x`
0	-	-	`(exp.f64 x)`
0	-	-	`#s(literal 1 binary64)`

Results

96.0ms	504×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 25 to 14 computations (44% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-exp: 37.0ms (56.2% of total)

ival-sub: 22.0ms (33.4% of total)

backward-pass: 6.0ms (9.1% of total)

const: 1.0ms (1.5% of total)

eval0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(expm1.f64 x)

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(expm1.f64 x)

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`exp-lowering-exp.f32`
2×	`expm1-lowering-expm1.f32`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3
1	10	3
2	11	3
0	11	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (exp x) 1)
x

Outputs
(- (exp x) 1)
(expm1.f64 x)
x

localize42.0ms (0.7%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(expm1.f64 x)

Results

36.0ms	252×	5	exit
0.0ms	4×	0	valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

backward-pass: 4.0ms (31.9% of total)

compiled-spec: 4.0ms (31.9% of total)

ival-exp: 2.0ms (16% of total)

ival-sub: 2.0ms (16% of total)

const: 0.0ms (0% of total)

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (- (exp x) 1)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(- (exp x) 1)
0.0ms	x	@	-inf	(- (exp x) 1)
0.0ms	x	@	inf	(- (exp x) 1)

rewrite101.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

574×	`/-lowering-/.f32`
574×	`/-lowering-/.f64`
536×	`-lowering-.f32`
536×	`-lowering-.f64`
284×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	2
1	23	2
2	134	2
0	1209	2

Stop Event

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

Counts

1 → 69

Calls

Call 1

Inputs
(- (exp x) 1)

Outputs
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))))
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))))
(-.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64))))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(expm1.f64 x)
(neg.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))))
(neg.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))
(/.f64 (expm1.f64 x) #s(literal 1 binary64))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (*.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))) (-.f64 #s(literal -1 binary64) (exp.f64 x)))
(/.f64 (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64)) (.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))))
(/.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) (.f64 (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))) (+.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) (+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)))))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))
(/.f64 (.f64 (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (expm1.f64 x))
(.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))))
(.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64))))))
(.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (.f64 (expm1.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))))
(.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (expm1.f64 (*.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 x))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (exp.f64 x)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1430×	`fma-define`
1068×	`fma-lowering-fma.f32`
1068×	`fma-lowering-fma.f64`
336×	`-lowering-.f32`
336×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	72	44
2	190	41
3	465	41
4	978	41
5	1401	41
6	1557	41
7	1559	41
0	1559	41

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)

eval10.0ms (0.1%)

Compiler: Compiled 1522 to 213 computations (86% saved)

prune30.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Accuracy

100.0%

Counts

82 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
▶	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	99.5%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	100.0%	(expm1.f64 x)
▶	98.6%	x

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))

Rules

1430×	`fma-define`
1068×	`fma-lowering-fma.f32`
1068×	`fma-lowering-fma.f64`
336×	`-lowering-.f32`
336×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	126
1	66	106
2	184	103
3	457	103
4	967	103
5	1391	103
6	1552	103
7	1554	103
0	1554	103

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* x (+ 1 (* x 1/2)))
x
(+ 1 (* x 1/2))
1
(* x 1/2)
1/2
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
1
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))
x
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))
1
(* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
1/2
(* x (+ 1/6 (* x 1/24)))
(+ 1/6 (* x 1/24))
1/6
(* x 1/24)
1/24

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

localize96.0ms (1.5%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))

Results

66.0ms

256×

valid

Compiler

Compiled 128 to 21 computations (83.6% saved)

Precisions

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

ival-mult: 18.0ms (52.8% of total)

...c/correct-round.rkt:119:19: 8.0ms (23.5% of total)

ival-add: 7.0ms (20.5% of total)

const: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Counts

15 → 180

Calls

Call 1

Inputs
#<alt (* x (+ 1 (* x 1/2)))>
#<alt (+ 1 (* x 1/2))>
#<alt (* x 1/2)>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
#<alt (+ 1/2 (* x 1/6))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))>
#<alt (+ 1/2 (* x (+ 1/6 (* x 1/24))))>
#<alt (* x 1/6)>
#<alt (* x (+ 1/6 (* x 1/24)))>
#<alt (* x 1/24)>
#<alt (+ 1/6 (* x 1/24))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 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>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 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 (* 1/24 x)>
#<alt 1/6>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>

