Details

analyze244.0ms (3%)

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)

sample4.1s (49.2%)

Results

2.3s	2816×	body	1024	valid
878.0ms	3802×	body	256	valid
598.0ms	1359×	body	512	valid
276.0ms	279×	body	2048	valid
11.0ms	53×	body	256	infinite
0.0ms	1×	body	256	unsamplable

Bogosity

preprocess62.0ms (0.7%)

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)

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

series5.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms	x	@	-inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms	x	@	0	(+.f64 1 (exp.f64 x))
0.0ms	x	@	inf	(+.f64 1 (exp.f64 x))

rewrite84.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

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

Outputs

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

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

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

66 → 71

Calls

Call 1

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

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

eval61.0ms (0.7%)

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

prune26.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Error

Counts

72 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1))
▶	0.0b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
▶	0.7b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
▶	21.6b	(sqrt.f64 (+.f64 2 x))
▶	18.2b	(sqrt.f64 2)
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	20.6b	(sqrt.f64 (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))

Compiler

Compiled 102 to 89 computations (12.7% saved)

localize26.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)

Compiler

Compiled 25 to 17 computations (32% saved)

series105.0ms (1.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
47.0ms	x	@	-inf	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
47.0ms	x	@	inf	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
3.0ms	x	@	inf	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
3.0ms	x	@	0	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
3.0ms	x	@	-inf	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`pow1_binary64`
744×	`add-log-exp_binary64`
743×	`log1p-expm1-u_binary64`
743×	`expm1-log1p-u_binary64`
727×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	195	17
2	2164	17

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

Inputs
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)

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

Outputs

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

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

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

592×	`associate-/r/_binary64`
478×	`associate-/l/_binary64`
419×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`
291×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	491
1	204	409
2	671	381
3	3149	365

