Details

analyze175.0ms (2.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
28.6%	25%	62.5%	0%	0%	0%	12.5%	4
30.8%	25%	56.2%	0%	0%	0%	18.7%	5
36%	28.1%	50%	0%	0%	0%	21.9%	6
38.8%	29.7%	46.9%	0%	0%	0%	23.4%	7
40.2%	30.5%	45.3%	0%	0%	0%	24.2%	8
40.7%	30.8%	44.9%	0%	0%	0%	24.2%	9
41.2%	31.2%	44.5%	0%	0%	0%	24.2%	10
41.4%	31.3%	44.4%	0%	0%	0%	24.2%	11
41.5%	31.4%	44.3%	0%	0%	0%	24.3%	12

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.5s (34.8%)

Results

1.3s	2754×	body	1024	valid
546.0ms	3846×	body	256	valid
492.0ms	1367×	body	512	valid
219.0ms	289×	body	2048	valid
6.0ms	48×	body	256	infinite
0.0ms	2×	body	256	unsamplable

Bogosity

preprocess65.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

633×	`associate-/l*_binary64`
580×	`associate-l_binary64`
568×	`associate-r_binary64`
505×	`associate-/r*_binary64`
380×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	127	11
5	349	8
6	1341	8
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify31.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-/l*_binary64`
580×	`associate-l_binary64`
568×	`associate-r_binary64`
505×	`associate-/r*_binary64`
380×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	127	11
5	349	8
6	1341	8

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval1.0ms (0%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

prune2.0ms (0%)

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

Click to see full alt table

Status	Error	Program
▶	36.0b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 19 to 16 computations (15.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 14 to 8 computations (42.9% saved)

series3.0ms (0%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	0	(+.f64 1 (exp.f64 x))
0.0ms	x	@	inf	(+.f64 1 (exp.f64 x))

rewrite59.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`pow1_binary64`
512×	`add-log-exp_binary64`
512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
500×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	118	14
2	1429	14

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (exp.f64 x))

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

Outputs

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

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

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
525×	`cancel-sign-sub-inv_binary64`
434×	`fma-neg_binary64`
433×	`associate-r_binary64`
405×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	169
1	109	137
2	339	131
3	1110	103
4	5494	103

Stop Event

1×	node limit

Counts

66 → 71

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (.f64 x x) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 (fma.f64 1/2 x 1) x 2)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
(fma.f64 (fma.f64 1/2 x 1) x (fma.f64 1/6 (pow.f64 x 3) 2))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 (fma.f64 1/2 x 1) x 2))

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
✓	5.6b	(-.f64 (exp.f64 (*.f64 2 x)) 1)
✓	5.7b	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 46 to 33 computations (28.3% saved)

series24.0ms (0.3%)

Counts

4 → 16

Calls

12 calls:

Time	Variable		Point	Expression
19.0ms	x	@	inf	(-.f64 (exp.f64 (*.f64 2 x)) 1)
1.0ms	x	@	inf	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
1.0ms	x	@	-inf	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
0.0ms	x	@	0	(-.f64 (exp.f64 x) 1)
0.0ms	x	@	0	(-.f64 (exp.f64 (*.f64 2 x)) 1)

rewrite105.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`prod-diff_binary64`
497×	`log-prod_binary64`
257×	`pow2_binary64`
222×	`fma-def_binary64`
210×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	237	23
2	3178	23

Stop Event

1×	node limit

Counts

4 → 256

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

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

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-l_binary64`
565×	`associate-r_binary64`
525×	`cancel-sign-sub-inv_binary64`
436×	`fma-neg_binary64`
328×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	272
1	166	236
2	496	226
3	1638	203
4	6360	203

Stop Event

1×	node limit

Counts

272 → 285

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(*.f64 2 x)
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (.f64 2 x))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))

Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x))
(.f64 2 (+.f64 (.f64 x x) x))
(*.f64 2 (fma.f64 x x x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 2 (.f64 x x) (fma.f64 4/3 (pow.f64 x 3) (.f64 x 2)))
(+.f64 (.f64 2 (fma.f64 x x x)) (.f64 (pow.f64 x 3) 4/3))
(fma.f64 2 (fma.f64 x x x) (*.f64 (pow.f64 x 3) 4/3))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (.f64 2 x))))
(fma.f64 2 (.f64 x x) (fma.f64 2/3 (pow.f64 x 4) (fma.f64 4/3 (pow.f64 x 3) (.f64 x 2))))
(+.f64 (fma.f64 (pow.f64 x 4) 2/3 (.f64 (pow.f64 x 3) 4/3)) (.f64 2 (fma.f64 x x x)))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 2 (fma.f64 x x x) (*.f64 (pow.f64 x 3) 4/3)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (/.f64 3/8 (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
2
(+.f64 2 x)
(+.f64 x 2)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 x (fma.f64 x (*.f64 x 1/2) 2))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 x (fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/2) 2)))

eval189.0ms (2.6%)

Compiler: Compiled 7073 to 4471 computations (36.8% saved)

prune67.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	352	4	356
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	353	5	358

Error

Counts

358 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.6b	(sqrt.f64 (+.f64 x 2))
▶	21.5b	(sqrt.f64 2)
▶	25.4b	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 31 to 27 computations (12.9% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 x))
✓	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 19 to 9 computations (52.6% saved)

series57.0ms (0.8%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	x	@	inf	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
20.0ms	x	@	-inf	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
1.0ms	x	@	0	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
0.0ms	x	@	0	(log1p.f64 (exp.f64 x))
0.0ms	x	@	inf	(log1p.f64 (exp.f64 x))

rewrite51.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`pow1_binary64`
525×	`add-sqr-sqrt_binary64`
500×	`add-log-exp_binary64`
500×	`expm1-log1p-u_binary64`
499×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	131	13
2	1430	13