Calls

45 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* x (+ 1 (* x 1/2)))
1.0ms	x	@	inf	(* x (+ 1/6 (* x 1/24)))
1.0ms	x	@	inf	(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
1.0ms	x	@	-inf	(* x (+ 1 (* x 1/2)))
0.0ms	x	@	-inf	(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))

rewrite445.0ms (6.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3810×	`-lowering-.f32`
3810×	`-lowering-.f64`
3484×	`/-lowering-/.f32`
3484×	`/-lowering-/.f64`
1980×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	113
1	137	93
2	1290	90
0	8131	90

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 512

Calls

Call 1

Inputs
(* x (+ 1 (* x 1/2)))
(+ 1 (* x 1/2))
(* x 1/2)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))
(* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
(* x 1/6)
(* x (+ 1/6 (* x 1/24)))
(* x 1/24)
(+ 1/6 (* x 1/24))

Outputs
(+.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x x)
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))))) (-.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (-.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 x x) (.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) x)
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))))))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1 binary64))) (neg.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (+.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(*.f64 x #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
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(/.f64 (+.f64 (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64))))) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) x) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) x) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
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(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))))
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(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) x)
(.f64 (+.f64 (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
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(.f64 (.f64 x (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))))
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(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64))
(+.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 #s(literal 1/144 binary64) x))) (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/36 binary64))))
(/.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 #s(literal 1/144 binary64) x))))
(/.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 #s(literal 1/144 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/36 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (.f64 (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/10077696 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/46656 binary64) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (.f64 #s(literal 1/2985984 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1/46656 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1/46656 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/1296 binary64) (+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/1296 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/36 binary64))) (neg.f64 (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))))
(.f64 (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/36 binary64) (*.f64 #s(literal 1/144 binary64) x)))))
(.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))
(.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/6 binary64))))

simplify373.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

3042×	`-lowering-.f32`
3042×	`-lowering-.f64`
1980×	`+-lowering-+.f64`
1980×	`+-lowering-+.f32`
1858×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	84	1184
1	313	976
2	1004	942
3	3992	926
4	7166	923
0	8339	923

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 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
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 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)
(* 1/24 x)
1/6
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))

Outputs
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 x x) (neg.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 x x) (neg.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (*.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.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 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.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 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 x (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x #s(literal -1/24 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))
(-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.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 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.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 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 x (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x #s(literal -1/24 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 x (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x #s(literal -1/24 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.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 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.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 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.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 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.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 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.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))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))

eval116.0ms (1.8%)

Compiler: Compiled 19894 to 2188 computations (89% saved)

prune92.0ms (1.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	690	2	692
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	691	6	697

Accuracy

100.0%

Counts

697 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.2%	(/.f64 (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
▶	99.5%	(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
✓	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	100.0%	(expm1.f64 x)
✓	98.6%	x

Compiler

Compiled 137 to 47 computations (65.7% saved)

simplify225.0ms (3.5%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))
✓	cost-diff	256	(+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (.f64 x (.f64 x x)))
✓	cost-diff	1024	(+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x)))
✓	cost-diff	1536	(/.f64 (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)

Rules

2418×	`+-lowering-+.f64`
2418×	`+-lowering-+.f32`
2204×	`-lowering-.f32`
2204×	`-lowering-.f64`
2026×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	213
1	72	184
2	250	183
3	1262	181
4	5555	178
0	8187	178

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* x (* x 1/2)) x)
(* x (* x 1/2))
x
(* x 1/2)
1/2
(/ (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x)))
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))))
(* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
1/2
(* x (+ 1/6 (* x 1/24)))
x
(+ 1/6 (* x 1/24))
1/6
(* x 1/24)
1/24
(* x x)
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))
(* x (* x x))
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))
(- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)