Stop Event

1×	node limit

Counts

62 → 53

Calls

Call 1

Inputs
(sqrt.f64 8)
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (+.f64 (sqrt.f64 8) (.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3))))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (*.f64 (sqrt.f64 8) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 15/32 (sqrt.f64 8)) (.f64 3/16 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (pow.f64 (sqrt.f64 8) 2)))) (pow.f64 x 2)) (pow.f64 (sqrt.f64 2) 2))) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (sqrt.f64 8) x)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 15/32 (sqrt.f64 8)) (.f64 3/16 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (pow.f64 (sqrt.f64 8) 2)))) (pow.f64 x 2)) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 27/128 (sqrt.f64 8)) (+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)) 1/3) (.f64 (-.f64 (.f64 15/32 (sqrt.f64 8)) (.f64 3/16 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (pow.f64 (sqrt.f64 8) 2)))) (sqrt.f64 8)))) (.f64 1/64 (/.f64 (pow.f64 (sqrt.f64 8) 3) (pow.f64 (sqrt.f64 2) 2))))) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 2))) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (sqrt.f64 8) x))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Outputs
(sqrt.f64 8)
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(fma.f64 3/4 (*.f64 (sqrt.f64 8) x) (sqrt.f64 8))
(.f64 (+.f64 (.f64 3/4 x) 1) (sqrt.f64 8))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(fma.f64 3/4 (.f64 (sqrt.f64 8) x) (fma.f64 15/32 (.f64 (sqrt.f64 8) (*.f64 x x)) (sqrt.f64 8)))
(fma.f64 3/4 (.f64 (sqrt.f64 8) x) (fma.f64 (.f64 (sqrt.f64 8) 15/32) (*.f64 x x) (sqrt.f64 8)))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 3/4 x) (.f64 x (.f64 x 15/32)))))
(+.f64 (sqrt.f64 8) (.f64 (.f64 (sqrt.f64 8) x) (+.f64 3/4 (*.f64 x 15/32))))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (+.f64 (sqrt.f64 8) (.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3))))))
(fma.f64 3/4 (.f64 (sqrt.f64 8) x) (+.f64 (fma.f64 15/32 (.f64 (sqrt.f64 8) (.f64 x x)) (sqrt.f64 8)) (.f64 27/128 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))))
(fma.f64 3/4 (.f64 (sqrt.f64 8) x) (fma.f64 15/32 (.f64 (sqrt.f64 8) (.f64 x x)) (fma.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3)) (sqrt.f64 8))))
(fma.f64 (sqrt.f64 8) (.f64 3/4 x) (+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 x (.f64 x 15/32)) (*.f64 27/128 (pow.f64 x 3))))))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 3/4 x) (.f64 (.f64 x x) (+.f64 15/32 (*.f64 27/128 x))))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (*.f64 (sqrt.f64 8) x))))
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2))) (sqrt.f64 8)) x)))
(fma.f64 1/4 (.f64 x (.f64 (sqrt.f64 8) (cbrt.f64 1/2))) (sqrt.f64 2))
(fma.f64 (.f64 (sqrt.f64 8) x) (.f64 1/4 (cbrt.f64 1/2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 15/32 (sqrt.f64 8)) (.f64 3/16 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (pow.f64 (sqrt.f64 8) 2)))) (pow.f64 x 2)) (pow.f64 (sqrt.f64 2) 2))) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (sqrt.f64 8) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/3 (/.f64 (-.f64 (.f64 (sqrt.f64 8) 15/32) (.f64 (.f64 3/16 (cbrt.f64 (/.f64 1 (sqrt.f64 2)))) (pow.f64 (sqrt.f64 8) 2))) (/.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))) (.f64 1/4 (.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2))) (sqrt.f64 8)) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 x (.f64 (sqrt.f64 8) (cbrt.f64 1/2))) (.f64 1/3 (.f64 (/.f64 (fma.f64 (sqrt.f64 8) 15/32 (.f64 -3/2 (cbrt.f64 (/.f64 1 (sqrt.f64 2))))) 2) (.f64 x x)))))
(+.f64 (sqrt.f64 2) (fma.f64 (.f64 (sqrt.f64 8) x) (.f64 1/4 (cbrt.f64 1/2)) (.f64 1/6 (.f64 x (.f64 x (fma.f64 -3/2 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) (.f64 (sqrt.f64 8) 15/32)))))))
(+.f64 (fma.f64 (.f64 (sqrt.f64 8) x) (.f64 1/4 (cbrt.f64 1/2)) (sqrt.f64 2)) (.f64 1/6 (.f64 x (.f64 x (fma.f64 (sqrt.f64 8) 15/32 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) -3/2))))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 15/32 (sqrt.f64 8)) (.f64 3/16 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (pow.f64 (sqrt.f64 8) 2)))) (pow.f64 x 2)) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 27/128 (sqrt.f64 8)) (+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)) 1/3) (.f64 (-.f64 (.f64 15/32 (sqrt.f64 8)) (.f64 3/16 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (pow.f64 (sqrt.f64 8) 2)))) (sqrt.f64 8)))) (.f64 1/64 (/.f64 (pow.f64 (sqrt.f64 8) 3) (pow.f64 (sqrt.f64 2) 2))))) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 2))) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (sqrt.f64 8) x))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/3 (/.f64 (-.f64 (.f64 (sqrt.f64 8) 15/32) (.f64 (.f64 3/16 (cbrt.f64 (/.f64 1 (sqrt.f64 2)))) (pow.f64 (sqrt.f64 8) 2))) (/.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))) (fma.f64 1/3 (/.f64 (-.f64 (.f64 (sqrt.f64 8) 27/128) (fma.f64 1/2 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (-.f64 (.f64 (sqrt.f64 8) 15/32) (.f64 (.f64 3/16 (cbrt.f64 (/.f64 1 (sqrt.f64 2)))) (pow.f64 (sqrt.f64 8) 2)))) (sqrt.f64 8)) (.f64 1/64 (/.f64 (pow.f64 (sqrt.f64 8) 3) (pow.f64 (sqrt.f64 2) 2))))) (/.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2))) (sqrt.f64 8)) x)))))
(+.f64 (.f64 1/3 (+.f64 (.f64 (/.f64 (fma.f64 (sqrt.f64 8) 15/32 (.f64 -3/2 (cbrt.f64 (/.f64 1 (sqrt.f64 2))))) 2) (.f64 x x)) (/.f64 (-.f64 (.f64 (sqrt.f64 8) 27/128) (fma.f64 1/64 (/.f64 (sqrt.f64 8) 1/4) (.f64 (.f64 (.f64 1/2 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))) (sqrt.f64 8)) (fma.f64 (sqrt.f64 8) 15/32 (.f64 -3/2 (cbrt.f64 (/.f64 1 (sqrt.f64 2)))))))) (/.f64 2 (pow.f64 x 3))))) (fma.f64 1/4 (.f64 x (*.f64 (sqrt.f64 8) (cbrt.f64 1/2))) (sqrt.f64 2)))
(fma.f64 1/3 (fma.f64 (/.f64 (fma.f64 -3/2 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) (.f64 (sqrt.f64 8) 15/32)) 2) (.f64 x x) (.f64 (pow.f64 x 3) (/.f64 (+.f64 (fma.f64 (sqrt.f64 8) 27/128 (.f64 (.f64 4 (sqrt.f64 8)) -1/64)) (.f64 (+.f64 15/4 (.f64 (sqrt.f64 8) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) -3/2))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) -1/2))) 2))) (fma.f64 (.f64 (sqrt.f64 8) x) (*.f64 1/4 (cbrt.f64 1/2)) (sqrt.f64 2)))
(+.f64 (fma.f64 (.f64 (sqrt.f64 8) x) (.f64 1/4 (cbrt.f64 1/2)) (sqrt.f64 2)) (.f64 1/6 (+.f64 (.f64 x (.f64 x (fma.f64 (sqrt.f64 8) 15/32 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) -3/2)))) (.f64 (pow.f64 x 3) (fma.f64 (sqrt.f64 8) (+.f64 27/128 (.f64 (fma.f64 (sqrt.f64 8) 15/32 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) -3/2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) -1/2))) (*.f64 -1/16 (sqrt.f64 8)))))))
(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)))