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

Inputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(log1p.f64 (exp.f64 x))

Outputs

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

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

simplify118.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
574×	`fma-def_binary64`
490×	`distribute-lft-out_binary64`
386×	`*-commutative_binary64`
382×	`associate-/l/_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	41	230
1	102	228
2	235	222
3	649	202
4	2220	199
5	3448	198
6	5140	198
7	5517	198
8	6461	198

Stop Event

1×	node limit

Counts

61 → 54

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (log.f64 2)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 2) (.f64 (.f64 x x) 3/32))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (.f64 x (.f64 x 3/32)))))
(fma.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 x 3/32))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 1/4 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 2) (*.f64 (pow.f64 x 3) 7/384)))))
(+.f64 (sqrt.f64 2) (fma.f64 (sqrt.f64 2) (.f64 x (.f64 x 3/32)) (.f64 (sqrt.f64 2) (+.f64 (.f64 7/384 (pow.f64 x 3)) (*.f64 1/4 x)))))
(fma.f64 (sqrt.f64 2) (.f64 (.f64 x x) (+.f64 (.f64 x 7/384) 3/32)) (.f64 (sqrt.f64 2) (fma.f64 1/4 x 1)))
(.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/4 x 1) (.f64 x (.f64 x (+.f64 3/32 (.f64 x 7/384))))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(fma.f64 1/2 x (log.f64 2))
(fma.f64 x 1/2 (log.f64 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (log.f64 2)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (log.f64 2)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 x 1/2 (log.f64 2)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (log.f64 2)))
(fma.f64 x (fma.f64 x 1/8 1/2) (log.f64 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 x 1/2 (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (fma.f64 x 1/8 1/2) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2)))
(fma.f64 -1/192 (pow.f64 x 4) (fma.f64 x (fma.f64 x 1/8 1/2) (log.f64 2)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))

localize2.0ms (0%)

Compiler: Compiled 4 to 4 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 2))

Compiler

Compiled 10 to 7 computations (30% saved)

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sqrt.f64 (+.f64 x 2))
1.0ms	x	@	0	(sqrt.f64 (+.f64 x 2))
1.0ms	x	@	-inf	(sqrt.f64 (+.f64 x 2))

rewrite51.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`pow1_binary64`
514×	`add-log-exp_binary64`
513×	`log1p-expm1-u_binary64`
513×	`expm1-log1p-u_binary64`
504×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	111	6
2	1367	6

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x 2))

Outputs

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

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1230×	`associate-/l/_binary64`
989×	`fma-def_binary64`
558×	`unswap-sqr_binary64`
360×	`times-frac_binary64`
349×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	90
1	67	82
2	188	78
3	578	70
4	2939	66
5	4279	66
6	5352	66
7	6287	66
8	6557	66
9	6855	66

Stop Event

1×	node limit

Counts

26 → 29

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2)))

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓	0.4b	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 25 to 21 computations (16% saved)

series3.0ms (0%)

Counts

2 → 3

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 x (sqrt.f64 2))
1.0ms	x	@	inf	(/.f64 x (sqrt.f64 2))
1.0ms	x	@	-inf	(/.f64 x (sqrt.f64 2))
0.0ms	x	@	0	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
0.0ms	x	@	inf	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))

rewrite71.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

953×	`pow1_binary64`
893×	`add-log-exp_binary64`
892×	`log1p-expm1-u_binary64`
892×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	179	18
2	2388	18

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs
(/.f64 x (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))

Outputs

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

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	10	21
2	14	21
3	18	21
4	19	21

Stop Event

1×

saturated

Counts

71 → 70

Calls

Call 1

Inputs
(sqrt.f64 2)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))

Outputs
(sqrt.f64 2)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))

eval79.0ms (1.1%)

Compiler: Compiled 1858 to 1528 computations (17.8% saved)

prune23.0ms (0.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	150	8	158

Error

Counts

158 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
▶	61.9b	(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
✓	25.6b	(sqrt.f64 (+.f64 x 2))
✓	21.5b	(sqrt.f64 2)
▶	24.7b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	26.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
✓	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 67 to 57 computations (14.9% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.4b	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 16 to 13 computations (18.8% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/4 (*.f64 x 3/32))
✓	0.1b	(.f64 x (+.f64 1/4 (.f64 x 3/32)))
✓	0.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))

Compiler

Compiled 44 to 35 computations (20.5% saved)

series24.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
21.0ms	x	@	0	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
1.0ms	x	@	inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
1.0ms	x	@	inf	(.f64 x (+.f64 1/4 (.f64 x 3/32)))
0.0ms	x	@	0	(.f64 x (+.f64 1/4 (.f64 x 3/32)))

rewrite88.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`prod-diff_binary64`
554×	`log-prod_binary64`
447×	`fma-def_binary64`
216×	`pow1/3_binary64`
213×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	266	27
2	3444	27