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

localize102.0ms (1.6%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	33.1%	(/.f64 (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
✓	accuracy	100.0%	(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))

Results

61.0ms

256×

valid

Compiler

Compiled 359 to 22 computations (93.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 17.0ms (44.9% of total)

ival-add: 9.0ms (23.8% of total)

...c/correct-round.rkt:119:19: 8.0ms (21.1% of total)

ival-div: 2.0ms (5.3% of total)

ival-sub: 1.0ms (2.6% of total)

const: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (+ (* x (* x 1/2)) x)>
#<alt (* x (* x 1/2))>
#<alt (* x 1/2)>
#<alt (/ (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))>
#<alt (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))>
#<alt (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x)))>
#<alt (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))>
#<alt (* x (+ 1/6 (* x 1/24)))>
#<alt (* x 1/24)>
#<alt (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/2 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* 1/12 x) 1/2))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* x (+ 1/12 (* 1/8 x))) 1/2))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/8 (/ 1 x))) x)) 1/72) x))))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (* 1/8 (pow x 3))))>
#<alt (* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))>
#<alt (* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 7/96 x)))))))>
#<alt (* 1/13824 (pow x 12))>
#<alt (* (pow x 12) (+ 1/13824 (* 1/1152 (/ 1 x))))>
#<alt (* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (* 1/1152 (/ 1 x)))))>
#<alt (* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (+ (* 1/1152 (/ 1 x)) (* 11/432 (/ 1 (pow x 3)))))))>
#<alt (* 1/13824 (pow x 12))>
#<alt (* (pow x 12) (+ 1/13824 (* 1/1152 (/ 1 x))))>
#<alt (* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (* 1/1152 (/ 1 x)))))>
#<alt (* (pow x 12) (+ 1/13824 (* -1 (/ (- (* -1 (/ (+ 7/1152 (* 11/432 (/ 1 x))) x)) 1/1152) x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/2 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* -1/6 x) 1/2))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))>
#<alt (* -1/24 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))>
#<alt (* (pow x 5) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))>
#<alt (* -1/24 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (* -1 (/ (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/6) x)))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 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 (* 1/24 x)>
#<alt (* 1/4 (pow x 4))>
#<alt (* (pow x 4) (+ 1/4 (* 1/6 x)))>
#<alt (* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))>
#<alt (* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))>

Calls

30 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
0.0ms	x	@	-inf	(/ (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
0.0ms	x	@	0	(/ (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
0.0ms	x	@	0	(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x)))
0.0ms	x	@	inf	(+ (* x (* x 1/2)) x)

rewrite532.0ms (8.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3496×	`-lowering-.f32`
3496×	`-lowering-.f64`
2746×	`/-lowering-/.f32`
2746×	`/-lowering-/.f64`
1934×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	149
1	163	129
2	1611	97
0	8585	97

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 364

Calls

Call 1

Inputs
(+ (* x (* x 1/2)) x)
(* x (* x 1/2))
(* x 1/2)
(/ (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))) (* x (* x x)))
(- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))
(* x (+ 1/6 (* x 1/24)))
(* x 1/24)
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))

Outputs
(+.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x x)
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (+.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x)))))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) (.f64 x x))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))))) (neg.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x))))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x))) (+.f64 (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))))))
(pow.f64 (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x)))))))
(.f64 (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)))
(.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))))))) (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))))) (.f64 x (.f64 x x)))) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) #s(literal 1 binary64)) (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))))) (/.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x)))) (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))))) (.f64 x (.f64 x x)))) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) #s(literal 1 binary64)) (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))))))
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(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) x)
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) #s(literal 2 binary64))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x))))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 x (.f64 x (*.f64 x x))))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (*.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x))))
(.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))) x)
(.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x))) x) x)
(.f64 (exp.f64 (log.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (exp.f64 (log.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)))))

simplify260.0ms (4%)

Algorithm

1×	egg-herbie

Rules

3684×	`-lowering-.f32`
3684×	`-lowering-.f64`
2090×	`+-lowering-+.f64`
2090×	`+-lowering-+.f32`
1798×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	976
1	708	872
2	2207	846
3	6688	846
0	8002	846