localize4.0ms (0.1%)

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

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 10 to 7 computations (30% saved)

series5.0ms (0.1%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt.f64 (+.f64 2 x))
2.0ms	x	@	inf	(sqrt.f64 (+.f64 2 x))
1.0ms	x	@	-inf	(sqrt.f64 (+.f64 2 x))

rewrite71.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

26 → 29

Calls

Call 1

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

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

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 32 to 22 computations (31.3% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite108.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`pow1_binary64`
841×	`add-log-exp_binary64`
839×	`log1p-expm1-u_binary64`
839×	`expm1-log1p-u_binary64`
825×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	182	20
2	2643	20

Stop Event

1×	node limit

Counts

3 → 115

Calls

Call 1

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

Outputs

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

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

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

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
525×	`cancel-sign-sub-inv_binary64`
434×	`fma-neg_binary64`
432×	`associate-r_binary64`
411×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	363
1	128	331
2	376	325
3	1206	293
4	5656	293

Stop Event

1×	node limit

Counts

151 → 137

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

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 30 to 20 computations (33.3% saved)

series4.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite123.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

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

Outputs

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

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

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

95 → 93

Calls

Call 1

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

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

eval266.0ms (3.2%)

Compiler: Compiled 6687 to 5138 computations (23.2% saved)

prune81.0ms (1%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	1	0	1
Picked	0	1	1
Done	1	4	5
Total	463	9	472

Error

Counts

472 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	18.8b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓	21.6b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
✓	0.7b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
✓	18.2b	(sqrt.f64 2)
▶	22.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
▶	0.0b	(sqrt.f64 (+.f64 2 (expm1.f64 x)))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	21.6b	(sqrt.f64 (-.f64 (+.f64 x 3) 1))

Compiler

Compiled 62 to 55 computations (11.3% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 2 (expm1.f64 x)))

Compiler

Compiled 14 to 8 computations (42.9% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (+.f64 2 (expm1.f64 x)))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 2 (expm1.f64 x)))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 2 (expm1.f64 x)))

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

631×	`pow1_binary64`
592×	`add-log-exp_binary64`
591×	`log1p-expm1-u_binary64`
591×	`expm1-log1p-u_binary64`
580×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	8
2	1576	8

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))

Outputs

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

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-out_binary64`
525×	`cancel-sign-sub-inv_binary64`
438×	`fma-neg_binary64`
416×	`fma-def_binary64`
394×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	199
1	97	167
2	290	161
3	949	137
4	5004	137

Stop Event

1×	node limit

Counts

34 → 30

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)))

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)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (.f64 x x) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
(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)))

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (+.f64 x 3) 1))
✓	0.0b	(-.f64 (+.f64 x 3) 1)

Compiler

Compiled 18 to 14 computations (22.2% saved)

series3.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite114.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`pow1_binary64`
740×	`add-log-exp_binary64`
738×	`log1p-expm1-u_binary64`
738×	`expm1-log1p-u_binary64`
727×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	158	10
2	2001	10

Stop Event

1×	node limit

Counts

2 → 67

Calls

Call 1

Inputs
(-.f64 (+.f64 x 3) 1)
(sqrt.f64 (-.f64 (+.f64 x 3) 1))

