Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.5s (33.1%)

Results

1.5s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 142 to 66 computations (53.5% saved)

preprocess28.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

642×	`distribute-lft-out_binary64`
588×	`associate-/l*_binary64`
406×	`associate-/r*_binary64`
400×	`*-commutative_binary64`
244×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	251	41
3	1208	37
4	2394	37
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Outputs
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (fma.f64 2 (fabs.f64 x) (.f64 2/3 (.f64 (fabs.f64 x) (.f64 x x)))) (.f64 1/5 (.f64 (fabs.f64 x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 1/21 (.f64 (fabs.f64 x) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))))))
(fabs.f64 (/.f64 (fma.f64 1/21 (.f64 (.f64 x x) (.f64 (.f64 x x) (pow.f64 (fabs.f64 x) 3))) (fma.f64 1/5 (.f64 (.f64 x x) (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 (*.f64 2/3 x) x))))) (sqrt.f64 (PI.f64))))
(fabs.f64 (/.f64 (.f64 (fabs.f64 x) (+.f64 (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 4) (*.f64 1/21 (pow.f64 (fabs.f64 x) 6))))) (sqrt.f64 (PI.f64))))
(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Compiler

Compiled 68 to 31 computations (54.4% saved)

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-lft-out_binary64`
588×	`associate-/l*_binary64`
406×	`associate-/r*_binary64`
400×	`*-commutative_binary64`
244×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	251	41
3	1208	37
4	2394	37

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Outputs
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (fma.f64 2 (fabs.f64 x) (.f64 2/3 (.f64 (fabs.f64 x) (.f64 x x)))) (.f64 1/5 (.f64 (fabs.f64 x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 1/21 (.f64 (fabs.f64 x) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))))))
(fabs.f64 (/.f64 (fma.f64 1/21 (.f64 (.f64 x x) (.f64 (.f64 x x) (pow.f64 (fabs.f64 x) 3))) (fma.f64 1/5 (.f64 (.f64 x x) (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 (*.f64 2/3 x) x))))) (sqrt.f64 (PI.f64))))
(fabs.f64 (/.f64 (.f64 (fabs.f64 x) (+.f64 (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 4) (*.f64 1/21 (pow.f64 (fabs.f64 x) 6))))) (sqrt.f64 (PI.f64))))
(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Status

Error

Program

▶

0.2b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

0.5b

(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Compiler

Compiled 278 to 149 computations (46.4% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
✓	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series9.0ms (0.2%)

Counts

4 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	x	@	-inf	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	x	@	-inf	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	x	@	0	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	x	@	inf	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))

rewrite53.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`log-prod_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
196×	`log-pow_binary64`
155×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	344	22
2	3574	22

Stop Event

1×	node limit

Counts

4 → 78

Calls

Call 1

Inputs
(sqrt.f64 (PI.f64))
(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (exp.f64 (sqrt.f64 (PI.f64)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) 1/4) (pow.f64 (PI.f64) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (PI.f64) 2))) (sqrt.f64 (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (PI.f64) 2)) 1/2) (pow.f64 (cbrt.f64 (PI.f64)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (PI.f64) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (PI.f64) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 2/3) (pow.f64 x 3))) (cbrt.f64 (pow.f64 (exp.f64 2/3) (pow.f64 x 3))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2/3) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2/3) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2/3) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2/3 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2/3 (pow.f64 x 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (cbrt.f64 2/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 2/3) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 4/9 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2/3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2/3 (pow.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 3 (log.f64 x) (log.f64 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 3 (log.f64 x) (log.f64 2/3)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))) (cbrt.f64 (exp.f64 (pow.f64 x 3))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x 6))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (neg.f64 x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (.f64 x x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 3 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 3 (log.f64 x)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/5 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 1/5) (pow.f64 x 5))) (cbrt.f64 (pow.f64 (exp.f64 1/5) (pow.f64 x 5))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/5) (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/5) (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/5 (pow.f64 x 5)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/5 (pow.f64 x 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/5 (pow.f64 x 5)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/5 (pow.f64 x 5))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/5 (pow.f64 x 5))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (pow.f64 x 5) 2) 1/25))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/5) (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/5 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/5 (pow.f64 x 5)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/5 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/5 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/5 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 1/5 (pow.f64 x 5))) 1))))))

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

828×	`sqr-pow_binary64`
416×	`unswap-sqr_binary64`
388×	`pow-sqr_binary64`
332×	`cube-prod_binary64`
252×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	288
1	25	288
2	52	288
3	114	288
4	243	288
5	630	288
6	923	288
7	1559	288
8	1667	288
9	1829	288
10	2044	288
11	2374	288
12	2830	288
13	3427	288
14	4176	288