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 x)))
(* (pow x 2) (+ 1 (* x (- (* 1/12 x) 1/2))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 1/12 (* 1/8 x))) 1/2))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/8 (/ 1 x))) x)) 1/72) x))))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/8 (pow x 3))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 7/96 x)))))))
(* 1/13824 (pow x 12))
(* (pow x 12) (+ 1/13824 (* 1/1152 (/ 1 x))))
(* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (* 1/1152 (/ 1 x)))))
(* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (+ (* 1/1152 (/ 1 x)) (* 11/432 (/ 1 (pow x 3)))))))
(* 1/13824 (pow x 12))
(* (pow x 12) (+ 1/13824 (* 1/1152 (/ 1 x))))
(* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (* 1/1152 (/ 1 x)))))
(* (pow x 12) (+ 1/13824 (* -1 (/ (- (* -1 (/ (+ 7/1152 (* 11/432 (/ 1 x))) x)) 1/1152) x))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 x)))
(* (pow x 2) (+ 1 (* x (- (* -1/6 x) 1/2))))
(* (pow x 2) (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))
(* -1/24 (pow x 5))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(* (pow x 5) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1/24 (pow x 5))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(* -1 (* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1 (* (pow x 5) (+ 1/24 (* -1 (/ (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/6) x)))))
(* 1/6 x)
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 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)
(* 1/24 x)
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/6 x)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))

Outputs
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -1/6 binary64)) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/2 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(* (pow x 2) (+ 1 (* x (- (* 1/12 x) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/12 binary64))))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 1/12 (* 1/8 x))) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/12 binary64) (*.f64 x #s(literal 1/8 binary64))))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (+.f64 (/.f64 #s(literal 5/72 binary64) (.f64 x x)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/8 (/ 1 x))) x)) 1/72) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1/576 binary64) (/.f64 (-.f64 #s(literal -1/72 binary64) (/.f64 (+.f64 #s(literal 5/72 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) x)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (* 1/8 (pow x 3))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64)))))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 7/96 x)))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 7/96 binary64))))))))))
(* 1/13824 (pow x 12))
(*.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 12 binary64)))
(* (pow x 12) (+ 1/13824 (* 1/1152 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal 1/13824 binary64) (/.f64 #s(literal 1/1152 binary64) x)))
(* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (* 1/1152 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal 1/13824 binary64) (+.f64 (/.f64 #s(literal 1/1152 binary64) x) (/.f64 #s(literal 7/1152 binary64) (.f64 x x)))))
(* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (+ (* 1/1152 (/ 1 x)) (* 11/432 (/ 1 (pow x 3)))))))
(.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 (/.f64 #s(literal 1/1152 binary64) x) (+.f64 (/.f64 #s(literal 7/1152 binary64) (.f64 x x)) (+.f64 #s(literal 1/13824 binary64) (/.f64 #s(literal 11/432 binary64) (.f64 x (.f64 x x)))))))
(* 1/13824 (pow x 12))
(*.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 12 binary64)))
(* (pow x 12) (+ 1/13824 (* 1/1152 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal 1/13824 binary64) (/.f64 #s(literal 1/1152 binary64) x)))
(* (pow x 12) (+ 1/13824 (+ (/ 7/1152 (pow x 2)) (* 1/1152 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal 1/13824 binary64) (+.f64 (/.f64 #s(literal 1/1152 binary64) x) (/.f64 #s(literal 7/1152 binary64) (.f64 x x)))))
(* (pow x 12) (+ 1/13824 (* -1 (/ (- (* -1 (/ (+ 7/1152 (* 11/432 (/ 1 x))) x)) 1/1152) x))))
(*.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 #s(literal 1/13824 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -7/1152 binary64) (/.f64 #s(literal -11/432 binary64) x)) x) #s(literal -1/1152 binary64)) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/2 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(* (pow x 2) (+ 1 (* x (- (* -1/6 x) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal -1/6 binary64))))))
(* (pow x 2) (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x #s(literal -1/24 binary64))))))))
(* -1/24 (pow x 5))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (-.f64 #s(literal -1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 5) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) (/.f64 #s(literal -1/6 binary64) x)))
(* -1/24 (pow x 5))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* -1 (* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal -1/24 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(* -1 (* (pow x 5) (+ 1/24 (* -1 (/ (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/6) x)))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) x))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.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))
(* 1/4 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64))
(* (pow x 4) (+ 1/4 (* 1/6 x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 5/72 binary64))))))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 5/72 binary64) (*.f64 x #s(literal 1/72 binary64))))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 5/72 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x)))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1/576 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) x) #s(literal -5/72 binary64)) x) #s(literal -1/72 binary64)) x)))