Stop Event

1×	node limit

Counts

3 → 168

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
(.f64 x (+.f64 1/4 (.f64 x 3/32)))
(+.f64 1/4 (*.f64 x 3/32))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x (fma.f64 x 3/32 1/4) 1)) (sqrt.f64 2))) (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x (fma.f64 x 3/32 1/4) 1)) (sqrt.f64 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x (fma.f64 x 3/32 1/4) 1)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x (fma.f64 x 3/32 1/4) 1)) (sqrt.f64 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x (fma.f64 x 3/32 1/4) 1)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 2 (sqrt.f64 2) (pow.f64 (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))) 3)) (+.f64 2 (-.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))) (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))) (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4))))) (-.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (*.f64 x (fma.f64 x 3/32 1/4)) 3)) (sqrt.f64 2)) (fma.f64 (*.f64 x (fma.f64 x 3/32 1/4)) (fma.f64 x (fma.f64 x 3/32 1/4) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 3/32 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/16 (+.f64 1/4 (*.f64 -3/32 x))) (/.f64 (*.f64 (*.f64 x x) 9/1024) (+.f64 1/4 (*.f64 -3/32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 3/32 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 3/32 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 3/32 1/4)) (pow.f64 (cbrt.f64 (fma.f64 x 3/32 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 3/32 1/4)) 2) (cbrt.f64 (fma.f64 x 3/32 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 3/32 1/4)) (sqrt.f64 (fma.f64 x 3/32 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3) 27/32768 1/64) (/.f64 1 (fma.f64 (*.f64 x 3/32) (fma.f64 x 3/32 -1/4) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/16 (*.f64 (*.f64 x x) 9/1024)) (/.f64 1 (+.f64 1/4 (*.f64 -3/32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 x 3/32) (fma.f64 x 3/32 -1/4) 1/16) (fma.f64 (pow.f64 x 3) 27/32768 1/64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (*.f64 -3/32 x)) (-.f64 1/16 (*.f64 (*.f64 x x) 9/1024))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 27/32768 1/64) (fma.f64 (*.f64 x 3/32) (fma.f64 x 3/32 -1/4) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 27/32768 1/64) (fma.f64 (*.f64 x x) 9/1024 (-.f64 1/16 (*.f64 3/128 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/16 (*.f64 (*.f64 x x) 9/1024)) (+.f64 1/4 (*.f64 -3/32 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3) 27/32768 1/64)) (neg.f64 (fma.f64 (*.f64 x 3/32) (fma.f64 x 3/32 -1/4) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/16 (*.f64 (*.f64 x x) 9/1024))) (neg.f64 (+.f64 1/4 (*.f64 -3/32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (*.f64 x x) 9/1024 -1/16) (fma.f64 x 3/32 -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 3/32 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 3/32 1/4) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 3/32 1/4)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 3/32 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 x 3/32) (fma.f64 x 3/32 -1/4) 1/16) (fma.f64 (pow.f64 x 3) 27/32768 1/64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1/4 (*.f64 -3/32 x)) (-.f64 1/16 (*.f64 (*.f64 x x) 9/1024))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 3/32 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 3/32 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 3/32 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 3/32 1/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 3/32 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 3/32 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 3/32 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 3/32 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 3/32) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 3/32 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 3/32 x 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 3/32) 1 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 3/32)) (cbrt.f64 (*.f64 (*.f64 x x) 9/1024)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 9/1024)) (cbrt.f64 (*.f64 x 3/32)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) 3/32) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 3/32)) (sqrt.f64 (*.f64 x 3/32)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 3/32) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 3/32 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 3/32 (sqrt.f64 x)) (sqrt.f64 x) 1/4)))))

simplify172.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
751×	`sqr-pow_binary64`
610×	`fabs-mul_binary64`
584×	`cube-prod_binary64`
378×	`associate-l_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	428
1	44	408
2	85	317
3	176	303
4	472	303
5	1415	291
6	2375	291
7	3029	291
8	3147	291
9	3282	291
10	3451	291
11	3692	291
12	4009	291
13	4379	291
14	4836	291
15	5429	291
16	6139	291
17	6999	291
18	7425	291
19	7739	291

Stop Event

1×	node limit

Counts

204 → 186

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(*.f64 1/4 x)
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(*.f64 3/32 (pow.f64 x 2))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(*.f64 3/32 (pow.f64 x 2))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
1/4
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 3/32 x))
(*.f64 3/32 x)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 3/32 x))
(*.f64 3/32 x)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 3/32 x))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4))))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4))))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (sqrt.f64 2) (.f64 x (*.f64 x 3/32)))
(.f64 (.f64 x x) (*.f64 (sqrt.f64 2) 3/32))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x))))
(.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4)))
(.f64 (.f64 (sqrt.f64 2) x) (fma.f64 x 3/32 1/4))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4))))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4))))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (sqrt.f64 2) (.f64 x (*.f64 x 3/32)))
(.f64 (.f64 x x) (*.f64 (sqrt.f64 2) 3/32))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x))))
(.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4)))
(.f64 (.f64 (sqrt.f64 2) x) (fma.f64 x 3/32 1/4))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4))))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (fma.f64 x 3/32 1/4))))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x (fma.f64 x 3/32 1/4) 1))
(*.f64 1/4 x)
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(.f64 x (.f64 x 3/32))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(.f64 x (.f64 x 3/32))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 3/32 (.f64 x x) (.f64 1/4 x))
(*.f64 x (fma.f64 x 3/32 1/4))
1/4
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(*.f64 3/32 x)
(*.f64 x 3/32)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(*.f64 3/32 x)
(*.f64 x 3/32)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)
(+.f64 1/4 (*.f64 3/32 x))
(+.f64 1/4 (*.f64 x 3/32))
(fma.f64 x 3/32 1/4)

localize56.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (*.f64 x 7/384)))))
✓	0.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
✓	0.1b	(.f64 x (+.f64 3/32 (.f64 x 7/384)))
✓	0.5b	(*.f64 x 7/384)

Compiler

Compiled 73 to 57 computations (21.9% saved)

series12.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(*.f64 x 7/384)
1.0ms	x	@	0	(*.f64 x 7/384)
1.0ms	x	@	-inf	(.f64 x (+.f64 3/32 (.f64 x 7/384)))
1.0ms	x	@	inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
1.0ms	x	@	inf	(.f64 x (+.f64 3/32 (.f64 x 7/384)))

rewrite120.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

739×	`log-prod_binary64`
615×	`fma-def_binary64`
280×	`expm1-udef_binary64`
280×	`log1p-udef_binary64`
247×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	343	42
2	4644	42

