Details

analyze565.0ms (15.6%)

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)

sample2.0s (54.2%)

Results

1.1s	2728×	body	1024	valid
403.0ms	3811×	body	256	valid
309.0ms	1410×	body	512	valid
149.0ms	307×	body	2048	valid
5.0ms	43×	body	256	infinite
0.0ms	1×	body	256	unsamplable

Bogosity

preprocess42.0ms (1.2%)

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)

simplify29.0ms (0.8%)

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 → 5

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 41 to 29 computations (29.3% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	2	6

Error

0.0b

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))
0.0ms	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))

rewrite46.0ms (1.3%)

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

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

695×	`times-frac_binary64`
576×	`distribute-rgt-in_binary64`
535×	`distribute-lft-in_binary64`
421×	`fma-def_binary64`
231×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	947
1	361	825
2	1202	653
3	3686	639

Stop Event

1×	node limit

Counts

66 → 96

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))))))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(.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)))))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 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)))))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 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))
(.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)))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 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))
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))

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))
(+.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)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 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 x x) (/.f64 (sqrt.f64 2) (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2))))) (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 (*.f64 x x) (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 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))))))
(+.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 x x) (/.f64 (sqrt.f64 2) (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2))))) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(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 1 (+.f64 1 (exp.f64 x))) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(*.f64 1 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 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)))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 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)))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(.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))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 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)))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(exp.f64 (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(fma.f64 1 (exp.f64 x) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 2 (expm1.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 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))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 2) x))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 2) x))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	0.0b	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

Compiler

Compiled 26 to 6 computations (76.9% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
0.0ms	x	@	-inf	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
0.0ms	x	@	0	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
0.0ms	x	@	inf	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

rewrite54.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

752×	`pow1_binary64`
704×	`add-log-exp_binary64`
703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
687×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	151	24
2	2106	24

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

Inputs
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

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

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

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

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

530×	`log-prod_binary64`
387×	`log-div_binary64`
381×	`fma-neg_binary64`
340×	`fma-def_binary64`
306×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	1402
1	445	1316
2	1568	1306
3	6658	1306

Stop Event

1×	node limit

Counts

89 → 101

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)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(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 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))
(.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(.f64 (.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4)) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(.f64 (.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (expm1.f64 x) 3)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(*.f64 1 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))
(/.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) 2)
(fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))

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))
(+.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)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
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(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 3)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) 2)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

eval49.0ms (1.4%)

Compiler: Compiled 2723 to 1490 computations (45.3% saved)

prune22.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	20.7b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	17.3b	(sqrt.f64 2)

Compiler

Compiled 20 to 17 computations (15% saved)

localize2.0ms (0.1%)

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

localize4.0ms (0.1%)

Compiler: Compiled 10 to 7 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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))

rewrite42.0ms (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 exp.f64 (*.f64 1/2 (log1p.f64 (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 +.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 exp.f64 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))))))

simplify45.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-l_binary64`
390×	`associate-/l*_binary64`
383×	`associate-r_binary64`
358×	`fma-def_binary64`
324×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	633
1	276	574
2	905	534
3	4424	499