eval402.0ms (6.2%)

Compiler: Compiled 97439 to 2238 computations (97.7% saved)

prune72.0ms (1.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	765	1	766
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	766	6	772

Accuracy

100.0%

Counts

772 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.2%	(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))
✓	99.5%	(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
✓	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	100.0%	(expm1.f64 x)
✓	98.6%	x

Compiler

Compiled 109 to 53 computations (51.4% saved)

simplify254.0ms (3.9%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64)))))))
✓	cost-diff	128	(-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))
✓	cost-diff	1024	(+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x)))
✓	cost-diff	1024	(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))

Rules

5304×	`+-lowering-+.f64`
5304×	`+-lowering-+.f32`
5118×	`-lowering-.f32`
5118×	`-lowering-.f64`
1894×	`distribute-lft-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	215
1	93	184
2	346	179
3	1588	177
0	8333	177

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
(* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))
(* x (* x x))
x
(* x x)
(+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))
1
(* (* x x) (* x (+ 1/8 (* x 1/8))))
(* x (+ 1/8 (* x 1/8)))
(+ 1/8 (* x 1/8))
1/8
(* x 1/8)
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))
(* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
1/2
(* x (+ 1/6 (* x 1/24)))
(+ 1/6 (* x 1/24))
1/6
(* x 1/24)
1/24
(- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)

Outputs
(/ (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
(/.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))))) (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))))))
(* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64)))))))))
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64)))))))
1
#s(literal 1 binary64)
(* (* x x) (* x (+ 1/8 (* x 1/8))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))
(* x (+ 1/8 (* x 1/8)))
(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))
(+ 1/8 (* x 1/8))
(+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64)))
1/8
#s(literal 1/8 binary64)
(* x 1/8)
(*.f64 x #s(literal 1/8 binary64))
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))))))
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (*.f64 x x)))))
(* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
1/2
#s(literal 1/2 binary64)
(* x (+ 1/6 (* x 1/24)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(+ 1/6 (* x 1/24))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
1/6
#s(literal 1/6 binary64)
(* x 1/24)
(*.f64 x #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))))
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))

localize128.0ms (2%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	33.1%	(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))

Results

83.0ms

256×

valid

Compiler

Compiled 286 to 25 computations (91.3% saved)

Precisions

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

ival-add: 23.0ms (44.5% of total)

ival-mult: 18.0ms (34.8% of total)

...c/correct-round.rkt:119:19: 7.0ms (13.5% of total)

ival-div: 2.0ms (3.9% of total)

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

const: 1.0ms (1.9% of total)

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

series4.0ms (0.1%)

