Details

analyze195.0ms (4.4%)

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)

sample2.2s (50.1%)

Results

1.1s	2754×	body	1024	valid
524.0ms	3843×	body	256	valid
326.0ms	1383×	body	512	valid
140.0ms	276×	body	2048	valid
7.0ms	53×	body	256	infinite
0.0ms	4×	body	256	unsamplable

Bogosity

preprocess39.0ms (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)

simplify106.0ms (2.4%)

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)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

series3.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

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

rewrite51.0ms (1.1%)

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

Outputs
((#(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)))))
((#(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))))))

Outputs

((#(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)))))

((#(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))))))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	169
1	109	137
2	339	131
3	1104	103
4	5462	103

Stop Event

1×	node limit

Counts

66 → 71

Calls

Call 1

Inputs
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)))
(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))))))

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

eval20.0ms (0.5%)

Compiler: Compiled 818 to 581 computations (29% saved)

prune12.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	5	72

Error

Counts

72 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.0b	(sqrt.f64 2)
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.0b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	20.6b	(sqrt.f64 (+.f64 2 x))
▶	0.6b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize13.0ms (0.3%)

Local error

Found 8 expressions with local error:

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

Compiler

Compiled 30 to 20 computations (33.3% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite66.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`pow1_binary64`
832×	`add-log-exp_binary64`
832×	`log1p-expm1-u_binary64`
832×	`expm1-log1p-u_binary64`
816×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	179	19
2	2590	19

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

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

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

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

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
525×	`cancel-sign-sub-inv_binary64`
438×	`fma-neg_binary64`
398×	`associate-r_binary64`
359×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	346
1	118	282
2	354	270
3	1117	222
4	5443	222

Stop Event

1×	node limit

Counts

95 → 93

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))))))
(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)))
(+.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 1/2 (/.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 (+.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)))))))

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 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (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 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (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)))
(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)))
(+.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 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1)
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.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 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) 1))
(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))) (+.f64 (sqrt.f64 2) 1))
(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))) (+.f64 (sqrt.f64 2) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.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) (+.f64 (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))))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (/.f64 (.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) 1)))
(+.f64 (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)))) 1))
(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))) (+.f64 (sqrt.f64 2) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) 1)))

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 10 to 7 computations (30% saved)

series2.0ms (0.1%)

Counts

1 → 4

Calls

3 calls:

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

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`pow1_binary64`
522×	`add-log-exp_binary64`
521×	`log1p-expm1-u_binary64`
521×	`expm1-log1p-u_binary64`
512×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	111	6
2	1381	6

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify114.0ms (2.5%)

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)))

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 13 to 6 computations (53.8% saved)

series3.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

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

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

436×	`pow1_binary64`
417×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
401×	`add-log-exp_binary64`
400×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	109	13
2	1153	13

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

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

Outputs

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

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

simplify113.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
529×	`cancel-sign-sub-inv_binary64`
439×	`fma-neg_binary64`
438×	`associate-r_binary64`
418×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	238
1	122	204
2	363	198
3	1180	168
4	5660	168

Stop Event

1×	node limit

Counts

59 → 57

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))))))
(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)))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))

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 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (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 3/8 (*.f64 x x)))))
(+.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 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (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 3/8 (*.f64 x x)))) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) (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)))
(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)))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) 1/8 1))
(fma.f64 x (fma.f64 x 1/8 1/2) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 1) (.f64 (pow.f64 x 3) 1/48)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 1/2 x (fma.f64 (pow.f64 x 3) 1/48 1)))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 3) 1/48 (fma.f64 1/2 x 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/48 1/8) 1))
(fma.f64 x (fma.f64 x 1/8 1/2) (fma.f64 (pow.f64 x 3) 1/48 1))

localize3.0ms (0.1%)

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

eval186.0ms (4.2%)

Compiler: Compiled 3492 to 2720 computations (22.1% saved)

prune73.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	0	0	0
Picked	0	1	1
Done	2	2	4
Total	248	7	255

Error

Counts

255 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	19.5b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
▶	21.2b	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
✓	17.0b	(sqrt.f64 2)
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	17.7b	(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓	20.6b	(sqrt.f64 (+.f64 2 x))
▶	21.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)

Compiler

Compiled 46 to 41 computations (10.9% saved)

localize12.0ms (0.3%)

Local error

Found 6 expressions with local error:

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

Compiler

Compiled 25 to 20 computations (20% saved)

series3.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

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

rewrite65.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

915×	`pow1_binary64`
862×	`add-log-exp_binary64`
861×	`log1p-expm1-u_binary64`
861×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	186	15
2	2610	15

Stop Event

1×	node limit

Counts

2 → 80

Calls

Call 1

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

Outputs

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

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

simplify102.0ms (2.3%)

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

88 → 94

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)))

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite85.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`pow1_binary64`
536×	`add-log-exp_binary64`
535×	`log1p-expm1-u_binary64`
535×	`expm1-log1p-u_binary64`
527×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	137	3
2	1769	3

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

38 → 38

Calls

Call 1

Inputs

Outputs

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
	0.0b	(pow.f64 (+.f64 2 x) 1/4)
✓	0.0b	(pow.f64 (+.f64 2 x) 1/4)
✓	0.7b	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series8.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
1.0ms	x	@	-inf	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
1.0ms	x	@	0	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
1.0ms	x	@	inf	(pow.f64 (+.f64 2 x) 1/4)
1.0ms	x	@	-inf	(pow.f64 (+.f64 2 x) 1/4)

rewrite53.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`pow1_binary64`
655×	`add-log-exp_binary64`
654×	`log1p-expm1-u_binary64`
654×	`expm1-log1p-u_binary64`
641×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	163	13
2	1893	13

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

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

Outputs

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

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

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`associate-/r*_binary64`
500×	`fma-def_binary64`
471×	`associate-*l/_binary64`
316×	`associate-+l+_binary64`
266×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	904
1	332	869
2	954	693
3	3720	503