Outputs

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

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

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1236×	`associate-/l/_binary64`
992×	`fma-def_binary64`
558×	`unswap-sqr_binary64`
360×	`times-frac_binary64`
349×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	129
1	69	121
2	190	117
3	581	109
4	2949	105
5	4292	105
6	5365	105
7	6300	105
8	6570	105
9	6868	105

Stop Event

1×	node limit

Counts

83 → 76

Calls

Call 1

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

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

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 25 to 20 computations (20% saved)

series21.0ms (0.2%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	x	@	-inf	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
1.0ms	x	@	0	(+.f64 1 (sqrt.f64 (+.f64 2 x)))
1.0ms	x	@	inf	(+.f64 1 (sqrt.f64 (+.f64 2 x)))
1.0ms	x	@	-inf	(+.f64 1 (sqrt.f64 (+.f64 2 x)))
1.0ms	x	@	0	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)

rewrite85.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 80

Calls

Call 1

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

Outputs

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

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

simplify124.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

88 → 94

Calls

Call 1

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

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

localize24.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

42 → 42

Calls

Call 1

Inputs

Outputs

eval115.0ms (1.4%)

Compiler: Compiled 3236 to 2825 computations (12.7% saved)

prune41.0ms (0.5%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	0	0	0
Picked	0	1	1
Done	1	7	8
Total	269	11	280

Error

Counts

280 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.8b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓	21.6b	(sqrt.f64 (+.f64 2 x))
▶	22.8b	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
✓	21.6b	(sqrt.f64 (-.f64 (+.f64 x 3) 1))
✓	0.0b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
✓	0.7b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
▶	22.9b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
▶	21.6b	(sqrt.f64 (+.f64 3 (-.f64 x 1)))
✓	18.2b	(sqrt.f64 2)
✓	22.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓	0.0b	(sqrt.f64 (+.f64 2 (expm1.f64 x)))

Compiler

Compiled 91 to 80 computations (12.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 3 (-.f64 x 1))
✓	0.0b	(sqrt.f64 (+.f64 3 (-.f64 x 1)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sqrt.f64 (+.f64 3 (-.f64 x 1)))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 3 (-.f64 x 1)))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 3 (-.f64 x 1)))
0.0ms	x	@	0	(+.f64 3 (-.f64 x 1))
0.0ms	x	@	inf	(+.f64 3 (-.f64 x 1))

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

794×	`pow1_binary64`
746×	`add-log-exp_binary64`
745×	`log1p-expm1-u_binary64`
745×	`expm1-log1p-u_binary64`
733×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	157	10
2	2007	10

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 3 (-.f64 x 1)))
(+.f64 3 (-.f64 x 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 2)) (cbrt.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 2))) (cbrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 2) 1/4) (pow.f64 (+.f64 x 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 9 (pow.f64 (+.f64 x -1) 2))) (sqrt.f64 (+.f64 (-.f64 3 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 27 (pow.f64 (+.f64 x -1) 3))) (sqrt.f64 (+.f64 9 (*.f64 (+.f64 x -1) (-.f64 (+.f64 x -1) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x 2))))))))

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

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1223×	`associate-/l/_binary64`
992×	`fma-def_binary64`
558×	`unswap-sqr_binary64`
360×	`times-frac_binary64`
349×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	129
1	69	121
2	190	117
3	583	109
4	2955	105
5	4298	105
6	5371	105
7	6306	105
8	6576	105
9	6877	105

Stop Event

1×	node limit

Counts

77 → 71

Calls

Call 1

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

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

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
	0.0b	(sqrt.f64 (+.f64 2 x))
✓	0.6b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
✓	1.0b	(-.f64 1 (sqrt.f64 (+.f64 2 x)))

Compiler

Compiled 43 to 34 computations (20.9% saved)

series11.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

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

rewrite170.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`prod-diff_binary64`
514×	`log-prod_binary64`
326×	`fma-def_binary64`
283×	`fma-neg_binary64`
207×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	258	24
2	3764	24

Stop Event

1×	node limit

Counts

3 → 264

Calls

Call 1

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

Outputs

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

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
416×	`distribute-rgt-in_binary64`
392×	`distribute-lft-in_binary64`
323×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	999
1	229	972
2	806	874
3	3751	841