Counts

7 → 84

Calls

Call 1

Inputs
#<alt (/ (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))>
#<alt (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))>
#<alt (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))>
#<alt (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))>
#<alt (* x (+ 1/6 (* x 1/24)))>
#<alt (* x 1/24)>
#<alt (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (/ 72 x)>
#<alt (/ (- 72 (* 504 (/ 1 x))) x)>
#<alt (/ (- (+ 72 (/ 1152 (pow x 2))) (* 504 (/ 1 x))) x)>
#<alt (/ (- (+ 72 (+ (* 5760 (/ 1 (pow x 3))) (/ 1152 (pow x 2)))) (* 504 (/ 1 x))) x)>
#<alt (/ 72 x)>
#<alt (* -1 (/ (- (* 504 (/ 1 x)) 72) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1152 (/ 1 x)) 504) x)) 72) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (+ (* 1152 (/ 1 x)) (/ 5760 (pow x 2))) 504) x)) 72) x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/2 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* 1/12 x) 1/2))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* x (+ 1/12 (* 1/8 x))) 1/2))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/8 (/ 1 x))) x)) 1/72) x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/2 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* -1/6 x) 1/2))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))>
#<alt (* -1/24 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))>
#<alt (* (pow x 5) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))>
#<alt (* -1/24 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))>
#<alt (* -1 (* (pow x 5) (+ 1/24 (* -1 (/ (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/6) x)))))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (* 1/8 (pow x 3))))>
#<alt (* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))>
#<alt (* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))>
#<alt (* 1/8 (pow x 7))>
#<alt (* (pow x 7) (+ 1/8 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 7) (+ 1/8 (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 4)))))>
#<alt (* (pow x 7) (+ 1/8 (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 4)))))>
#<alt (* 1/8 (pow x 7))>
#<alt (* (pow x 7) (+ 1/8 (* 1/8 (/ 1 x))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 3))) x)) 1/8)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 3))) x)) 1/8)))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 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 (* 1/24 x)>
#<alt (* 1/4 (pow x 4))>
#<alt (* (pow x 4) (+ 1/4 (* 1/6 x)))>
#<alt (* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))>
#<alt (* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))>
#<alt (* 1/576 (pow x 8))>
#<alt (* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))>
#<alt (* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))>

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))
0.0ms	x	@	inf	(* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))
0.0ms	x	@	-inf	(/ (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
0.0ms	x	@	inf	(/ (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
0.0ms	x	@	0	(* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))

rewrite351.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3592×	`-lowering-.f32`
3592×	`-lowering-.f64`
2752×	`/-lowering-/.f32`
2752×	`/-lowering-/.f64`
1724×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	130
1	186	109
2	1752	106
0	8198	106

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 316

Calls

Call 1

Inputs
(/ (* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8)))))) (+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))))
(+ (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))) (- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)))
(- (* x x) (* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x))
(* (* x (* x x)) (+ 1 (* (* x x) (* x (+ 1/8 (* x 1/8))))))
(* x (+ 1/6 (* x 1/24)))
(* x 1/24)
(* (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64)))))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))))
(neg.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))))
(neg.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))) (neg.f64 (.f64 x (.f64 x x)))) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64))))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64))))))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64)))))) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))) (neg.f64 (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64))))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))) (neg.f64 (.f64 x (.f64 x x))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))))
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(pow.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 x (.f64 x (*.f64 x x))))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (*.f64 x x))
(.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))) x)
(.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))) x) x)
(.f64 (exp.f64 (log.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))) (exp.f64 (log.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))))

simplify222.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

4150×	`-lowering-.f32`
4150×	`-lowering-.f64`
1820×	`+-lowering-+.f64`
1820×	`+-lowering-+.f32`
1572×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	792
1	687	718
2	2012	699
3	5851	699
0	8069	699

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(/ 72 x)
(/ (- 72 (* 504 (/ 1 x))) x)
(/ (- (+ 72 (/ 1152 (pow x 2))) (* 504 (/ 1 x))) x)
(/ (- (+ 72 (+ (* 5760 (/ 1 (pow x 3))) (/ 1152 (pow x 2)))) (* 504 (/ 1 x))) x)
(/ 72 x)
(* -1 (/ (- (* 504 (/ 1 x)) 72) x))
(* -1 (/ (- (* -1 (/ (- (* 1152 (/ 1 x)) 504) x)) 72) x))
(* -1 (/ (- (* -1 (/ (- (+ (* 1152 (/ 1 x)) (/ 5760 (pow x 2))) 504) x)) 72) x))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 x)))
(* (pow x 2) (+ 1 (* x (- (* 1/12 x) 1/2))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 1/12 (* 1/8 x))) 1/2))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/8 (/ 1 x))) x)) 1/72) x))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 x)))
(* (pow x 2) (+ 1 (* x (- (* -1/6 x) 1/2))))
(* (pow x 2) (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))
(* -1/24 (pow x 5))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(* (pow x 5) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1/24 (pow x 5))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(* -1 (* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1 (* (pow x 5) (+ 1/24 (* -1 (/ (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/6) x)))))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/8 (pow x 3))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(* 1/8 (pow x 7))
(* (pow x 7) (+ 1/8 (* 1/8 (/ 1 x))))
(* (pow x 7) (+ 1/8 (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 4)))))
(* (pow x 7) (+ 1/8 (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 4)))))
(* 1/8 (pow x 7))
(* (pow x 7) (+ 1/8 (* 1/8 (/ 1 x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 3))) x)) 1/8)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 3))) x)) 1/8)))
(* 1/6 x)
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 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)
(* 1/24 x)
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/6 x)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))
(* 1/576 (pow x 8))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))

