Details

analyze3.0ms (0.2%)

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
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.0s (49.9%)

Results

1.0s	8256×	body	256	valid
0.0ms	3×	body	256	invalid

Bogosity

preprocess149.0ms (7.2%)

Algorithm

2×	egg-herbie

Rules

600×	`unsub-neg_binary64`
586×	`distribute-rgt-out--_binary64`
492×	`fma-neg_binary64`
430×	`distribute-neg-in_binary64`
411×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	20	9
3	31	9
4	48	9
5	76	9
6	123	9
7	340	9
8	707	9
9	1496	9
10	2853	9
11	4280	9
12	5252	9
13	5562	9
14	5866	9
15	5962	9
16	6040	9
17	6308	9
18	7254	9
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify140.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

600×	`unsub-neg_binary64`
586×	`distribute-rgt-out--_binary64`
492×	`fma-neg_binary64`
430×	`distribute-neg-in_binary64`
411×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	20	9
3	31	9
4	48	9
5	76	9
6	123	9
7	340	9
8	707	9
9	1496	9
10	2853	9
11	4280	9
12	5252	9
13	5562	9
14	5866	9
15	5962	9
16	6040	9
17	6308	9
18	7254	9

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 8 computations (52.9% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

580×	`pow1_binary64`
544×	`add-log-exp_binary64`
543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
531×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	126	9
2	1548	9

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (pow.f64 (-.f64 1 (.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2))))))

simplify54.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-l_binary64`
633×	`fma-def_binary64`
591×	`distribute-neg-frac_binary64`
560×	`associate-r_binary64`
223×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	276
1	151	256
2	460	244
3	1607	238
4	6771	238

Stop Event

1×	node limit

Counts

34 → 45

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (.f64 -1/8 (pow.f64 x 4)))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/8 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/2 (.f64 x x)))))
(fma.f64 -1/8 (pow.f64 x 4) (fma.f64 -1/16 (pow.f64 x 6) (fma.f64 x (*.f64 -1/2 x) 1)))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))
(+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 -1/8 (.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (.f64 x (sqrt.f64 -1)) (.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (.f64 x x)) 1/2)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (-.f64 (+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (fma.f64 x (sqrt.f64 -1) (/.f64 -1/8 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 (/.f64 -1 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (.f64 x x)) 1/2)))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (.f64 x x)) 1/2)))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 x))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(fma.f64 (neg.f64 (sqrt.f64 -1)) x (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))))
(-.f64 (/.f64 -1/2 (.f64 x (sqrt.f64 -1))) (.f64 x (sqrt.f64 -1)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 (neg.f64 (sqrt.f64 -1)) x (/.f64 -1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(-.f64 (+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (neg.f64 (.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 (neg.f64 (sqrt.f64 -1)) x (/.f64 -1/2 (.f64 x (sqrt.f64 -1))))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))) (/.f64 -1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))
(-.f64 (.f64 (/.f64 -1 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (.f64 x x)) 1/2)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))

eval15.0ms (0.7%)

Compiler: Compiled 606 to 461 computations (23.9% saved)

prune7.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Error

Counts

46 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	0.5b	(fma.f64 x (*.f64 -1/2 x) 1)
	1.0b	1
▶	0b	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Compiler

Compiled 25 to 19 computations (24% saved)

localize11.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)

Compiler

Compiled 29 to 10 computations (65.5% saved)

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
1.0ms	x	@	inf	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
1.0ms	x	@	-inf	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)

rewrite47.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

508×	`pow1_binary64`
494×	`add-sqr-sqrt_binary64`
469×	`add-log-exp_binary64`
468×	`expm1-log1p-u_binary64`
467×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	142	9
2	1686	9

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)

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

Outputs

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

simplify237.0ms (11.5%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
643×	`times-frac_binary64`
413×	`unswap-sqr_binary64`
396×	`associate-l_binary64`
365×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	302
1	153	282
2	432	267
3	1356	264
4	5380	264

Stop Event

1×	node limit

Counts

23 → 35

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/4 (pow.f64 x 4)))
(+.f64 (.f64 -1/6 (pow.f64 x 6)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/4 (pow.f64 x 4))))
(+.f64 (.f64 -1/6 (pow.f64 x 6)) (+.f64 (.f64 -1/8 (pow.f64 x 8)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/4 (pow.f64 x 4)))))
(.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x)))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x))))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x))))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x))))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/6 (/.f64 1 (pow.f64 x 6))))))
(.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1)))
(-.f64 (.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/6 (/.f64 1 (pow.f64 x 6))))))