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

Inputs
(*.f64 x 7/384)
(.f64 x (+.f64 3/32 (.f64 x 7/384)))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
(.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (*.f64 x 7/384)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x 7/384))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 7/384)) (cbrt.f64 (pow.f64 (exp.f64 x) 7/384)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 7/384))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 7/384))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 7/384))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x 7/384))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x 7/384) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x 7/384)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x 7/384)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x 7/384) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x 7/384) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 7/384))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x 7/384))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x 7/384) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x 7/384)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x 7/384)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x 7/384)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 x 7/384)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x (fma.f64 x 7/384 3/32)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (.f64 x 7/384)) (.f64 x 3/32))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x 3/32) (.f64 x (.f64 x 7/384)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x 3/32) 1) (.f64 (.f64 x (.f64 x 7/384)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 7/384 3/32))) (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 7/384 3/32))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 7/384 3/32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 7/384 3/32)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 7/384 3/32)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (fma.f64 x 7/384 3/32)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x 3/32) 3) (pow.f64 (.f64 x 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3/32))) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x (fma.f64 x 7/384 3/32))) (sqrt.f64 x)) (.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/4 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 x (.f64 x (fma.f64 x 7/384 3/32))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/4 (sqrt.f64 x)) (sqrt.f64 x) (.f64 x (.f64 x (fma.f64 x 7/384 3/32))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x 7/384 3/32))) 2)) (cbrt.f64 (.f64 x (fma.f64 x 7/384 3/32))) (.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (sqrt.f64 (.f64 x (fma.f64 x 7/384 3/32)))) (sqrt.f64 (.f64 x (fma.f64 x 7/384 3/32))) (.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 x (fma.f64 x 7/384 3/32)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 x (fma.f64 x 7/384 3/32)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/4))))))

simplify174.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

580×	`*-commutative_binary64`
509×	`fma-def_binary64`
494×	`distribute-lft-out_binary64`
444×	`associate-+l+_binary64`
442×	`sqr-pow_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	33	625
1	88	623
2	203	557
3	522	465
4	1823	462
5	2730	459
6	3558	459
7	3674	459
8	3879	459
9	4159	459
10	4799	459
11	5937	459
12	7543	459

Stop Event

1×	node limit

Counts

241 → 221

Calls

Call 1

Inputs
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 3/32 x)
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(*.f64 7/384 (pow.f64 x 2))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(*.f64 7/384 (pow.f64 x 2))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(*.f64 1/4 x)
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(*.f64 7/384 (pow.f64 x 3))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(*.f64 7/384 (pow.f64 x 3))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (.f64 3/32 (pow.f64 x 2)))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))

