Details

analyze7.0ms (0.2%)

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 (53.3%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 142 to 66 computations (53.5% saved)

preprocess29.0ms (1%)

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)

simplify22.0ms (0.8%)

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 (0.2%)

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
▶	0.1b	(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))))))
	0.6b	(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

▶

0.1b

(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))))))

0.6b

(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 (0.8%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.6%)

Counts

4 → 36

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(.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)))))
2.0ms	x	@	0	(.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)))))
2.0ms	x	@	-inf	(.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)))))
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	@	-inf	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))

rewrite36.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

294×	`add-sqr-sqrt_binary64`
277×	`*-un-lft-identity_binary64`
277×	`pow1_binary64`
276×	`add-cbrt-cube_binary64`
274×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	89
1	619	89

Stop Event

1×	node limit

Counts

4 → 31

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

simplify81.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2001×	`fma-def_binary64`
650×	`associate-l_binary64`
454×	`associate-r_binary64`
213×	`sqr-pow_binary64`
198×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	720
1	63	720
2	161	720
3	500	696
4	1307	696
5	3566	696
6	3947	696
7	4045	696
8	4175	696
9	4373	696
10	4664	696

Stop Event

1×	node limit

Counts

67 → 35

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))
(*.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))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.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))
(*.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))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) 2 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))

prune46.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	34	3	37

Error

Counts

37 → 3

Alt Table

Status	Error	Program
	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))))))
▶	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	0.6b	(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

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))))))

▶

0.1b

(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))

0.6b

(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 2372 to 1033 computations (56.5% saved)

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
✓	0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
✓	0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

series4.0ms (0.1%)

Counts

4 → 0

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
0.0ms	x	@	0	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
0.0ms	x	@	0	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.0ms	x	@	inf	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
0.0ms	x	@	inf	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite39.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`add-sqr-sqrt_binary64`
259×	`add-log-exp_binary64`
259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
257×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	69
1	566	69

Stop Event

1×	node limit

Counts

4 → 26

Calls

Call 1

Inputs
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.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))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))))))
((#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.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))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (/.f64 1 (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))))))
((#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

26 → 26

Calls

Call 1

Inputs

Outputs

prune41.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Error

Counts

29 → 3

Alt Table

Status	Error	Program
	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))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
▶	0.6b	(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

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))))))

✓

0.1b

(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))

▶

0.6b

(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 1159 to 793 computations (31.6% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series6.0ms (0.2%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(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)))
1.0ms	x	@	-inf	(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	@	inf	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))

rewrite55.0ms (1.9%)

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

simplify66.0ms (2.3%)

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))

prune93.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Error

Counts

99 → 3

Alt Table

Status

Error

Program

▶

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))))))

✓

0.1b

(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))

✓

0.6b

(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 2943 to 1862 computations (36.7% saved)

localize27.0ms (0.9%)

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)))
	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))
✓	1.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))

series0.0ms (0%)

Counts: 1 → 0

rewrite34.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

331×	`pow1_binary64`
320×	`add-sqr-sqrt_binary64`
308×	`add-log-exp_binary64`
308×	`expm1-log1p-u_binary64`
307×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	78	4
2	873	4

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))

Outputs

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

23 → 23

Calls

Call 1

Inputs

Outputs

prune47.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	47	3	50

Error

Counts

50 → 3

Alt Table

Status

Error

Program

✓

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))))))

✓

0.1b

(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))

✓

0.6b

(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 3418 to 1252 computations (63.4% saved)

regimes498.0ms (17.4%)

Accuracy

Total 0.1b remaining (91.5%)

Threshold costs 0.1b (91.5%)

Counts

64 → 1

Compiler

Compiled 12806 to 8487 computations (33.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	32	55

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fabs.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))

Outputs

(fabs.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))

end108.0ms (3.8%)

Stop Event

1×

done

Compiler

Compiled 197 to 130 computations (34% saved)

Details

analyze7.0ms (0.2%)

sample1.5s (53.3%)

preprocess29.0ms (1%)

simplify22.0ms (0.8%)

prune5.0ms (0.2%)

localize24.0ms (0.8%)

series17.0ms (0.6%)

rewrite36.0ms (1.3%)

simplify81.0ms (2.8%)

prune46.0ms (1.6%)

localize20.0ms (0.7%)

series4.0ms (0.1%)

rewrite39.0ms (1.4%)

simplify6.0ms (0.2%)

prune41.0ms (1.4%)

localize18.0ms (0.6%)

series6.0ms (0.2%)

rewrite55.0ms (1.9%)

simplify66.0ms (2.3%)

prune93.0ms (3.3%)

localize27.0ms (0.9%)

series0.0ms (0%)

rewrite34.0ms (1.2%)

simplify6.0ms (0.2%)

prune47.0ms (1.7%)

regimes498.0ms (17.4%)

simplify2.0ms (0.1%)

end108.0ms (3.8%)

Profiling