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/4 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 -1/4 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/4) -1/2)))
(+.f64 (.f64 -1/6 (pow.f64 x 6)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/4 (pow.f64 x 4))))
(fma.f64 -1/6 (pow.f64 x 6) (fma.f64 -1/2 (.f64 x x) (.f64 -1/4 (pow.f64 x 4))))
(fma.f64 -1/2 (.f64 x x) (fma.f64 -1/4 (pow.f64 x 4) (.f64 -1/6 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/4) -1/2) (*.f64 -1/6 (pow.f64 x 6)))
(+.f64 (.f64 -1/6 (pow.f64 x 6)) (+.f64 (.f64 -1/8 (pow.f64 x 8)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/4 (pow.f64 x 4)))))
(fma.f64 -1/6 (pow.f64 x 6) (fma.f64 -1/8 (pow.f64 x 8) (fma.f64 -1/2 (.f64 x x) (.f64 -1/4 (pow.f64 x 4)))))
(fma.f64 -1/6 (pow.f64 x 6) (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/4 (pow.f64 x 4) (.f64 -1/8 (pow.f64 x 8)))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/8 -1/4) (fma.f64 -1/2 (.f64 x x) (.f64 -1/6 (pow.f64 x 6))))
(.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x)))))
(.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (neg.f64 (log.f64 x)))))
(*.f64 1/2 (fma.f64 -2 (neg.f64 (log.f64 x)) (log.f64 -1)))
(fma.f64 1/2 (log.f64 -1) (log.f64 x))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x))))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (neg.f64 (log.f64 x))))) (/.f64 1/2 (*.f64 x x)))
(fma.f64 1/2 (fma.f64 -2 (neg.f64 (log.f64 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x)))
(+.f64 (fma.f64 1/2 (log.f64 -1) (log.f64 x)) (/.f64 -1/2 (*.f64 x x)))
(fma.f64 1/2 (-.f64 (log.f64 -1) (/.f64 1 (*.f64 x x))) (log.f64 x))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x))))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (neg.f64 (log.f64 x))))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4))))
(-.f64 (fma.f64 1/2 (fma.f64 -2 (neg.f64 (log.f64 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 4)))
(+.f64 (fma.f64 1/2 (log.f64 -1) (log.f64 x)) (+.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 -1/4 (pow.f64 x 4))))
(+.f64 (fma.f64 1/2 (log.f64 -1) (log.f64 x)) (-.f64 (/.f64 -1/4 (pow.f64 x 4)) (/.f64 1/2 (*.f64 x x))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (log.f64 (/.f64 1 x))))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/6 (/.f64 1 (pow.f64 x 6))))))
(-.f64 (.f64 1/2 (+.f64 (log.f64 -1) (.f64 -2 (neg.f64 (log.f64 x))))) (+.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/6 (pow.f64 x 6)))))
(-.f64 (-.f64 (fma.f64 1/2 (fma.f64 -2 (neg.f64 (log.f64 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 4))) (/.f64 1/6 (pow.f64 x 6)))
(+.f64 (fma.f64 1/2 (log.f64 -1) (log.f64 x)) (+.f64 (/.f64 -1/4 (pow.f64 x 4)) (+.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 -1/6 (pow.f64 x 6)))))
(+.f64 (+.f64 (fma.f64 1/2 (log.f64 -1) (log.f64 x)) (/.f64 -1/4 (pow.f64 x 4))) (+.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 -1/6 (pow.f64 x 6))))
(.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1)))
(*.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(fma.f64 1/2 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 x))))
(-.f64 (*.f64 1/2 (log.f64 -1)) (log.f64 (/.f64 -1 x)))
(fma.f64 1/2 (log.f64 -1) (-.f64 (log.f64 x) (log.f64 -1)))
(-.f64 (.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 1/2 (.f64 x x)))
(fma.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x)))
(fma.f64 1/2 (log.f64 -1) (-.f64 (/.f64 -1/2 (*.f64 x x)) (log.f64 (/.f64 -1 x))))
(-.f64 (.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 1/4 (pow.f64 x 4))))
(-.f64 (fma.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 4)))
(+.f64 (fma.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x))) (/.f64 -1/4 (pow.f64 x 4)))
(+.f64 (fma.f64 1/2 (log.f64 -1) (-.f64 (/.f64 -1/2 (*.f64 x x)) (log.f64 (/.f64 -1 x)))) (/.f64 -1/4 (pow.f64 x 4)))
(-.f64 (.f64 1/2 (+.f64 (.f64 -2 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/6 (/.f64 1 (pow.f64 x 6))))))
(-.f64 (.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 1/6 (pow.f64 x 6)))))
(-.f64 (-.f64 (fma.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1)) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 4))) (/.f64 1/6 (pow.f64 x 6)))
(fma.f64 1/2 (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 -1)) (+.f64 (/.f64 -1/4 (pow.f64 x 4)) (+.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 -1/6 (pow.f64 x 6)))))
(+.f64 (fma.f64 1/2 (log.f64 -1) (-.f64 (/.f64 -1/2 (*.f64 x x)) (log.f64 (/.f64 -1 x)))) (+.f64 (/.f64 -1/4 (pow.f64 x 4)) (/.f64 -1/6 (pow.f64 x 6))))