Stop Event

1×	node limit

Counts

63 → 83

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 (+.f64 (.f64 1/64 (sqrt.f64 2)) (.f64 -3/64 (sqrt.f64 2))) (pow.f64 x 2)) (.f64 1/4 (*.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (+.f64 (.f64 7/512 (sqrt.f64 2)) (.f64 -3/512 (sqrt.f64 2))) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 1/64 (sqrt.f64 2)) (.f64 -3/64 (sqrt.f64 2))) (pow.f64 x 2)) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(+.f64 (.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(+.f64 (.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 7/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))
(+.f64 (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x) (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))
(+.f64 (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 3/8 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -7/8 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x) (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(pow.f64 2 1/4)
(+.f64 (pow.f64 2 1/4) (.f64 1/8 (.f64 (pow.f64 2 1/4) x)))
(+.f64 (pow.f64 2 1/4) (+.f64 (.f64 1/8 (.f64 (pow.f64 2 1/4) x)) (.f64 -3/128 (.f64 (pow.f64 2 1/4) (pow.f64 x 2)))))
(+.f64 (.f64 7/1024 (.f64 (pow.f64 2 1/4) (pow.f64 x 3))) (+.f64 (pow.f64 2 1/4) (+.f64 (.f64 1/8 (.f64 (pow.f64 2 1/4) x)) (.f64 -3/128 (.f64 (pow.f64 2 1/4) (pow.f64 x 2))))))
(pow.f64 x 1/4)
(+.f64 (*.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (pow.f64 x 1/4))
(+.f64 (.f64 -3/8 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (pow.f64 x 1/4)))
(+.f64 (.f64 -3/8 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (+.f64 (*.f64 7/16 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (pow.f64 x 1/4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/2 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 7/16 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (.f64 (.f64 1/4 (sqrt.f64 2)) x))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(fma.f64 (sqrt.f64 2) (*.f64 1/4 x) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (+.f64 (.f64 1/64 (sqrt.f64 2)) (.f64 -3/64 (sqrt.f64 2))) (pow.f64 x 2)) (.f64 1/4 (*.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 (.f64 (sqrt.f64 2) -1/32) (.f64 x x) (.f64 (.f64 1/4 (sqrt.f64 2)) x)))
(+.f64 (sqrt.f64 2) (fma.f64 (.f64 (sqrt.f64 2) 1/4) x (.f64 (sqrt.f64 2) (.f64 -1/32 (.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (.f64 (.f64 x x) -1/32))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 -1/32 x)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (+.f64 (.f64 7/512 (sqrt.f64 2)) (.f64 -3/512 (sqrt.f64 2))) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 1/64 (sqrt.f64 2)) (.f64 -3/64 (sqrt.f64 2))) (pow.f64 x 2)) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 (.f64 (sqrt.f64 2) 1/128) (pow.f64 x 3) (fma.f64 (.f64 (sqrt.f64 2) -1/32) (.f64 x x) (.f64 (*.f64 1/4 (sqrt.f64 2)) x))))
(+.f64 (sqrt.f64 2) (fma.f64 (.f64 (sqrt.f64 2) 1/128) (pow.f64 x 3) (fma.f64 (.f64 (sqrt.f64 2) 1/4) x (.f64 (sqrt.f64 2) (.f64 -1/32 (*.f64 x x))))))
(+.f64 (sqrt.f64 2) (fma.f64 (sqrt.f64 2) (.f64 (.f64 x x) -1/32) (.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) 1/128) (*.f64 1/4 x)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (.f64 (.f64 x x) (+.f64 -1/32 (*.f64 1/128 x))))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x)))
(+.f64 (.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(fma.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))))
(+.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)) (fma.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(+.f64 (sqrt.f64 x) (fma.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/2)))
(+.f64 (.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 7/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))))
(fma.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 7/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))))
(fma.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (sqrt.f64 x))) (fma.f64 7/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (fma.f64 -3/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))) (fma.f64 7/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (sqrt.f64 x)))))
(+.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)
(sqrt.f64 (exp.f64 (log.f64 x)))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x))
(+.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x))
(+.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x))
(+.f64 (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x) (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))
(fma.f64 -3/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (+.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (.f64 1/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x))))))
(+.f64 (fma.f64 1/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 x x)) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x)) (fma.f64 -3/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 x x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (+.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) -1/2)))
(+.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (*.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x) (+.f64 (/.f64 -3/4 x) (+.f64 (/.f64 1/4 x) 1))))
(+.f64 (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 3/8 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -7/8 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x) (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(fma.f64 -3/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/2) (pow.f64 x 3)) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (+.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (.f64 1/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)))))))
(fma.f64 -3/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 x x)) (-.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (fma.f64 1/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 x x)) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x))) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (/.f64 (pow.f64 x 3) -1/2))))
(+.f64 (.f64 (+.f64 (/.f64 1/4 x) 1) (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x)) (+.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (.f64 x x)) (-.f64 -3/4 (/.f64 -1/2 x)))))
(+.f64 (+.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x)) (.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (.f64 x x)) (+.f64 -1/2 (/.f64 1/2 x))))
(pow.f64 2 1/4)
(+.f64 (pow.f64 2 1/4) (.f64 1/8 (.f64 (pow.f64 2 1/4) x)))
(+.f64 (pow.f64 2 1/4) (.f64 1/8 (.f64 x (pow.f64 2 1/4))))
(fma.f64 1/8 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (+.f64 (.f64 x 1/8) 1) (pow.f64 2 1/4))
(+.f64 (pow.f64 2 1/4) (+.f64 (.f64 1/8 (.f64 (pow.f64 2 1/4) x)) (.f64 -3/128 (.f64 (pow.f64 2 1/4) (pow.f64 x 2)))))
(+.f64 (pow.f64 2 1/4) (fma.f64 1/8 (.f64 x (pow.f64 2 1/4)) (.f64 -3/128 (.f64 (.f64 x x) (pow.f64 2 1/4)))))
(+.f64 (pow.f64 2 1/4) (fma.f64 1/8 (.f64 x (pow.f64 2 1/4)) (.f64 (.f64 x x) (.f64 (pow.f64 2 1/4) -3/128))))
(+.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (+.f64 (.f64 x 1/8) (.f64 x (.f64 x -3/128)))))
(.f64 (pow.f64 2 1/4) (+.f64 (.f64 x 1/8) (+.f64 (.f64 (.f64 -3/128 x) x) 1)))
(+.f64 (.f64 7/1024 (.f64 (pow.f64 2 1/4) (pow.f64 x 3))) (+.f64 (pow.f64 2 1/4) (+.f64 (.f64 1/8 (.f64 (pow.f64 2 1/4) x)) (.f64 -3/128 (.f64 (pow.f64 2 1/4) (pow.f64 x 2))))))
(fma.f64 7/1024 (.f64 (pow.f64 x 3) (pow.f64 2 1/4)) (+.f64 (pow.f64 2 1/4) (fma.f64 1/8 (.f64 x (pow.f64 2 1/4)) (.f64 -3/128 (.f64 (*.f64 x x) (pow.f64 2 1/4))))))
(+.f64 (fma.f64 1/8 (.f64 x (pow.f64 2 1/4)) (.f64 (.f64 x x) (.f64 (pow.f64 2 1/4) -3/128))) (fma.f64 7/1024 (*.f64 (pow.f64 x 3) (pow.f64 2 1/4)) (pow.f64 2 1/4)))
(+.f64 (.f64 (+.f64 (.f64 x 1/8) 1) (pow.f64 2 1/4)) (.f64 (pow.f64 2 1/4) (+.f64 (.f64 x (.f64 x -3/128)) (.f64 (pow.f64 x 3) 7/1024))))
(+.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (+.f64 (.f64 x 1/8) (.f64 (.f64 x x) (+.f64 -3/128 (*.f64 7/1024 x))))))
(pow.f64 x 1/4)
(+.f64 (*.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (pow.f64 x 1/4))
(fma.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4))
(+.f64 (.f64 -3/8 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (pow.f64 x 1/4)))
(fma.f64 -3/8 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (fma.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4)))
(+.f64 (.f64 -3/8 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (+.f64 (*.f64 7/16 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (pow.f64 x 1/4))))
(fma.f64 -3/8 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (fma.f64 1/2 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 7/16 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4))
(pow.f64 (exp.f64 1/4) (log.f64 x))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/2 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (*.f64 1/2 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (.f64 (pow.f64 -1 1/4) 1/2)) x))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (pow.f64 (exp.f64 1/4) (log.f64 x)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (/.f64 (.f64 -3/8 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (.f64 x x))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -3/8 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x))))
(fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/2 (/.f64 -3/8 x))))
(+.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) x) (+.f64 1/2 (/.f64 -3/8 x))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 7/16 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 7/16 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (/.f64 (.f64 -3/8 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (.f64 x x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 7/16 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -3/8 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x)))))
(fma.f64 7/16 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/2 (/.f64 -3/8 x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) x) (+.f64 1/2 (+.f64 (/.f64 7/16 (.f64 x x)) (/.f64 -3/8 x)))))