Stop Event

1×	node limit

Counts

276 → 286

Calls

Call 1

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

Outputs
(-.f64 1 (sqrt.f64 2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x (sqrt.f64 2))) (sqrt.f64 2)))
(-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) 1) (sqrt.f64 2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 x (sqrt.f64 2))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))) (sqrt.f64 2))
(+.f64 1 (-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) (.f64 1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)))) (sqrt.f64 2)))
(+.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) 1) (-.f64 (.f64 1/16 (/.f64 (.f64 x x) (sqrt.f64 2))) (sqrt.f64 2)))
(-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) 1)) (sqrt.f64 2))
(+.f64 (-.f64 1 (sqrt.f64 2)) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 -1/2 (/.f64 (.f64 x 1/8) 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 x (sqrt.f64 2))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))) (sqrt.f64 2))
(+.f64 1 (-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (.f64 1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))))) (sqrt.f64 2)))
(+.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) 1) (-.f64 (fma.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (.f64 1/16 (/.f64 (.f64 x x) (sqrt.f64 2)))) (sqrt.f64 2)))
(+.f64 1 (-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (/.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 x 3))))) (sqrt.f64 2)))
(+.f64 1 (-.f64 (fma.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 -1/2 (/.f64 (.f64 x 1/8) 2)))) (sqrt.f64 2)))
(*.f64 -1 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) 1))
(neg.f64 (+.f64 1 (/.f64 1 (-.f64 1 (sqrt.f64 2)))))
(+.f64 -1 (/.f64 -1 (-.f64 1 (sqrt.f64 2))))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))))) x)) (*.f64 -1 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) 1)))
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(-.f64 (fma.f64 -1 (.f64 x (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))))) (fma.f64 (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 (sqrt.f64 2) (-.f64 1 (sqrt.f64 2)))) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 x x) (neg.f64 (.f64 (pow.f64 x 3) (-.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))) (fma.f64 1/2 (/.f64 (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 (sqrt.f64 2) (-.f64 1 (sqrt.f64 2)))) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 (sqrt.f64 2) (-.f64 1 (sqrt.f64 2)))) (.f64 1/8 (/.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (*.f64 (-.f64 1 (sqrt.f64 2)) (pow.f64 (sqrt.f64 2) 3)))))))))) (/.f64 1 (-.f64 1 (sqrt.f64 2))))
(+.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 (sqrt.f64 2) (-.f64 1 (sqrt.f64 2)))) (/.f64 1/8 (.f64 (sqrt.f64 2) (.f64 2 (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))))) (.f64 (pow.f64 x 3) (-.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))) (fma.f64 1/8 (/.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 (-.f64 1 (sqrt.f64 2)) (.f64 2 (sqrt.f64 2)))) (.f64 1/2 (/.f64 (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (.f64 (sqrt.f64 2) (-.f64 1 (sqrt.f64 2)))) (/.f64 1/8 (.f64 (sqrt.f64 2) (.f64 2 (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))))) (.f64 (sqrt.f64 2) (-.f64 1 (sqrt.f64 2))))))))) (fma.f64 (neg.f64 (+.f64 (/.f64 1 (-.f64 1 (sqrt.f64 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))))) x (/.f64 -1 (-.f64 1 (sqrt.f64 2)))))
(+.f64 (.f64 (.f64 x x) (-.f64 (+.f64 (/.f64 (+.f64 (/.f64 -1/2 (-.f64 1 (sqrt.f64 2))) (/.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (+.f64 (sqrt.f64 2) -2)) (/.f64 (/.f64 1/16 (sqrt.f64 2)) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))) (.f64 x (-.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 -1/2 (-.f64 1 (sqrt.f64 2))) (/.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (+.f64 (sqrt.f64 2) -2)) (/.f64 (/.f64 1/16 (sqrt.f64 2)) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2))) (+.f64 (sqrt.f64 2) -2)) (/.f64 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 2)) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)) (/.f64 1/8 (-.f64 1 (sqrt.f64 2)))) (+.f64 (.f64 2 (sqrt.f64 2)) -4))))))) (fma.f64 x (+.f64 (/.f64 -1 (-.f64 1 (sqrt.f64 2))) (/.f64 -1/2 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (/.f64 -1 (-.f64 1 (sqrt.f64 2)))))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 (+.f64 (/.f64 -1/2 (-.f64 1 (sqrt.f64 2))) (/.f64 -1/4 (.f64 (-.f64 1 (sqrt.f64 2)) (+.f64 (sqrt.f64 2) -2)))) (+.f64 (sqrt.f64 2) -2)) (/.f64 1/16 (.f64 (-.f64 1 (sqrt.f64 2)) (+.f64 (sqrt.f64 2) -2)))) (+.f64 (/.f64 -1 (-.f64 1 (sqrt.f64 2))) (/.f64 -1/2 (.f64 (-.f64 1 (sqrt.f64 2)) (+.f64 (sqrt.f64 2) -2))))) (fma.f64 (pow.f64 x 3) (+.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 -1/2 (-.f64 1 (sqrt.f64 2))) (/.f64 -1/4 (.f64 (-.f64 1 (sqrt.f64 2)) (+.f64 (sqrt.f64 2) -2)))) (+.f64 (sqrt.f64 2) -2)) (/.f64 1/16 (.f64 (-.f64 1 (sqrt.f64 2)) (+.f64 (sqrt.f64 2) -2)))) (+.f64 (sqrt.f64 2) -2)) (/.f64 (.f64 (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 2) -2)) 1) (/.f64 1/8 (-.f64 1 (sqrt.f64 2)))) (+.f64 (.f64 2 (sqrt.f64 2)) -4))) (/.f64 -1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (-.f64 1 (sqrt.f64 2)) 2)))) (/.f64 -1 (-.f64 1 (sqrt.f64 2)))))