localize6.0ms (0.3%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

eval116.0ms (5.6%)

Compiler: Compiled 551 to 425 computations (22.9% saved)

prune13.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	35	4	39

Error

Counts

39 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.5b	(fma.f64 x (*.f64 -1/2 x) 1)
	1.0b	1
✓	0b	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Compiler

Compiled 25 to 19 computations (24% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.5b	(fma.f64 x (*.f64 -1/2 x) 1)
	1.0b	1
✓	0b	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Compiler

Compiled 25 to 19 computations (24% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.5b	(fma.f64 x (*.f64 -1/2 x) 1)
	1.0b	1
✓	0b	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Compiler

Compiled 25 to 19 computations (24% saved)

regimes65.0ms (3.2%)

Counts

4 → 1

Calls

Call 1

Inputs
1
(fma.f64 x (*.f64 -1/2 x) 1)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Outputs
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Calls

7 calls:

36.0ms	x
6.0ms	(*.f64 x x)
5.0ms	(*.f64 x x)
4.0ms	(-.f64 1 (*.f64 x x))
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`(sqrt.f64 (-.f64 1 (*.f64 x x)))`
0b	1	`(sqrt.f64 (-.f64 1 (*.f64 x x)))`
0b	1	`(-.f64 1 (*.f64 x x))`
0b	1	`(-.f64 1 (*.f64 x x))`
0b	1	`(*.f64 x x)`
0b	1	`(*.f64 x x)`

Compiler

Compiled 58 to 39 computations (32.8% saved)

regimes23.0ms (1.1%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Calls

4 calls:

8.0ms	x
4.0ms	(*.f64 x x)
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
4.0ms	(-.f64 1 (*.f64 x x))

Results

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

Compiler

Compiled 33 to 22 computations (33.3% saved)

regimes8.0ms (0.4%)

Accuracy

Total -0.5b remaining (-100.8%)

Threshold costs -0.5b (-100.8%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(fma.f64 x (*.f64 -1/2 x) 1)

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
0.5b	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	27	31
2	32	31
3	35	31
4	36	31

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(fma.f64 x (*.f64 -1/2 x) 1)
1

Outputs
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(exp.f64 (.f64 (log1p.f64 (neg.f64 (.f64 x x))) 1/2))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(fma.f64 x (*.f64 -1/2 x) 1)
(fma.f64 x (*.f64 x -1/2) 1)
1

Compiler

Compiled 25 to 19 computations (24% saved)

soundness0.0ms (0%)

end58.0ms (2.8%)

Compiler: Compiled 22 to 15 computations (31.8% saved)

Details

analyze3.0ms (0.2%)

sample1.0s (49.9%)

preprocess149.0ms (7.2%)

simplify140.0ms (6.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite51.0ms (2.5%)

simplify54.0ms (2.6%)

eval15.0ms (0.7%)

prune7.0ms (0.3%)

localize11.0ms (0.6%)

series3.0ms (0.2%)

rewrite47.0ms (2.3%)

simplify237.0ms (11.5%)

localize6.0ms (0.3%)

eval116.0ms (5.6%)

prune13.0ms (0.6%)

eval0.0ms (0%)

prune3.0ms (0.2%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes65.0ms (3.2%)

regimes23.0ms (1.1%)

regimes8.0ms (0.4%)

simplify10.0ms (0.5%)

soundness0.0ms (0%)

end58.0ms (2.8%)

Profiling