Outputs
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(/ 72 x)
(/.f64 #s(literal 72 binary64) x)
(/ (- 72 (* 504 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 72 binary64) (/.f64 #s(literal 504 binary64) x)) x)
(/ (- (+ 72 (/ 1152 (pow x 2))) (* 504 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1152 binary64) x) #s(literal -504 binary64)) x)) x)
(/ (- (+ 72 (+ (* 5760 (/ 1 (pow x 3))) (/ 1152 (pow x 2)))) (* 504 (/ 1 x))) x)
(/.f64 (+.f64 (+.f64 #s(literal 72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1152 binary64) x) #s(literal -504 binary64)) x)) (/.f64 #s(literal 5760 binary64) (.f64 x (.f64 x x)))) x)
(/ 72 x)
(/.f64 #s(literal 72 binary64) x)
(* -1 (/ (- (* 504 (/ 1 x)) 72) x))
(/.f64 (-.f64 #s(literal 72 binary64) (/.f64 #s(literal 504 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1152 (/ 1 x)) 504) x)) 72) x))
(/.f64 (+.f64 #s(literal 72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1152 binary64) x) #s(literal -504 binary64)) x)) x)
(* -1 (/ (- (* -1 (/ (- (+ (* 1152 (/ 1 x)) (/ 5760 (pow x 2))) 504) x)) 72) x))
(/.f64 (+.f64 #s(literal 72 binary64) (.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1152 binary64) x) #s(literal -504 binary64)) (/.f64 #s(literal 5760 binary64) (.f64 x x))) x))) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/2 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(* (pow x 2) (+ 1 (* x (- (* 1/12 x) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/12 binary64))))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 1/12 (* 1/8 x))) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/12 binary64) (*.f64 x #s(literal 1/8 binary64))))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)) (+.f64 (/.f64 #s(literal 5/72 binary64) (.f64 x x)) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/8 (/ 1 x))) x)) 1/72) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1/576 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -5/72 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal -1/72 binary64)) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/2 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(* (pow x 2) (+ 1 (* x (- (* -1/6 x) 1/2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal -1/6 binary64))))))
(* (pow x 2) (+ 1 (* x (- (* x (- (* -1/24 x) 1/6)) 1/2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x #s(literal -1/24 binary64)))))))))
(* -1/24 (pow x 5))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 5) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (+.f64 #s(literal -1/24 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 5) (- (/ 1 (pow x 3)) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (-.f64 (/.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(* -1/24 (pow x 5))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (+ 1/24 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* -1 (* (pow x 5) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal -1/6 binary64) x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(* -1 (* (pow x 5) (+ 1/24 (* -1 (/ (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/6) x)))))
(.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (* 1/8 (pow x 3))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64))))))
(* (pow x 3) (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/8 binary64))))))
(* 1/8 (pow x 7))
(*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/8 (* 1/8 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* (pow x 7) (+ 1/8 (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 7) (+ 1/8 (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* 1/8 (pow x 7))
(*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/8 (* 1/8 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 3))) x)) 1/8)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal 1/8 binary64)) x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 3))) x)) 1/8)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal 1/8 binary64)) x))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x))))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/4 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64))
(* (pow x 4) (+ 1/4 (* 1/6 x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* 5/72 x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 5/72 binary64))))))
(* (pow x 4) (+ 1/4 (* x (+ 1/6 (* x (+ 5/72 (* 1/72 x)))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 5/72 binary64) (*.f64 x #s(literal 1/72 binary64))))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (+ (* 1/72 (/ 1 x)) (* 1/6 (/ 1 (pow x 3)))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 5/72 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)) (/.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))))
(* 1/576 (pow x 8))
(*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/576 (* 1/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 1/72 binary64) x)))
(* (pow x 8) (+ 1/576 (+ (/ 5/72 (pow x 2)) (* 1/72 (/ 1 x)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/72 binary64) x) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal 5/72 binary64) (.f64 x x)))))
(* (pow x 8) (+ 1/576 (* -1 (/ (- (* -1 (/ (+ 5/72 (* 1/6 (/ 1 x))) x)) 1/72) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1/576 binary64) (/.f64 (-.f64 #s(literal -1/72 binary64) (/.f64 (+.f64 #s(literal 5/72 binary64) (/.f64 #s(literal 1/6 binary64) x)) x)) x)))