Stop Event

1×	node limit

Counts

59 → 80

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)))))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 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)))))))
(+.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)))))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (sqrt.f64 (exp.f64 x)))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (exp.f64 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))))))
(-.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (exp.f64 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 x) 1/2)
(pow.f64 (sqrt.f64 (exp.f64 x)) 1)
(pow.f64 (pow.f64 (exp.f64 x) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (exp.f64 x) 1/4) 2)
(fabs.f64 (sqrt.f64 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))
(cbrt.f64 (pow.f64 (exp.f64 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 x))))
(exp.f64 (*.f64 x 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 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 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (/.f64 3/8 (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(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 1/2 x (fma.f64 x (*.f64 x 1/8) 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 1/2 x (fma.f64 (pow.f64 x 3) 1/48 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 3) 1/48 1)))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 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)))))))
(sqrt.f64 (+.f64 1 (exp.f64 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)))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3) 1/3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 0 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 x))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))))
(sqrt.f64 (exp.f64 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))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (exp.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))))
(-.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(sqrt.f64 (exp.f64 x))
(*.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) 1)
(sqrt.f64 (exp.f64 x))
(*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (sqrt.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))
(*.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (exp.f64 x) 1/4))
(sqrt.f64 (exp.f64 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (fabs.f64 (cbrt.f64 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(pow.f64 (cbrt.f64 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (fabs.f64 (cbrt.f64 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(pow.f64 (cbrt.f64 (exp.f64 x)) 3/2)
(pow.f64 (exp.f64 x) 1/2)
(sqrt.f64 (exp.f64 x))
(pow.f64 (sqrt.f64 (exp.f64 x)) 1)
(sqrt.f64 (exp.f64 x))
(pow.f64 (pow.f64 (exp.f64 x) 3/2) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 x) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 3)
(sqrt.f64 (exp.f64 x))
(pow.f64 (pow.f64 (exp.f64 x) 1/4) 2)
(sqrt.f64 (exp.f64 x))
(fabs.f64 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 x))
(log.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (exp.f64 x))
(cbrt.f64 (pow.f64 (exp.f64 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (exp.f64 x))
(exp.f64 (*.f64 x 1/2))
(sqrt.f64 (exp.f64 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (exp.f64 x))

eval21.0ms (0.6%)

Compiler: Compiled 991 to 714 computations (28% saved)

prune12.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	79	5	84

Error

Counts

84 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	19.6b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
▶	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
✓	20.7b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.3b	(sqrt.f64 2)

Compiler

Compiled 29 to 25 computations (13.8% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite40.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

526×	`pow1_binary64`
506×	`add-sqr-sqrt_binary64`
483×	`add-log-exp_binary64`
483×	`log1p-expm1-u_binary64`
483×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	131	8
2	1371	8

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

Outputs

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

simplify35.0ms (1%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
361×	`associate-/l*_binary64`
324×	`times-frac_binary64`
319×	`associate-l_binary64`
297×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	485
1	162	328
2	612	297
3	3345	273

Stop Event

1×	node limit

Counts

29 → 33

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 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.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 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3) 1/3)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 3))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(hypot.f64 1 (pow.f64 (exp.f64 x) 1/2))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	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))

rewrite42.0ms (1.2%)

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 exp.f64 (log.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))))))))

simplify114.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

871×	`associate-/l*_binary64`
550×	`associate-/r/_binary64`
291×	`distribute-rgt-in_binary64`
286×	`associate-/l/_binary64`
274×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	443
1	194	384
2	663	327
3	3401	289

Stop Event

1×	node limit

Counts

29 → 58

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)))
(-.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 1)
(*.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1)))
(*.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1)
(*.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))
(*.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))))
(*.f64 (sqrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) (sqrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(pow.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1)
(pow.f64 (pow.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 3) 1/3)
(pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)
(pow.f64 (sqrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)
(pow.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) 1/2)
(sqrt.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)))
(log.f64 (exp.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(exp.f64 (log.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(log1p.f64 (expm1.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))

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 (-.f64 1/4 (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 1/4 (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 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (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 x (/.f64 (sqrt.f64 2) 1/8))) (+.f64 1/2 (*.f64 x -1/8))))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(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 x) (fma.f64 1/2 x 1))
(-.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 (/.f64 1 x)) (+.f64 1 (/.f64 -2 (*.f64 x x))))
(+.f64 1 (+.f64 (/.f64 1 x) (fma.f64 1/2 x (/.f64 -2 (*.f64 x x)))))
(+.f64 (/.f64 1 x) (+.f64 (fma.f64 1/2 x (/.f64 -2 (*.f64 x x))) 1))
(*.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 (fma.f64 x -1/2 (/.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 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 1)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(*.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1)))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(*.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(*.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))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(*.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))))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(*.f64 (sqrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) (sqrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (pow.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 3) 1/3)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (sqrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) 1/2)
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(sqrt.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(log.f64 (exp.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(cbrt.f64 (pow.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 3))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(expm1.f64 (log1p.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(exp.f64 (log.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))
(+.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) -1)
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))

eval98.0ms (2.7%)