Outputs
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 7/384 x)
(*.f64 3/32 x)
(*.f64 x 3/32)
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(*.f64 7/384 (pow.f64 x 2))
(.f64 7/384 (.f64 x x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(*.f64 7/384 (pow.f64 x 2))
(.f64 7/384 (.f64 x x))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(+.f64 (.f64 7/384 (pow.f64 x 2)) (.f64 3/32 x))
(fma.f64 7/384 (.f64 x x) (.f64 x 3/32))
(.f64 x (+.f64 3/32 (.f64 7/384 x)))
(*.f64 x (fma.f64 7/384 x 3/32))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 x (sqrt.f64 2))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 (sqrt.f64 2) (*.f64 x 1/4) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (.f64 1/4 (.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (.f64 x (.f64 (sqrt.f64 2) 1/4))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
(fma.f64 x (*.f64 (sqrt.f64 2) (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (+.f64 (.f64 x (fma.f64 x 3/32 1/4)) 1))
(fma.f64 (sqrt.f64 2) (*.f64 x (fma.f64 x 3/32 1/4)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 1/4 (*.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 x (*.f64 (sqrt.f64 2) 1/4)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 x 3/32))))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 x (fma.f64 7/384 x 3/32))))))
(.f64 (sqrt.f64 2) (+.f64 (fma.f64 x 1/4 1) (.f64 x (*.f64 x (fma.f64 7/384 x 3/32)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 x (+.f64 (*.f64 x (fma.f64 7/384 x 3/32)) 1/4)) 1))
(.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2)))))
(.f64 (sqrt.f64 2) (.f64 x (.f64 x (+.f64 3/32 (.f64 7/384 x)))))
(.f64 (.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 x 3/32))
(.f64 (.f64 x (fma.f64 7/384 x 3/32)) (*.f64 x (sqrt.f64 2)))
(.f64 (.f64 x x) (*.f64 (sqrt.f64 2) (fma.f64 7/384 x 3/32)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 1/4 (*.f64 x (sqrt.f64 2)))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 x (*.f64 (sqrt.f64 2) 1/4))))
(fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 x 3/32)))))
(.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 x (fma.f64 7/384 x 3/32)))))
(.f64 x (.f64 (sqrt.f64 2) (+.f64 (*.f64 x (fma.f64 7/384 x 3/32)) 1/4)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 1/4 (*.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 x (*.f64 (sqrt.f64 2) 1/4)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 x 3/32))))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 x (fma.f64 7/384 x 3/32))))))
(.f64 (sqrt.f64 2) (+.f64 (fma.f64 x 1/4 1) (.f64 x (*.f64 x (fma.f64 7/384 x 3/32)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 x (+.f64 (*.f64 x (fma.f64 7/384 x 3/32)) 1/4)) 1))
(.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2)))))
(.f64 (sqrt.f64 2) (.f64 x (.f64 x (+.f64 3/32 (.f64 7/384 x)))))
(.f64 (.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 x 3/32))
(.f64 (.f64 x (fma.f64 7/384 x 3/32)) (*.f64 x (sqrt.f64 2)))
(.f64 (.f64 x x) (*.f64 (sqrt.f64 2) (fma.f64 7/384 x 3/32)))
(+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 1/4 (*.f64 x (sqrt.f64 2)))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 x (*.f64 (sqrt.f64 2) 1/4))))
(fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 x 3/32)))))
(.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 x (fma.f64 7/384 x 3/32)))))
(.f64 x (.f64 (sqrt.f64 2) (+.f64 (*.f64 x (fma.f64 7/384 x 3/32)) 1/4)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (.f64 x x) (sqrt.f64 2)) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 1/4 (*.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 x (*.f64 (sqrt.f64 2) 1/4)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 x 3/32))))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 x (fma.f64 7/384 x 3/32))))))
(.f64 (sqrt.f64 2) (+.f64 (fma.f64 x 1/4 1) (.f64 x (*.f64 x (fma.f64 7/384 x 3/32)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 x (+.f64 (*.f64 x (fma.f64 7/384 x 3/32)) 1/4)) 1))
(*.f64 1/4 x)
(*.f64 x 1/4)
(+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 1/4 x (.f64 3/32 (.f64 x x)))
(fma.f64 x 1/4 (.f64 x (.f64 x 3/32)))
(.f64 x (+.f64 1/4 (.f64 x 3/32)))
(*.f64 x (fma.f64 x 3/32 1/4))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 1/4 x (.f64 3/32 (.f64 x x))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 x 1/4 (.f64 x (.f64 x 3/32))))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (+.f64 1/4 (.f64 x 3/32))))
(.f64 x (+.f64 1/4 (.f64 x (fma.f64 7/384 x 3/32))))
(.f64 x (+.f64 (.f64 x (fma.f64 7/384 x 3/32)) 1/4))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 1/4 x (.f64 3/32 (.f64 x x))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 x 1/4 (.f64 x (.f64 x 3/32))))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (+.f64 1/4 (.f64 x 3/32))))
(.f64 x (+.f64 1/4 (.f64 x (fma.f64 7/384 x 3/32))))
(.f64 x (+.f64 (.f64 x (fma.f64 7/384 x 3/32)) 1/4))
(*.f64 7/384 (pow.f64 x 3))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 7/384 (pow.f64 x 3) (.f64 3/32 (.f64 x x)))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (.f64 x 3/32)))
(.f64 x (.f64 x (+.f64 3/32 (*.f64 7/384 x))))
(.f64 x (.f64 x (fma.f64 7/384 x 3/32)))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 1/4 x (.f64 3/32 (.f64 x x))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 x 1/4 (.f64 x (.f64 x 3/32))))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (+.f64 1/4 (.f64 x 3/32))))
(.f64 x (+.f64 1/4 (.f64 x (fma.f64 7/384 x 3/32))))
(.f64 x (+.f64 (.f64 x (fma.f64 7/384 x 3/32)) 1/4))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 1/4 x (.f64 3/32 (.f64 x x))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 x 1/4 (.f64 x (.f64 x 3/32))))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (+.f64 1/4 (.f64 x 3/32))))
(.f64 x (+.f64 1/4 (.f64 x (fma.f64 7/384 x 3/32))))
(.f64 x (+.f64 (.f64 x (fma.f64 7/384 x 3/32)) 1/4))
(*.f64 7/384 (pow.f64 x 3))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (.f64 3/32 (pow.f64 x 2)))
(fma.f64 7/384 (pow.f64 x 3) (.f64 3/32 (.f64 x x)))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (.f64 x 3/32)))
(.f64 x (.f64 x (+.f64 3/32 (*.f64 7/384 x))))
(.f64 x (.f64 x (fma.f64 7/384 x 3/32)))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 1/4 x (.f64 3/32 (.f64 x x))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 x 1/4 (.f64 x (.f64 x 3/32))))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (+.f64 1/4 (.f64 x 3/32))))
(.f64 x (+.f64 1/4 (.f64 x (fma.f64 7/384 x 3/32))))
(.f64 x (+.f64 (.f64 x (fma.f64 7/384 x 3/32)) 1/4))
(+.f64 (.f64 7/384 (pow.f64 x 3)) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 1/4 x (.f64 3/32 (.f64 x x))))
(fma.f64 7/384 (pow.f64 x 3) (fma.f64 x 1/4 (.f64 x (.f64 x 3/32))))
(fma.f64 7/384 (pow.f64 x 3) (.f64 x (+.f64 1/4 (.f64 x 3/32))))
(.f64 x (+.f64 1/4 (.f64 x (fma.f64 7/384 x 3/32))))
(.f64 x (+.f64 (.f64 x (fma.f64 7/384 x 3/32)) 1/4))

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 2))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 2)))
✓	0.6b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)

Compiler

Compiled 25 to 20 computations (20% saved)

series4.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 1 (sqrt.f64 (+.f64 x 2)))
1.0ms	x	@	inf	(+.f64 1 (sqrt.f64 (+.f64 x 2)))
1.0ms	x	@	-inf	(+.f64 1 (sqrt.f64 (+.f64 x 2)))
1.0ms	x	@	inf	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
1.0ms	x	@	0	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)

rewrite108.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`pow1_binary64`
855×	`add-log-exp_binary64`
854×	`log1p-expm1-u_binary64`
854×	`expm1-log1p-u_binary64`
841×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	186	15
2	2598	15

Stop Event

1×	node limit

Counts

2 → 78

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
(+.f64 1 (sqrt.f64 (+.f64 x 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (sqrt.f64 (+.f64 x 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 2)) (cbrt.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 2))) (cbrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 2) 1/4) (pow.f64 (+.f64 x 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) (+.f64 (sqrt.f64 (+.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) -1) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 (+.f64 x 2) 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 x 2) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) (+.f64 (sqrt.f64 (+.f64 x 2)) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) 2) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) (+.f64 (sqrt.f64 (+.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) -1) (+.f64 (sqrt.f64 (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) -1) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -4)) (sqrt.f64 (+.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 4 (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) (+.f64 (sqrt.f64 (+.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 2) -1)) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) -1) (+.f64 (sqrt.f64 (+.f64 x 2)) -1)) (+.f64 (sqrt.f64 (+.f64 x 2)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) -1) (+.f64 (sqrt.f64 (+.f64 x 2)) -1))) (-.f64 1 (+.f64 (sqrt.f64 (+.f64 x 2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 x 2) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 2) 1/4)) -1)))))