localize55.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 2 x))
✓	0.1b	(-.f64 (+.f64 2 x) 1)
✓	0.6b	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
✓	1.0b	(+.f64 (sqrt.f64 (+.f64 2 x)) -1)

Compiler

Compiled 49 to 40 computations (18.4% saved)

series9.0ms (0.1%)

Counts

3 → 20

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
2.0ms	x	@	inf	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
2.0ms	x	@	0	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
0.0ms	x	@	0	(+.f64 (sqrt.f64 (+.f64 2 x)) -1)
0.0ms	x	@	inf	(+.f64 (sqrt.f64 (+.f64 2 x)) -1)

rewrite82.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`prod-diff_binary64`
538×	`log-prod_binary64`
391×	`fma-neg_binary64`
352×	`fma-def_binary64`
213×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	258	25
2	3717	25

Stop Event

1×	node limit

Counts

3 → 173

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (cbrt.f64 (exp.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))) (pow.f64 (cbrt.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))) 2) (cbrt.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))) (sqrt.f64 (+.f64 -1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) (+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) -1) (/.f64 1 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)) 1) (-.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) (+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))) (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)) (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) (+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 1) 2) -1) (+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 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simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

824×	`times-frac_binary64`
683×	`distribute-rgt-in_binary64`
662×	`distribute-lft-in_binary64`
251×	`fma-neg_binary64`
228×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	568
1	229	508
2	793	467
3	3630	448

Stop Event

1×	node limit

Counts

193 → 192

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 2) 1)
(-.f64 (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) 1)
(-.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))) 1)
(-.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))) 1)
(-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) 1)
(-.f64 (+.f64 (.f64 (-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) x) (/.f64 1 (-.f64 (sqrt.f64 2) 1))) 1)
(-.f64 (+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) x) (/.f64 1 (-.f64 (sqrt.f64 2) 1)))) 1)
(-.f64 (+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) x) (+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 4) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2)))) (.f64 1/2 (/.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 2) 1))))))) (pow.f64 x 3)) (/.f64 1 (-.f64 (sqrt.f64 2) 1))))) 1)
1
(+.f64 1 x)
(+.f64 1 x)
(+.f64 1 x)
x
(+.f64 1 x)
(+.f64 1 x)
(+.f64 1 x)
x
(+.f64 1 x)
(+.f64 1 x)
(+.f64 1 x)

