Details

analyze170.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.3s (51.3%)

Results

1.3s	2756×	body	1024	valid
505.0ms	3800×	body	256	valid
318.0ms	1389×	body	512	valid
152.0ms	311×	body	2048	valid
5.0ms	46×	body	256	invalid

preprocess57.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify31.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize21.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite43.0ms (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	8
1	118	8
2	1429	8

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(sqrt.f64 (+.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))))))

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))))))

simplify117.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	135
1	91	103
2	286	97
3	936	73
4	4992	73

Stop Event

1×	node limit

Counts

27 → 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))))))

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 (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))))))
(+.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)))

eval9.0ms (0.2%)

Compiler: Compiled 351 to 277 computations (21.1% saved)

prune5.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Error

Counts

31 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	17.0b	(sqrt.f64 2)
▶	0.7b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize108.0ms (2.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 x))
✓	0.7b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 19 to 9 computations (52.6% saved)

series57.0ms (1.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	x	@	inf	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
26.0ms	x	@	-inf	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
1.0ms	x	@	0	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
0.0ms	x	@	0	(log1p.f64 (exp.f64 x))
0.0ms	x	@	inf	(log1p.f64 (exp.f64 x))

rewrite59.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

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

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

Outputs

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

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

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

61 → 54

Calls

Call 1

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

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

localize2.0ms (0%)

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

eval15.0ms (0.3%)

Compiler: Compiled 538 to 385 computations (28.4% saved)

prune9.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	52	5	57

Error

Counts

57 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.0b	(sqrt.f64 2)
▶	20.8b	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))
▶	20.6b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
▶	20.2b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))

Compiler

Compiled 49 to 42 computations (14.3% saved)

localize20.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/2 x) (log.f64 2))
✓	0.7b	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))

Compiler

Compiled 32 to 27 computations (15.6% saved)

series5.0ms (0.1%)

Counts

2 → 15

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(+.f64 (*.f64 1/2 x) (log.f64 2))
1.0ms	x	@	0	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))
0.0ms	x	@	inf	(+.f64 (*.f64 1/2 x) (log.f64 2))
0.0ms	x	@	-inf	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))
0.0ms	x	@	inf	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))

rewrite61.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`pow1_binary64`
827×	`add-log-exp_binary64`
826×	`log1p-expm1-u_binary64`
826×	`expm1-log1p-u_binary64`
810×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	187	18
2	2316	18

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))
(+.f64 (*.f64 1/2 x) (log.f64 2))

Outputs

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

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

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

872×	`times-frac_binary64`
641×	`distribute-lft-out_binary64`
454×	`fma-def_binary64`
335×	`*-commutative_binary64`
313×	`fma-neg_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	31	188
1	82	186
2	195	172
3	540	158
4	1997	147
5	3936	143
6	7422	143

Stop Event

1×	node limit

Counts

71 → 69

Calls

Call 1

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

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

localize18.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 44 to 35 computations (20.5% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite90.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	266	22
2	3444	22

Stop Event

1×	node limit

Counts

2 → 126

Calls

Call 1

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

Outputs

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

simplify171.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	356
1	40	354
2	81	297
3	184	249
4	491	249
5	1430	237
6	2387	237
7	3041	237
8	3159	237
9	3294	237
10	3466	237
11	3709	237
12	4024	237
13	4396	237
14	4855	237
15	5444	237
16	6154	237
17	7014	237
18	7442	237
19	7754	237

Stop Event

1×	node limit

Counts

150 → 140

Calls

Call 1

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

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

localize29.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (*.f64 x 7/384)))))
✓	0.1b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
✓	0.1b	(.f64 x (+.f64 3/32 (.f64 x 7/384)))
✓	0.4b	(*.f64 x 7/384)

Compiler

Compiled 73 to 57 computations (21.9% saved)

series6.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(.f64 x (+.f64 3/32 (.f64 x 7/384)))
1.0ms	x	@	inf	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
1.0ms	x	@	0	(*.f64 x 7/384)
0.0ms	x	@	inf	(.f64 x (+.f64 3/32 (.f64 x 7/384)))
0.0ms	x	@	inf	(*.f64 x 7/384)

rewrite96.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

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

Outputs
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simplify132.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

241 → 221

Calls

Call 1

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

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

eval319.0ms (7.2%)

Compiler: Compiled 8029 to 6438 computations (19.8% saved)

prune90.0ms (2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	429	1	430
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	429	6	435

Error

Counts

435 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.0b	(sqrt.f64 2)
▶	20.6b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
✓	20.8b	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))
✓	20.6b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
✓	20.2b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize14.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 23 to 19 computations (17.4% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite60.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×

saturated

Counts

38 → 31

Calls

Call 1

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

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

eval14.0ms (0.3%)

Compiler: Compiled 375 to 334 computations (10.9% saved)

prune7.0ms (0.2%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	31	6	37

Error

Counts

37 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	17.0b	(sqrt.f64 2)
✓	20.6b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x 1/4)))
✓	20.8b	(exp.f64 (.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 1/2))
✓	20.6b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (.f64 x (+.f64 3/32 (.f64 x 7/384)))))))
✓	20.2b	(.f64 (sqrt.f64 2) (+.f64 1 (.f64 x (+.f64 1/4 (*.f64 x 3/32)))))

Compiler

Compiled 58 to 50 computations (13.8% saved)

regimes42.0ms (1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

30.0ms	x
2.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
2.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
2.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
2.0ms	(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 123 to 101 computations (17.9% saved)

regimes5.0ms (0.1%)

Accuracy

Total -4.2b remaining (-24.5%)

Threshold costs -4.2b (-24.5%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
17.0b	1	`x`

Compiler

Compiled 41 to 34 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness73.0ms (1.7%)

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)

end23.0ms (0.5%)

Compiler: Compiled 8 to 7 computations (12.5% saved)

Details

analyze170.0ms (3.9%)

sample2.3s (51.3%)

preprocess57.0ms (1.3%)

simplify31.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize21.0ms (0.5%)

series2.0ms (0%)

rewrite43.0ms (1%)

simplify117.0ms (2.7%)

eval9.0ms (0.2%)

prune5.0ms (0.1%)

localize108.0ms (2.4%)

series57.0ms (1.3%)

rewrite59.0ms (1.3%)

simplify78.0ms (1.8%)

localize2.0ms (0%)

eval15.0ms (0.3%)

prune9.0ms (0.2%)

localize20.0ms (0.5%)

series5.0ms (0.1%)

rewrite61.0ms (1.4%)

simplify65.0ms (1.5%)

localize18.0ms (0.4%)

series3.0ms (0.1%)

rewrite90.0ms (2%)

simplify171.0ms (3.9%)

localize29.0ms (0.7%)

series6.0ms (0.1%)

rewrite96.0ms (2.2%)

simplify132.0ms (3%)

eval319.0ms (7.2%)

prune90.0ms (2%)

localize14.0ms (0.3%)

series2.0ms (0%)

rewrite60.0ms (1.3%)

simplify13.0ms (0.3%)

eval14.0ms (0.3%)

prune7.0ms (0.2%)

regimes42.0ms (1%)

regimes5.0ms (0.1%)

simplify2.0ms (0.1%)

soundness73.0ms (1.7%)

end23.0ms (0.5%)

Profiling