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

simplify130.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1221×	`associate-/l/_binary64`
942×	`associate-/r/_binary64`
558×	`unswap-sqr_binary64`
548×	`fma-def_binary64`
360×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	192
1	90	176
2	251	168
3	744	152
4	3437	152
5	4069	152
6	5142	152
7	5401	152
8	5644	152
9	5945	152

Stop Event

1×	node limit

Counts

86 → 92

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 -1/16 x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 -1/16 x)))))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) 1))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 1/2 (sqrt.f64 2)) x 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) 1)))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) 1)))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 -1/16 x))) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2))))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))))) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) 1))))
(+.f64 (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) 1)))
(+.f64 (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 -1/16 x))) (+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) 1)))

eval505.0ms (6.9%)

Compiler: Compiled 9908 to 8020 computations (19.1% saved)

prune209.0ms (2.9%)

Pruning

13 alts after pruning (6 fresh and 7 done)

	Pruned	Kept	Total
New	554	6	560
Fresh	0	0	0
Picked	1	0	1
Done	0	7	7
Total	555	13	568

Error

Counts

568 → 13

Alt Table

Click to see full alt table

Status	Error	Program
▶	61.9b	(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
▶	22.1b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓	25.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
✓	61.9b	(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
✓	24.7b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
▶	25.4b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
✓	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
▶	25.8b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
✓	25.6b	(sqrt.f64 (+.f64 x 2))
✓	21.5b	(sqrt.f64 2)
	25.5b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 7/384 (.f64 x x))))))
▶	61.4b	(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 176 to 149 computations (15.3% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)

Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite78.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`pow1_binary64`
516×	`add-log-exp_binary64`
515×	`log1p-expm1-u_binary64`
515×	`expm1-log1p-u_binary64`
507×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	138	3
2	1749	3

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

Inputs
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)

Outputs

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

42 → 42

Calls

Call 1

Inputs

Outputs

localize21.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 2 -1/2) x)

Compiler

Compiled 20 to 17 computations (15% saved)

series4.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite76.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

515×	`pow1_binary64`
504×	`add-sqr-sqrt_binary64`
480×	`add-log-exp_binary64`
479×	`log1p-expm1-u_binary64`
479×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	126	6
2	1349	6

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(*.f64 (pow.f64 2 -1/2) x)

Outputs

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

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

23 → 12

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)

Outputs
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)

localize47.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
✓	0.6b	(.f64 x (.f64 (sqrt.f64 2) 3/32))
✓	1.0b	(*.f64 (sqrt.f64 2) 3/32)

Compiler

Compiled 24 to 20 computations (16.7% saved)

series6.0ms (0.1%)

Counts

3 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 x (.f64 (sqrt.f64 2) 3/32))
1.0ms	x	@	0	(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
1.0ms	x	@	0	(.f64 x (.f64 (sqrt.f64 2) 3/32))
1.0ms	x	@	inf	(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
1.0ms	x	@	-inf	(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))

rewrite103.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

710×	`pow1_binary64`
661×	`add-log-exp_binary64`
661×	`log1p-expm1-u_binary64`
661×	`expm1-log1p-u_binary64`
648×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	164	18
2	1835	18

Stop Event

1×	node limit

Counts

3 → 37

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) 3/32)
(.f64 x (.f64 (sqrt.f64 2) 3/32))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 9/512)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 9/512) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 27/16384 (sqrt.f64 2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 9/512)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 9/512)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 9/512)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 9/512)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 27/16384 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 9/512)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 9/512)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 9/512)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 9/512) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 9/512) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 9/512) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 9/512) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 9/512) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 9/512 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 9/512)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 9/512) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 27/16384 (sqrt.f64 2)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (*.f64 27/16384 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 9/512) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 9/512) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 9/512) x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 9/512) (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (sqrt.f64 9/512))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 9/512)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 (sqrt.f64 9/512) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 9/512) x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 9/512) (*.f64 x x))))))))

simplify197.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2020×	`unswap-sqr_binary64`
1080×	`sqr-pow_binary64`
636×	`fabs-mul_binary64`
612×	`pow-sqr_binary64`
610×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	252
1	22	252
2	45	252
3	87	252
4	236	252
5	817	252
6	1053	252
7	1467	252
8	1566	252
9	1701	252
10	1870	252
11	2113	252
12	2428	252
13	2800	252
14	3258	252
15	3843	252
16	4551	252
17	5407	252
18	5835	252
19	6153	252
20	6459	252
21	6537	252
22	6571	252

Stop Event

1×	node limit

Counts

61 → 40

Calls

Call 1

Inputs
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))

Outputs
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (sqrt.f64 2) (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 3/32 (sqrt.f64 2)))
(.f64 x (.f64 3/32 (*.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))

localize39.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))

Compiler

Compiled 23 to 19 computations (17.4% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
1.0ms	x	@	inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))

rewrite84.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`pow1_binary64`
796×	`add-log-exp_binary64`
795×	`log1p-expm1-u_binary64`
795×	`expm1-log1p-u_binary64`
781×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	189	10
2	2252	10