Outputs
(-.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) -1)
(-.f64 (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) 1)
(+.f64 (sqrt.f64 2) (-.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 2)) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) -1))
(-.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))) 1)
(+.f64 (sqrt.f64 2) (-.f64 (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (/.f64 (.f64 1/2 x) (sqrt.f64 2))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) -1)))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2))) -1)
(+.f64 (+.f64 (sqrt.f64 2) -1) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 (.f64 x -1/8) 2))))
(-.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))) 1)
(+.f64 (sqrt.f64 2) (-.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (/.f64 (.f64 1/2 x) (sqrt.f64 2)))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))))) -1))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) -1))))
(+.f64 (+.f64 (sqrt.f64 2) -1) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 (.f64 x -1/8) 2)))))
(-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) 1)
(+.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) -1)
(-.f64 (+.f64 (.f64 (-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) x) (/.f64 1 (-.f64 (sqrt.f64 2) 1))) 1)
(+.f64 (fma.f64 (-.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 1/2 (*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) x (/.f64 1 (+.f64 (sqrt.f64 2) -1))) -1)
(+.f64 (fma.f64 x (+.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 -1/2 (*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) (/.f64 1 (+.f64 (sqrt.f64 2) -1))) -1)
(+.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (fma.f64 x (-.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) -1))
(+.f64 (+.f64 (.f64 (+.f64 1 x) (/.f64 1 (+.f64 (sqrt.f64 2) -1))) (/.f64 (.f64 -1/2 x) (*.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 2 (sqrt.f64 2))))) -1)
(-.f64 (+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) x) (/.f64 1 (-.f64 (sqrt.f64 2) 1)))) 1)
(+.f64 (fma.f64 (+.f64 (/.f64 1/4 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (-.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))))) (.f64 x x) (fma.f64 (-.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 1/2 (*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) x (/.f64 1 (+.f64 (sqrt.f64 2) -1)))) -1)
(+.f64 (fma.f64 (.f64 x x) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (fma.f64 1/8 (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 -1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))))) (fma.f64 x (+.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 -1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) (/.f64 1 (+.f64 (sqrt.f64 2) -1)))) -1)
(+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 1 (+.f64 (sqrt.f64 2) -1))) (fma.f64 (.f64 x x) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (.f64 (/.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)) -7/8)) -1))
(+.f64 (+.f64 (.f64 (+.f64 1 x) (/.f64 1 (+.f64 (sqrt.f64 2) -1))) (/.f64 (.f64 -1/2 x) (.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 2 (sqrt.f64 2))))) (fma.f64 x (.f64 x (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (.f64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 2 (sqrt.f64 2)))) -7/16))) -1))
(-.f64 (+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) x) (+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 4) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2)))) (.f64 1/2 (/.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (-.f64 (sqrt.f64 2) 1) 3)))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (-.f64 (sqrt.f64 2) 1) 2))))) (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 2) 1))))))) (pow.f64 x 3)) (/.f64 1 (-.f64 (sqrt.f64 2) 1))))) 1)
(+.f64 (fma.f64 (+.f64 (/.f64 1/4 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (-.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))))) (.f64 x x) (fma.f64 (-.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) x (fma.f64 (+.f64 (/.f64 1/4 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (-.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (+.f64 (+.f64 (/.f64 1/16 (.f64 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3) (pow.f64 (sqrt.f64 2) 4))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) (.f64 1/2 (/.f64 (+.f64 (/.f64 1/4 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 2) -1))))))) (pow.f64 x 3) (/.f64 1 (+.f64 (sqrt.f64 2) -1))))) -1)
(+.f64 (fma.f64 (.f64 x x) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (fma.f64 1/8 (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 -1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))))) (fma.f64 x (+.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 -1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))) (fma.f64 (pow.f64 x 3) (-.f64 (fma.f64 1/8 (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (+.f64 (/.f64 1/64 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (fma.f64 1/2 (/.f64 (fma.f64 1/8 (/.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (+.f64 2 (.f64 -1 (sqrt.f64 2)))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))))) (/.f64 1 (+.f64 (sqrt.f64 2) -1))))) -1)
(+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 (sqrt.f64 2) -1)) (/.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (fma.f64 (pow.f64 x 3) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 (/.f64 1/16 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (-.f64 (/.f64 -1/64 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 (fma.f64 1/2 (/.f64 1/16 (.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2))) (/.f64 1/16 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3))) (+.f64 2 (neg.f64 (sqrt.f64 2)))))))) (/.f64 1 (+.f64 (sqrt.f64 2) -1)))) (fma.f64 (.f64 x x) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (*.f64 (/.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)) -7/8)) -1))
(+.f64 (fma.f64 x (.f64 x (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (.f64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 2 (sqrt.f64 2)))) -7/16))) (+.f64 (.f64 (+.f64 1 x) (/.f64 1 (+.f64 (sqrt.f64 2) -1))) (/.f64 (.f64 -1/2 x) (.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 2 (sqrt.f64 2)))))) (fma.f64 (pow.f64 x 3) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 (.f64 (/.f64 1/2 (-.f64 2 (sqrt.f64 2))) (-.f64 (/.f64 1/8 (+.f64 (sqrt.f64 2) -1)) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (/.f64 1/16 (.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 2 (sqrt.f64 2))))))) (+.f64 (/.f64 -1/64 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (/.f64 -1/16 (*.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 (+.f64 (sqrt.f64 2) -1) 2)))))) -1))
1
(+.f64 1 x)
(+.f64 1 x)
(+.f64 1 x)
x
(+.f64 1 x)
(+.f64 1 x)
(+.f64 1 x)
x
(+.f64 1 x)
(+.f64 1 x)
(+.f64 1 x)

eval495.0ms (6%)