Stop Event

1×	node limit

Counts

114 → 81

Calls

Call 1

Inputs
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

Outputs
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(pow.f64 (fabs.f64 x) 3)
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

prune192.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Error

0.0b

Counts

125 → 4

Alt Table

Status	Error	Program
▶	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	1.1b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Compiler

Compiled 8431 to 3428 computations (59.3% saved)

localize27.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))
✓	9.7b	(sqrt.f64 (pow.f64 x 6))

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (pow.f64 x 6))
1.0ms	x	@	inf	(sqrt.f64 (pow.f64 x 6))
0.0ms	x	@	-inf	(sqrt.f64 (pow.f64 x 6))

rewrite29.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

404×	`pow1_binary64`
382×	`add-log-exp_binary64`
382×	`log1p-expm1-u_binary64`
382×	`expm1-log1p-u_binary64`
371×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	105	4
2	1138	4

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(sqrt.f64 (pow.f64 x 6))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 x 12))) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 x 12)) 1/2) (pow.f64 (.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 9) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 9))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) 3))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x 12))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x 12)) 1/2) (pow.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 9) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 9))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) 3))))))

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

912×	`fma-def_binary64`
450×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
279×	`associate-r_binary64`
271×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	56
1	16	56
2	44	56
3	74	56
4	143	56
5	409	56
6	1418	56
7	2697	56
8	4527	56

Stop Event

1×	node limit

Counts

37 → 27

Calls

Call 1

Inputs
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(*.f64 -1 (pow.f64 x 3))
(*.f64 -1 (pow.f64 x 3))
(*.f64 -1 (pow.f64 x 3))
(*.f64 -1 (pow.f64 x 3))

Outputs
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(*.f64 -1 (pow.f64 x 3))
(neg.f64 (pow.f64 x 3))
(*.f64 -1 (pow.f64 x 3))
(neg.f64 (pow.f64 x 3))
(*.f64 -1 (pow.f64 x 3))
(neg.f64 (pow.f64 x 3))
(*.f64 -1 (pow.f64 x 3))
(neg.f64 (pow.f64 x 3))

prune163.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	113	3	116

Error

0.0b

Counts

116 → 3

Alt Table

Status

Error

Program

✓

0.2b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

▶

0.5b

(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

1.0b

(fabs.f64 (*.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 7343 to 3704 computations (49.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
✓	0.1b	(*.f64 1/21 (pow.f64 x 6))
✓	0.3b	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))

series8.0ms (0.2%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
1.0ms	x	@	0	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
1.0ms	x	@	0	(*.f64 1/21 (pow.f64 x 6))
1.0ms	x	@	-inf	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
1.0ms	x	@	inf	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))

rewrite52.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
185×	`log-pow_binary64`
142×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	300	28
2	3455	28

Stop Event

1×	node limit

Counts

3 → 81

Calls

Call 1

Inputs
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
(*.f64 1/21 (pow.f64 x 6))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64))))) (cbrt.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 (PI.f64) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))) (cbrt.f64 (/.f64 (*.f64 x x) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 x x) (PI.f64))) (cbrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (pow.f64 (PI.f64) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) 1) (/.f64 (cbrt.f64 x) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (PI.f64))) (/.f64 x (cbrt.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 (PI.f64))) (cbrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (PI.f64))) (/.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (PI.f64) 1/4)) (/.f64 (cbrt.f64 x) (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (PI.f64)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (PI.f64) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (sqrt.f64 (PI.f64)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/21 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6))) (cbrt.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/21 (pow.f64 x 6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/21 (pow.f64 x 6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/21 (pow.f64 x 6)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 1/21) (*.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/21) (pow.f64 x 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 12) 1/441))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/21 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/21 (pow.f64 x 6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/21 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/21 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/21 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/21 (pow.f64 x 6))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/21 (pow.f64 x 6)) (*.f64 1/5 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/5 (pow.f64 x 4)) (*.f64 1/21 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/5 (pow.f64 x 4)) 1) (*.f64 1/21 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))))) (cbrt.f64 (exp.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/5 (pow.f64 x 4)) 3) (pow.f64 (*.f64 1/21 (pow.f64 x 6)) 3)) (fma.f64 (*.f64 1/5 (pow.f64 x 4)) (*.f64 1/5 (pow.f64 x 4)) (-.f64 (*.f64 (pow.f64 x 12) 1/441) (*.f64 (*.f64 1/5 (pow.f64 x 4)) (*.f64 1/21 (pow.f64 x 6))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/5 (pow.f64 x 4)) (*.f64 1/5 (pow.f64 x 4))) (*.f64 (pow.f64 x 12) 1/441)) (-.f64 (*.f64 1/5 (pow.f64 x 4)) (*.f64 1/21 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/21) (pow.f64 x 6)) (exp.f64 (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/21 (pow.f64 x 6)))) (exp.f64 (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 1/5 (pow.f64 x 4))) (+.f64 1 (expm1.f64 (*.f64 1/21 (pow.f64 x 6))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/21 (pow.f64 x 6) (*.f64 1/5 (pow.f64 x 4)))) 1))))))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