Compiler: Compiled 1245 to 1029 computations (17.3% saved)

prune14.0ms (0.4%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	87	9	96

Error

Counts

96 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.6b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
▶	62.2b	(-.f64 (*.f64 -1/2 x) 1)
▶	54.7b	(+.f64 1 (*.f64 1/2 x))
▶	61.1b	(*.f64 x -1/2)
▶	62.2b	(*.f64 1/2 x)
✓	20.7b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.3b	(sqrt.f64 2)

Compiler

Compiled 49 to 41 computations (16.3% saved)

localize2.0ms (0.1%)

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

localize2.0ms (0.1%)

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

localize5.0ms (0.1%)

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

localize5.0ms (0.1%)

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

eval0.0ms (0%)

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

prune4.0ms (0.1%)

Pruning

9 alts after pruning (0 fresh and 9 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	8	8
Total	9	9

Error

Counts

9 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.6b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
✓	62.2b	(-.f64 (*.f64 -1/2 x) 1)
✓	54.7b	(+.f64 1 (*.f64 1/2 x))
✓	61.1b	(*.f64 x -1/2)
✓	62.2b	(*.f64 1/2 x)
✓	20.7b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.3b	(sqrt.f64 2)

Compiler

Compiled 49 to 41 computations (16.3% saved)

regimes22.0ms (0.6%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

5 calls:

7.0ms	x
4.0ms	(/.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)))
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 118 to 93 computations (21.2% saved)

regimes7.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 37 to 29 computations (21.6% saved)

regimes20.0ms (0.5%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

18.0ms

Results

Error	Segments	Branch
17.3b	1	`x`

Compiler

Compiled 32 to 25 computations (21.9% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 x -1/2)
(+.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 -1.7b remaining (-2.8%)

Threshold costs -1.7b (-2.8%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 x -1/2)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
61.1b	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	16	35
1	22	35

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 30 to 25 computations (16.7% saved)

soundness64.0ms (1.8%)

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)

end76.0ms (2.1%)

Compiler: Compiled 25 to 20 computations (20% saved)

Details

analyze565.0ms (15.6%)

sample2.0s (54.2%)

preprocess42.0ms (1.2%)

simplify29.0ms (0.8%)

eval1.0ms (0%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite46.0ms (1.3%)

simplify49.0ms (1.4%)

localize8.0ms (0.2%)

series3.0ms (0.1%)

rewrite54.0ms (1.5%)

simplify63.0ms (1.7%)

eval49.0ms (1.4%)

prune22.0ms (0.6%)

localize2.0ms (0.1%)

localize4.0ms (0.1%)

localize5.0ms (0.1%)

series3.0ms (0.1%)

rewrite42.0ms (1.2%)

simplify45.0ms (1.2%)

eval21.0ms (0.6%)

prune12.0ms (0.3%)

localize7.0ms (0.2%)

series2.0ms (0.1%)

rewrite40.0ms (1.1%)

simplify35.0ms (1%)

localize9.0ms (0.3%)

series2.0ms (0%)

rewrite42.0ms (1.2%)

simplify114.0ms (3.1%)

eval98.0ms (2.7%)

prune14.0ms (0.4%)

localize2.0ms (0.1%)

localize2.0ms (0.1%)

localize5.0ms (0.1%)

localize5.0ms (0.1%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes22.0ms (0.6%)

regimes7.0ms (0.2%)

regimes20.0ms (0.5%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify4.0ms (0.1%)

soundness64.0ms (1.8%)

end76.0ms (2.1%)

Profiling