Compiler: Compiled 16529 to 14130 computations (14.5% saved)

prune93.0ms (1.1%)

Pruning

16 alts after pruning (5 fresh and 11 done)

	Pruned	Kept	Total
New	602	5	607
Fresh	0	0	0
Picked	0	1	1
Done	0	10	10
Total	602	16	618

Error

Counts

618 → 16

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.8b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓	21.6b	(sqrt.f64 (+.f64 2 x))
✓	22.2b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
	19.4b	(-.f64 (/.f64 1 (-.f64 (sqrt.f64 2) 1)) 1)
	22.9b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1))) 1)
✓	22.8b	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
✓	21.6b	(sqrt.f64 (-.f64 (+.f64 x 3) 1))
✓	0.0b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
✓	0.7b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
	22.3b	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) 1))) 1)
✓	22.9b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
✓	21.6b	(sqrt.f64 (+.f64 3 (-.f64 x 1)))
✓	18.2b	(sqrt.f64 2)
✓	0.0b	(sqrt.f64 (+.f64 2 (expm1.f64 x)))
	22.9b	(-.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 x 3) (*.f64 (+.f64 x 3) (+.f64 x 1)))) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) 1)
	22.9b	(-.f64 (/.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1) -1)) 1)

Compiler

Compiled 178 to 156 computations (12.4% saved)

regimes35.0ms (0.4%)

Counts

20 → 1

Calls

Call 1

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

Outputs
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)

Calls

5 calls:

11.0ms	x
3.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
3.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
3.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
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 251 to 210 computations (16.3% saved)

regimes16.0ms (0.2%)

Counts

18 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))

Calls

1 calls:

10.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 181 to 153 computations (15.5% saved)

regimes12.0ms (0.1%)

Accuracy

Total -5.6b remaining (-30.6%)

Threshold costs -5.6b (-30.6%)

Counts

13 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
18.2b	1	`x`

Compiler

Compiled 143 to 123 computations (14% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	4294967306
1	18	4294967306

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 2)

Outputs
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 2)

Compiler

Compiled 18 to 16 computations (11.1% saved)

soundness97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Compiler

Compiled 92 to 70 computations (23.9% saved)

end48.0ms (0.6%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

Details

analyze244.0ms (3%)

sample4.1s (49.2%)

preprocess62.0ms (0.7%)

simplify45.0ms (0.5%)

eval1.0ms (0%)

prune2.0ms (0%)

localize14.0ms (0.2%)

series5.0ms (0.1%)

rewrite84.0ms (1%)

simplify63.0ms (0.8%)

eval61.0ms (0.7%)

prune26.0ms (0.3%)

localize26.0ms (0.3%)

series105.0ms (1.3%)

rewrite69.0ms (0.8%)

simplify64.0ms (0.8%)

localize4.0ms (0.1%)

localize9.0ms (0.1%)

series5.0ms (0.1%)

rewrite71.0ms (0.9%)

simplify106.0ms (1.3%)

localize24.0ms (0.3%)

series5.0ms (0.1%)

rewrite108.0ms (1.3%)

simplify83.0ms (1%)

localize28.0ms (0.3%)

series4.0ms (0%)

rewrite123.0ms (1.5%)

simplify95.0ms (1.1%)

eval266.0ms (3.2%)

prune81.0ms (1%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite59.0ms (0.7%)

simplify49.0ms (0.6%)

localize15.0ms (0.2%)

series3.0ms (0%)

rewrite114.0ms (1.4%)

simplify120.0ms (1.4%)

localize25.0ms (0.3%)

series21.0ms (0.2%)

rewrite85.0ms (1%)

simplify124.0ms (1.5%)

localize24.0ms (0.3%)

series0.0ms (0%)

rewrite79.0ms (1%)

simplify13.0ms (0.2%)

eval115.0ms (1.4%)

prune41.0ms (0.5%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite59.0ms (0.7%)

simplify97.0ms (1.2%)

localize18.0ms (0.2%)

series11.0ms (0.1%)

rewrite170.0ms (2.1%)

simplify62.0ms (0.8%)

localize55.0ms (0.7%)

series9.0ms (0.1%)

rewrite82.0ms (1%)

simplify53.0ms (0.6%)

eval495.0ms (6%)

prune93.0ms (1.1%)

regimes35.0ms (0.4%)

regimes16.0ms (0.2%)

regimes12.0ms (0.1%)

simplify3.0ms (0%)

soundness97.0ms (1.2%)

end48.0ms (0.6%)

Profiling