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.0ms	x	@	inf	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.0ms	x	@	-inf	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))

rewrite61.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`pow1_binary64`
614×	`log1p-expm1-u_binary64`
614×	`expm1-log1p-u_binary64`
613×	`add-log-exp_binary64`
602×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	146	8
2	1710	8

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

Outputs

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

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

828×	`associate-/l*_binary64`
634×	`fma-def_binary64`
581×	`associate-r_binary64`
546×	`associate-l_binary64`
541×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	207
1	130	197
2	386	191
3	1610	153

Stop Event

1×	node limit

Counts

29 → 39

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 1/4 (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 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 -1/4 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 3))))))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 x) (/.f64 1 x))) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) 1)
(-.f64 (*.f64 -1/2 x) (+.f64 1 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (/.f64 1 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 1/4 (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 1/4 (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 1/4 (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 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 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 1/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 -1/4 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 3))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/4 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x)))) (.f64 -1/8 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (fma.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (fma.f64 -1/8 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (sqrt.f64 2)))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (.f64 (.f64 x (.f64 (/.f64 1/8 (sqrt.f64 2)) x)) (+.f64 1/2 (.f64 x -1/8))))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (fma.f64 1/2 x (/.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 x) (/.f64 1 x))) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1 (fma.f64 1/2 x (/.f64 1 x))) (/.f64 2 (*.f64 x x)))
(+.f64 (fma.f64 1/2 x 1) (-.f64 (/.f64 1 x) (/.f64 2 (*.f64 x x))))
(+.f64 (fma.f64 1/2 x 1) (+.f64 (/.f64 1 x) (/.f64 -2 (*.f64 x x))))
(+.f64 1 (+.f64 (/.f64 1 x) (fma.f64 1/2 x (/.f64 -2 (*.f64 x x)))))
(*.f64 -1/2 x)
(*.f64 x -1/2)
(-.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x -1)
(fma.f64 x -1/2 -1)
(-.f64 (*.f64 -1/2 x) (+.f64 1 (/.f64 1 x)))
(-.f64 (fma.f64 -1/2 x -1) (/.f64 1 x))
(-.f64 (fma.f64 x -1/2 -1) (/.f64 1 x))
(+.f64 (fma.f64 x -1/2 -1) (/.f64 -1 x))
(-.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (/.f64 1 x)))
(-.f64 (fma.f64 -1/2 x (/.f64 2 (*.f64 x x))) (+.f64 1 (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (-.f64 (fma.f64 x -1/2 -1) (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (fma.f64 x -1/2 -1) (/.f64 -1 x)))

eval178.0ms (4%)