eval80.0ms (1.2%)

Compiler: Compiled 56515 to 1770 computations (96.9% saved)

prune63.0ms (1%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	498	2	500
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	499	7	506

Accuracy

100.0%

Counts

506 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.2%	(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 5/72 binary64) (.f64 x #s(literal 1/72 binary64)))))))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))
	32.2%	(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 5/72 binary64)))))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
✓	99.5%	(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
✓	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	100.0%	(expm1.f64 x)
✓	98.6%	x

Compiler

Compiled 489 to 157 computations (67.9% saved)

regimes13.0ms (0.2%)

Counts

11 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 5/72 binary64)))))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 5/72 binary64) (.f64 x #s(literal 1/72 binary64)))))))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))
(/.f64 (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))

Outputs
(expm1.f64 x)

Calls

3 calls:

4.0ms	(exp.f64 x)
3.0ms	x
3.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 5/72 binary64)))))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 5/72 binary64) (.f64 x #s(literal 1/72 binary64)))))))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 1/8 binary64))))))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x))))
(/.f64 (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x)) x))))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	43
1	43	43

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
x

Outputs
(expm1.f64 x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)
(+.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
x

soundness371.0ms (5.8%)

Rules

3810×	`-lowering-.f32`
3810×	`-lowering-.f64`
3484×	`/-lowering-/.f32`
3484×	`/-lowering-/.f64`
1980×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	72	44
2	190	41
3	465	41
4	978	41
5	1401	41
6	1557	41
7	1559	41
0	1559	41
0	4	2
1	10	2
2	11	2
0	11	2
0	20	113
1	137	93
2	1290	90
0	8131	90

Stop Event

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

Compiler

Compiled 116 to 74 computations (36.2% saved)

preprocess52.0ms (0.8%)

Compiler: Compiled 104 to 58 computations (44.2% saved)

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2

analyze0.0ms (0%)

sample1.7s (26.7%)

preprocess17.0ms (0.3%)

explain123.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize42.0ms (0.7%)

series1.0ms (0%)

rewrite101.0ms (1.6%)

simplify53.0ms (0.8%)

eval10.0ms (0.1%)

prune30.0ms (0.5%)

simplify48.0ms (0.7%)

localize96.0ms (1.5%)

series12.0ms (0.2%)

rewrite445.0ms (6.9%)

simplify373.0ms (5.8%)

eval116.0ms (1.8%)

prune92.0ms (1.4%)

simplify225.0ms (3.5%)

localize102.0ms (1.6%)

series11.0ms (0.2%)

rewrite532.0ms (8.2%)

simplify260.0ms (4%)

eval402.0ms (6.2%)

prune72.0ms (1.1%)

simplify254.0ms (3.9%)

localize128.0ms (2%)

series4.0ms (0.1%)

rewrite351.0ms (5.4%)

simplify222.0ms (3.4%)

eval80.0ms (1.2%)

prune63.0ms (1%)

regimes13.0ms (0.2%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.1%)

soundness371.0ms (5.8%)

preprocess52.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2