518×	`sqr-pow_binary64`
487×	`associate-l_binary64`
467×	`unswap-sqr_binary64`
440×	`fma-def_binary64`
300×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	291
1	32	291
2	56	291
3	123	267
4	399	267
5	1478	267
6	2937	267
7	3286	267
8	3570	267
9	3854	267
10	4219	267
11	4698	267

Stop Event

1×	node limit

Counts

105 → 86

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 1/5 (pow.f64 x 4))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(*.f64 1/21 (pow.f64 x 6))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(*.f64 1/21 (pow.f64 x 6))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))

Outputs
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 1/5 (pow.f64 x 4))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(*.f64 1/21 (pow.f64 x 6))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(*.f64 1/21 (pow.f64 x 6))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))
(+.f64 (.f64 1/5 (pow.f64 x 4)) (.f64 1/21 (pow.f64 x 6)))
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
(.f64 (pow.f64 x 4) (fma.f64 1/21 (.f64 x x) 1/5))

prune132.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
	0.5b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 x 6) (.f64 1/5 (pow.f64 x 4)))) 2) (fma.f64 2/3 (*.f64 x x) 2))))
✓	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.2b	(fabs.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (.f64 x x) 2))))
	1.0b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 3514 to 2257 computations (35.8% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
	0.1b	(*.f64 1/21 (pow.f64 x 6))
✓	0.2b	(/.f64 x (pow.f64 (PI.f64) 1/4))
✓	0.3b	(*.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4)))

series49.0ms (1.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
46.0ms	x	@	0	(/.f64 x (pow.f64 (PI.f64) 1/4))
1.0ms	x	@	0	(*.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4)))
1.0ms	x	@	inf	(*.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4)))
1.0ms	x	@	-inf	(*.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4)))
0.0ms	x	@	-inf	(/.f64 x (pow.f64 (PI.f64) 1/4))

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`
86×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	196	15
2	2444	15