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (*.f64 x 1/4)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (*.f64 (sqrt.f64 2) (*.f64 x 1/4)) 3)) (+.f64 2 (-.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x 1/4)) (*.f64 (sqrt.f64 2) (*.f64 x 1/4))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x 1/4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x 1/4)) (*.f64 (sqrt.f64 2) (*.f64 x 1/4)))) (-.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 x 3) 1/64)) (sqrt.f64 2)) (+.f64 1 (+.f64 (pow.f64 (*.f64 x 1/4) 2) (*.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (*.f64 x 1/4) 2)) (sqrt.f64 2)) (+.f64 1 (*.f64 -1/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 (pow.f64 x 3) 1/64))) (+.f64 1 (+.f64 (pow.f64 (*.f64 x 1/4) 2) (*.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (pow.f64 (*.f64 x 1/4) 2))) (+.f64 1 (*.f64 -1/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (pow.f64 (fma.f64 x 1/4 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (fma.f64 x 1/4 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (fma.f64 x 1/4 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x 1/4 1) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 2) 1 (*.f64 (sqrt.f64 2) (*.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (*.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) (*.f64 (sqrt.f64 2) (*.f64 x 1/4)))))))

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
10×	`associate-r_binary64`
10×	`associate-l_binary64`
6×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	147
1	13	129
2	23	129
3	32	111
4	38	111
5	44	111
6	58	111
7	81	111
8	85	111
9	87	111

Stop Event

1×

saturated

Counts

38 → 31

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(.f64 1/4 (.f64 (sqrt.f64 2) x))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(.f64 1/4 (.f64 (sqrt.f64 2) x))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(.f64 1/4 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 x 1/4))
(.f64 (sqrt.f64 2) (.f64 1/4 x))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(.f64 1/4 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 x 1/4))
(.f64 (sqrt.f64 2) (.f64 1/4 x))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(.f64 (+.f64 (.f64 1/4 x) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))

localize32.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
✓	0.1b	(.f64 x (.f64 x 3/32))

Compiler

Compiled 32 to 24 computations (25% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
1.0ms	x	@	inf	(.f64 x (.f64 x 3/32))
1.0ms	x	@	0	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
1.0ms	x	@	0	(.f64 x (.f64 x 3/32))
0.0ms	x	@	-inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))

rewrite140.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`pow1_binary64`
905×	`add-log-exp_binary64`
904×	`log1p-expm1-u_binary64`
904×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	210	20
2	2551	20

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(.f64 x (.f64 x 3/32))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 x (*.f64 x 3/32) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 3/32)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 3/32))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 3/32)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 27/32768) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x 3/32)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x 3/32)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x 3/32)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 27/32768))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 3/32))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 3/32))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 3/32))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) (*.f64 (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))) 3)) (+.f64 2 (-.f64 (*.f64 (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 2 (*.f64 (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))))) (-.f64 (sqrt.f64 2) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 27/32768)) (sqrt.f64 2)) (+.f64 1 (-.f64 (pow.f64 (*.f64 x (*.f64 x 3/32)) 2) (*.f64 x (*.f64 x 3/32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (*.f64 x (*.f64 x 3/32)) 2)) (sqrt.f64 2)) (-.f64 1 (*.f64 x (*.f64 x 3/32))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 27/32768))) (+.f64 1 (-.f64 (pow.f64 (*.f64 x (*.f64 x 3/32)) 2) (*.f64 x (*.f64 x 3/32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (pow.f64 (*.f64 x (*.f64 x 3/32)) 2))) (-.f64 1 (*.f64 x (*.f64 x 3/32))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 3/32))) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (pow.f64 (fma.f64 x (*.f64 x 3/32) 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (fma.f64 x (*.f64 x 3/32) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (fma.f64 x (*.f64 x 3/32) 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x (*.f64 x 3/32) 1) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (fma.f64 x (*.f64 x 3/32) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 2) 1 (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 2) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) (*.f64 x (*.f64 (*.f64 x 3/32) (sqrt.f64 2))))))))

simplify208.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

2020×	`unswap-sqr_binary64`
1080×	`sqr-pow_binary64`
643×	`fabs-mul_binary64`
612×	`pow-sqr_binary64`
610×	`cube-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	264
1	21	246
2	46	246
3	102	228
4	285	228
5	904	228
6	1289	228
7	1705	228
8	1804	228
9	1937	228
10	2106	228
11	2347	228
12	2662	228
13	3032	228
14	3489	228
15	4080	228
16	4790	228
17	5650	228
18	6076	228
19	6394	228
20	6704	228
21	6788	228
22	6824	228

Stop Event

1×	node limit

Counts

63 → 46

Calls

Call 1

Inputs
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(*.f64 3/32 (pow.f64 x 2))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))

Outputs
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(*.f64 3/32 (pow.f64 x 2))
(.f64 3/32 (.f64 x x))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2)))
(.f64 (.f64 3/32 (*.f64 x x)) (sqrt.f64 2))
(.f64 x (.f64 (sqrt.f64 2) (*.f64 3/32 x)))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)))
(.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2)))
(.f64 (.f64 3/32 (*.f64 x x)) (sqrt.f64 2))
(.f64 x (.f64 (sqrt.f64 2) (*.f64 3/32 x)))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (.f64 3/32 (.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 3/32 (.f64 x (.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(.f64 (+.f64 (.f64 3/32 (*.f64 x x)) 1) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 x x) 1))

eval127.0ms (1.7%)

Compiler: Compiled 1844 to 1586 computations (14% saved)

prune31.0ms (0.4%)

Pruning

13 alts after pruning (3 fresh and 10 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	1	1
Picked	0	1	1
Done	2	9	11
Total	171	13	184

Error

Counts

184 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.7b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
✓	25.4b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
	61.4b	(.f64 x (.f64 x (sqrt.f64 9/512)))
✓	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
✓	25.8b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
✓	25.6b	(sqrt.f64 (+.f64 x 2))
✓	21.5b	(sqrt.f64 2)
✓	22.1b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
	61.4b	(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
✓	25.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
	25.5b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 7/384 (.f64 x x))))))
✓	61.4b	(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 118 to 98 computations (16.9% saved)

regimes37.0ms (0.5%)