Compiler: Compiled 3978 to 3469 computations (12.8% saved)

prune42.0ms (0.9%)

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	279	4	283
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	279	11	290

Error

Counts

290 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.5b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	21.2b	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
▶	54.7b	(+.f64 1 (*.f64 1/2 x))
✓	17.0b	(sqrt.f64 2)
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.7b	(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓	20.6b	(sqrt.f64 (+.f64 2 x))
✓	21.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
▶	62.1b	(*.f64 1/2 x)
▶	62.3b	(-.f64 (*.f64 -1/2 x) 1)
▶	61.3b	(*.f64 -1/2 x)

Compiler

Compiled 66 to 57 computations (13.6% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune38.0ms (0.9%)

Pruning

11 alts after pruning (0 fresh and 11 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	10	10
Total	11	11

Error

Counts

11 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.5b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	21.2b	(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
✓	54.7b	(+.f64 1 (*.f64 1/2 x))
✓	17.0b	(sqrt.f64 2)
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.7b	(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓	20.6b	(sqrt.f64 (+.f64 2 x))
✓	21.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓	62.1b	(*.f64 1/2 x)
✓	62.3b	(-.f64 (*.f64 -1/2 x) 1)
✓	61.3b	(*.f64 -1/2 x)

Compiler

Compiled 66 to 57 computations (13.6% saved)

regimes25.0ms (0.6%)

Counts

14 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 -1/2 x)
(+.f64 1 (*.f64 1/2 x))
(-.f64 (*.f64 -1/2 x) 1)
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

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

Calls

5 calls:

9.0ms	x
3.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
3.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
3.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
3.0ms	(sqrt.f64 (/.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 134 to 109 computations (18.7% saved)

regimes10.0ms (0.2%)

Counts

12 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 -1/2 x)
(+.f64 1 (*.f64 1/2 x))
(-.f64 (*.f64 -1/2 x) 1)
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 67 to 55 computations (17.9% saved)

regimes14.0ms (0.3%)

Counts

9 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
17.0b	1	`x`

Compiler

Compiled 46 to 38 computations (17.4% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
54.7b	1	`x`

Compiler

Compiled 19 to 14 computations (26.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total -1.5b remaining (-2.5%)

Threshold costs -1.5b (-2.5%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 -1/2 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
61.3b	1	`x`

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	21	34

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 29 to 24 computations (17.2% saved)

soundness72.0ms (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)

end66.0ms (1.5%)

Compiler: Compiled 24 to 18 computations (25% saved)

Details

analyze195.0ms (4.4%)

sample2.2s (50.1%)

preprocess39.0ms (0.9%)

simplify106.0ms (2.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.2%)

series3.0ms (0.1%)

rewrite51.0ms (1.1%)

simplify54.0ms (1.2%)

eval20.0ms (0.5%)

prune12.0ms (0.3%)

localize13.0ms (0.3%)

series2.0ms (0%)

rewrite66.0ms (1.5%)

simplify48.0ms (1.1%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite54.0ms (1.2%)

simplify114.0ms (2.5%)

localize9.0ms (0.2%)

series3.0ms (0.1%)

rewrite52.0ms (1.2%)

simplify113.0ms (2.5%)

localize3.0ms (0.1%)

eval186.0ms (4.2%)

prune73.0ms (1.6%)

localize12.0ms (0.3%)

series3.0ms (0.1%)

rewrite65.0ms (1.5%)

simplify102.0ms (2.3%)

localize8.0ms (0.2%)

series0.0ms (0%)

rewrite85.0ms (1.9%)

simplify7.0ms (0.1%)

localize11.0ms (0.2%)

series8.0ms (0.2%)

rewrite53.0ms (1.2%)

simplify58.0ms (1.3%)

localize12.0ms (0.3%)

series3.0ms (0.1%)

rewrite61.0ms (1.4%)

simplify35.0ms (0.8%)

eval178.0ms (4%)

prune42.0ms (0.9%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

eval0.0ms (0%)

prune38.0ms (0.9%)

regimes25.0ms (0.6%)

regimes10.0ms (0.2%)

regimes14.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify4.0ms (0.1%)

soundness72.0ms (1.6%)

end66.0ms (1.5%)

Profiling