Stop Event

1×	node limit

Counts

2 → 88

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4)))
(/.f64 x (pow.f64 (PI.f64) 1/4))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (pow.f64 (PI.f64) 1/4) (/.f64 (pow.f64 (PI.f64) 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 (pow.f64 (PI.f64) 1/4) x) (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (PI.f64)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (pow.f64 (PI.f64) -1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (PI.f64) -1/4) (/.f64 (pow.f64 (PI.f64) 1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (/.f64 (pow.f64 (PI.f64) 1/4) (pow.f64 (PI.f64) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) (pow.f64 (PI.f64) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 x (/.f64 x (sqrt.f64 (PI.f64))))) (/.f64 (pow.f64 (PI.f64) 1/4) (cbrt.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/8)) (/.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (neg.f64 (pow.f64 (PI.f64) 1/4)) (/.f64 (pow.f64 (PI.f64) 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (/.f64 (pow.f64 (PI.f64) 1/4) x) (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (*.f64 (neg.f64 (pow.f64 (PI.f64) 1/4)) (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (*.f64 (pow.f64 (PI.f64) 1/4) (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)) (neg.f64 (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (neg.f64 x)) (*.f64 (neg.f64 (pow.f64 (PI.f64) 1/4)) (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (pow.f64 (PI.f64) 1/4)) (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (*.f64 (pow.f64 (PI.f64) 1/4) (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) -1) (*.f64 (neg.f64 (pow.f64 (PI.f64) 1/4)) (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) (pow.f64 (PI.f64) 1/8)) (pow.f64 (PI.f64) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 1) (pow.f64 (PI.f64) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (*.f64 (pow.f64 (PI.f64) -1/4) x)) (neg.f64 (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) (pow.f64 (PI.f64) -1/4)) (neg.f64 (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (PI.f64) -1/4) (neg.f64 x)) (neg.f64 (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) -1) (neg.f64 (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 3) (pow.f64 (pow.f64 (PI.f64) 1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (PI.f64) -1/4) 3) (pow.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 3) (pow.f64 (pow.f64 (PI.f64) -1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (sqrt.f64 (PI.f64)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 (PI.f64) -1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1/4) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 (PI.f64) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)) (cbrt.f64 (*.f64 x (/.f64 x (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (/.f64 x (sqrt.f64 (PI.f64))))) (cbrt.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (PI.f64) -1/2)) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) -1/4)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (pow.f64 (PI.f64) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/8)) (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1/8) (/.f64 x (pow.f64 (PI.f64) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1/8) (*.f64 (pow.f64 (PI.f64) -1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 x (cbrt.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (pow.f64 (PI.f64) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (sqrt.f64 (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (PI.f64) 1/8)) (/.f64 (cbrt.f64 x) (pow.f64 (PI.f64) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (PI.f64) -1/8) (sqrt.f64 x)) (*.f64 (pow.f64 (PI.f64) -1/8) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (cbrt.f64 (pow.f64 (PI.f64) -1/2))) (cbrt.f64 (pow.f64 (PI.f64) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (pow.f64 (PI.f64) -1/8)) (pow.f64 (PI.f64) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (PI.f64) -1/4) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (PI.f64) -1/4) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 (PI.f64) -1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (PI.f64) 1/4) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (pow.f64 (PI.f64) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (/.f64 x (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (pow.f64 (PI.f64) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (pow.f64 (PI.f64) 1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (pow.f64 (PI.f64) -1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (PI.f64) -1/4) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (PI.f64) -1/4) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -1/4 (log.f64 (PI.f64))) (log.f64 x)))))))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

729×	`sqr-pow_binary64`
440×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	252
1	19	252
2	28	252
3	47	252
4	105	252
5	323	252
6	1174	252
7	1865	252
8	1955	252
9	2090	252
10	2249	252
11	2481	252
12	2803	252
13	3224	252
14	3724	252
15	4319	252

Stop Event

1×	node limit

Counts

112 → 91

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)

Outputs
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))
(*.f64 (pow.f64 (/.f64 1 (PI.f64)) 1/4) x)
(*.f64 x (pow.f64 (/.f64 1 (PI.f64)) 1/4))

prune188.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	139	4	143

Error

Counts

143 → 4

Alt Table

Status	Error	Program
	0.5b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 x 6) (.f64 1/5 (pow.f64 x 4)))) 2) (fma.f64 2/3 (*.f64 x x) 2))))
✓	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.2b	(fabs.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.f64 x (pow.f64 (PI.f64) 1/4))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (.f64 x x) 2))))
	1.0b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (pow.f64 x 6)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 4780 to 3470 computations (27.4% saved)

regimes1.6s (34.7%)

Accuracy

Total 0.1b remaining (93.1%)

Threshold costs 0.1b (93.1%)

Counts

238 → 1

Compiler

Compiled 10441 to 5767 computations (44.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`fabs-mul_binary64`
3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	36
1	28	36
2	33	36

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fabs.f64 (.f64 (.f64 (pow.f64 (PI.f64) -1/2) x) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (.f64 x x) 2))))

Outputs
(fabs.f64 (.f64 (.f64 (pow.f64 (PI.f64) -1/2) x) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (.f64 x x) 2))))

end132.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 239 to 162 computations (32.2% saved)

Details

analyze5.0ms (0.1%)

sample1.5s (33.1%)

preprocess28.0ms (0.6%)

simplify24.0ms (0.5%)

prune5.0ms (0.1%)

localize24.0ms (0.5%)

series9.0ms (0.2%)

rewrite53.0ms (1.2%)

simplify66.0ms (1.5%)

prune192.0ms (4.3%)

localize27.0ms (0.6%)

series2.0ms (0%)

rewrite29.0ms (0.6%)

simplify30.0ms (0.7%)

prune163.0ms (3.6%)

localize15.0ms (0.3%)

series8.0ms (0.2%)

rewrite52.0ms (1.1%)

simplify71.0ms (1.6%)

prune132.0ms (2.9%)

localize17.0ms (0.4%)

series49.0ms (1.1%)

rewrite49.0ms (1.1%)

simplify71.0ms (1.6%)

prune188.0ms (4.2%)

regimes1.6s (34.7%)

simplify2.0ms (0%)

end132.0ms (2.9%)

Profiling