Counts

18 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 x 2))
(.f64 x (.f64 x (sqrt.f64 9/512)))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 7/384 (.f64 x x))))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Calls

5 calls:

10.0ms	x
10.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
4.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
4.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
4.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
0.0b	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
0.0b	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`
0.0b	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Compiler

Compiled 200 to 163 computations (18.5% saved)

regimes23.0ms (0.3%)

Counts

14 → 2

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 x 2))
(.f64 x (.f64 x (sqrt.f64 9/512)))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 7/384 (.f64 x x))))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))

Outputs
(sqrt.f64 2)
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))

Calls

1 calls:

18.0ms

Results

Error	Segments	Branch
20.2b	2	`x`

Compiler

Compiled 118 to 96 computations (18.6% saved)

bsearch53.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
53.0ms	-10.621655339931833	-1.1094726718419596

Compiler

Compiled 17 to 14 computations (17.6% saved)

regimes28.0ms (0.4%)

Counts

13 → 2

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 x 2))
(.f64 x (.f64 x (sqrt.f64 9/512)))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 7/384 (.f64 x x))))))

Outputs
(sqrt.f64 2)
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))

Calls

1 calls:

21.0ms

Results

Error	Segments	Branch
20.4b	2	`x`

Compiler

Compiled 102 to 83 computations (18.6% saved)

bsearch57.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
57.0ms	-10.621655339931833	-1.1094726718419596

Compiler

Compiled 17 to 14 computations (17.6% saved)

regimes23.0ms (0.3%)

Accuracy

Total -40.9b remaining (-190.2%)

Threshold costs -40.9b (-190.2%)

Counts

11 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 x 2))
(.f64 x (.f64 x (sqrt.f64 9/512)))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
(.f64 (.f64 (sqrt.f64 2) x) (*.f64 3/32 x))
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
(.f64 x (.f64 x (*.f64 (sqrt.f64 2) 3/32)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)
(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (*.f64 x 3/32))))

Outputs
(sqrt.f64 2)

Calls

1 calls:

17.0ms

Results

Error	Segments	Branch
21.5b	1	`x`

Compiler

Compiled 76 to 62 computations (18.4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	71
1	43	71

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(if (<=.f64 x -5979460378871855/562949953421312) (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384))))))))
(if (<=.f64 x -5979460378871855/562949953421312) (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32))))))
(sqrt.f64 2)

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(if (<=.f64 x -5979460378871855/562949953421312) (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384))))))))
(if (<=.f64 x -5979460378871855/562949953421312) (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32))))))
(sqrt.f64 2)

Compiler

Compiled 51 to 43 computations (15.7% saved)

soundness114.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-/l*_binary64`
580×	`associate-l_binary64`
568×	`associate-r_binary64`
505×	`associate-/r*_binary64`
380×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	127	11
5	349	8
6	1341	8

Stop Event

1×	node limit

Compiler

Compiled 92 to 70 computations (23.9% saved)

end48.0ms (0.7%)

Compiler: Compiled 48 to 40 computations (16.7% saved)

Details

analyze175.0ms (2.4%)

sample2.5s (34.8%)

preprocess65.0ms (0.9%)

simplify31.0ms (0.4%)

eval1.0ms (0%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series3.0ms (0%)

rewrite59.0ms (0.8%)

simplify43.0ms (0.6%)

localize20.0ms (0.3%)

series24.0ms (0.3%)

rewrite105.0ms (1.4%)

simplify63.0ms (0.9%)

eval189.0ms (2.6%)

prune67.0ms (0.9%)

localize10.0ms (0.1%)

series57.0ms (0.8%)

rewrite51.0ms (0.7%)

simplify118.0ms (1.6%)

localize2.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite51.0ms (0.7%)

simplify96.0ms (1.3%)

localize13.0ms (0.2%)

series3.0ms (0%)

rewrite71.0ms (1%)

simplify7.0ms (0.1%)

eval79.0ms (1.1%)

prune23.0ms (0.3%)

localize8.0ms (0.1%)

localize18.0ms (0.3%)

series24.0ms (0.3%)

rewrite88.0ms (1.2%)

simplify172.0ms (2.4%)

localize56.0ms (0.8%)

series12.0ms (0.2%)

rewrite120.0ms (1.6%)

simplify174.0ms (2.4%)

localize22.0ms (0.3%)

series4.0ms (0.1%)

rewrite108.0ms (1.5%)

simplify130.0ms (1.8%)

eval505.0ms (6.9%)

prune209.0ms (2.9%)

localize13.0ms (0.2%)

series0.0ms (0%)

rewrite78.0ms (1.1%)

simplify12.0ms (0.2%)

localize21.0ms (0.3%)

series4.0ms (0.1%)

rewrite76.0ms (1%)

simplify13.0ms (0.2%)

localize47.0ms (0.6%)

series6.0ms (0.1%)

rewrite103.0ms (1.4%)

simplify197.0ms (2.7%)

localize39.0ms (0.5%)

series3.0ms (0%)

rewrite84.0ms (1.2%)

simplify24.0ms (0.3%)

localize32.0ms (0.4%)

series5.0ms (0.1%)

rewrite140.0ms (1.9%)

simplify208.0ms (2.9%)

eval127.0ms (1.7%)

prune31.0ms (0.4%)

regimes37.0ms (0.5%)

regimes23.0ms (0.3%)

bsearch53.0ms (0.7%)

regimes28.0ms (0.4%)

bsearch57.0ms (0.8%)

regimes23.0ms (0.3%)

simplify8.0ms (0.1%)

soundness114.0ms (1.6%)

end48.0ms (0.7%)

Profiling