Details

analyze118.0ms (3.7%)

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%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.0s (62%)

Results

1.0s	8256×	body	256	valid
798.0ms	7147×	body	256	infinite
131.0ms	1067×	body	256	invalid

Bogosity

preprocess149.0ms (4.7%)

Algorithm

2×	egg-herbie

Rules

864×	`fma-neg_binary64`
682×	`unsub-neg_binary64`
430×	`distribute-neg-in_binary64`
420×	`sub-neg_binary64`
353×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	76	12
5	152	12
6	359	12
7	756	12
8	2543	12
9	4491	12
10	5836	12
11	6572	12
12	6876	12
13	7073	12
14	7205	12
15	7549	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify134.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
682×	`unsub-neg_binary64`
430×	`distribute-neg-in_binary64`
420×	`sub-neg_binary64`
353×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	76	12
5	152	12
6	359	12
7	756	12
8	2543	12
9	4491	12
10	5836	12
11	6572	12
12	6876	12
13	7073	12
14	7205	12
15	7549	12

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize14.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	29.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 34 to 17 computations (50% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite48.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`pow1_binary64`
535×	`add-log-exp_binary64`
533×	`log1p-expm1-u_binary64`
533×	`expm1-log1p-u_binary64`
522×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	129	7
2	1590	7

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify46.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

674×	`associate-/l*_binary64`
564×	`unswap-sqr_binary64`
452×	`associate-/r*_binary64`
394×	`fma-def_binary64`
389×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	204
1	143	193
2	378	187
3	1227	185
4	6039	185

Stop Event

1×	node limit

Counts

36 → 46

Calls

Call 1

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

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

eval15.0ms (0.5%)

Compiler: Compiled 656 to 492 computations (25% saved)

prune7.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Error

Counts

47 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 x x))
✓	31.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	0b	(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))))))
▶	0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize7.0ms (0.2%)

Compiler: Compiled 9 to 3 computations (66.7% saved)

localize28.0ms (0.9%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 x 3)
✓	0.4b	(/.f64 -1/8 (pow.f64 x 3))

Compiler

Compiled 63 to 46 computations (27% saved)

series4.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 -1/8 (pow.f64 x 3))
1.0ms	x	@	-inf	(pow.f64 x 3)
1.0ms	x	@	inf	(pow.f64 x 3)
1.0ms	x	@	inf	(/.f64 -1/8 (pow.f64 x 3))
0.0ms	x	@	-inf	(/.f64 -1/8 (pow.f64 x 3))

rewrite59.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

559×	`pow1_binary64`
532×	`add-log-exp_binary64`
532×	`log1p-expm1-u_binary64`
532×	`expm1-log1p-u_binary64`
521×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	136	11
2	1480	11

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(/.f64 -1/8 (pow.f64 x 3))
(pow.f64 x 3)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 -1/8 (pow.f64 x -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/8 (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1/8 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 -1/8 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 -1/8) x) (pow.f64 (/.f64 (cbrt.f64 -1/8) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (cbrt.f64 -1/8) x) 2) (/.f64 (cbrt.f64 -1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)) (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (/.f64 1 (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -3) -1/8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/8 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 -1/8 (pow.f64 x -3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 -1/8) x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 3) -8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/64 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/8) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 -1/8 (pow.f64 x -3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -1/8 (pow.f64 x -3))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 x -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/8 (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/8 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 -1/8 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 -1/8) x) (pow.f64 (/.f64 (cbrt.f64 -1/8) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (cbrt.f64 -1/8) x) 2) (/.f64 (cbrt.f64 -1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)) (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (/.f64 1 (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -3) -1/8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/8 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/8 (pow.f64 x -3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 -1/8) x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) -8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/64 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/8) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/8 (pow.f64 x -3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/8 (pow.f64 x -3))))))))

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

39 → 39

Calls

Call 1

Inputs

Outputs

localize14.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 26 to 16 computations (38.5% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite60.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

933×	`pow1_binary64`
880×	`add-log-exp_binary64`
879×	`log1p-expm1-u_binary64`
879×	`expm1-log1p-u_binary64`
864×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	149	10
2	2320	10

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-def_binary64`
71×	`fma-neg_binary64`
30×	`associate-/r*_binary64`
30×	`cancel-sign-sub-inv_binary64`
23×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	102
1	23	84
2	37	84
3	54	84
4	79	84
5	116	84
6	184	84
7	253	84
8	334	84
9	448	84
10	569	84
11	579	84

Stop Event

1×

saturated

Counts

47 → 40

Calls

Call 1

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

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

eval28.0ms (0.9%)

Compiler: Compiled 1316 to 901 computations (31.5% saved)

prune29.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	0	0
Picked	0	1	1
Done	2	1	3
Total	80	3	83

Error

Counts

83 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (.f64 (.f64 x x) x))))))
✓	0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
✓	0.3b	(log.f64 (+.f64 x x))

Compiler

Compiled 31 to 20 computations (35.5% saved)

localize26.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x x) x)
✓	0.4b	(/.f64 -1/8 (.f64 (.f64 x x) x))

Compiler

Compiled 77 to 35 computations (54.5% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (.f64 x x) x)
0.0ms	x	@	-inf	(.f64 (.f64 x x) x)
0.0ms	x	@	0	(/.f64 -1/8 (.f64 (.f64 x x) x))
0.0ms	x	@	inf	(/.f64 -1/8 (.f64 (.f64 x x) x))
0.0ms	x	@	-inf	(/.f64 -1/8 (.f64 (.f64 x x) x))

rewrite51.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`pow1_binary64`
534×	`add-log-exp_binary64`
534×	`log1p-expm1-u_binary64`
534×	`expm1-log1p-u_binary64`
522×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	127	11
2	1532	11

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

Inputs
(/.f64 -1/8 (.f64 (.f64 x x) x))
(.f64 (.f64 x x) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 x -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/8 (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/8 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 -1/8 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 -1/8) x) (pow.f64 (/.f64 (cbrt.f64 -1/8) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (cbrt.f64 -1/8) x) 2) (/.f64 (cbrt.f64 -1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)) (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (/.f64 1 (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -3) -1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/8 (*.f64 x x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/8 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/8 (pow.f64 x -3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 -1/8) x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) -8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/64 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/8) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/8 (pow.f64 x -3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/8 (pow.f64 x -3))))))))

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

simplify170.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
469×	`fabs-mul_binary64`
455×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	132
1	14	132
2	25	132
3	39	132
4	74	132
5	216	132
6	779	132
7	2257	132
8	2345	132
9	2478	132
10	2636	132
11	2895	132
12	3223	132
13	3645	132
14	4148	132
15	4749	132
16	5467	132
17	5790	132
18	6072	132
19	6296	132
20	6472	132
21	6554	132
22	7494	132

Stop Event

1×	node limit

Counts

56 → 33

Calls

Call 1

Inputs
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)

Outputs
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(/.f64 -1/8 (pow.f64 x 3))
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)

eval12.0ms (0.4%)

Compiler: Compiled 546 to 409 computations (25.1% saved)

prune7.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	33	3	36

Error

Counts

36 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (.f64 (.f64 x x) x))))))
✓	0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
✓	0.3b	(log.f64 (+.f64 x x))

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes14.0ms (0.5%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (.f64 (.f64 x x) x))))))

Calls

3 calls:

4.0ms	x
4.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
4.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Results

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

Compiler

Compiled 73 to 47 computations (35.6% saved)

regimes5.0ms (0.2%)

Accuracy

Total -0.2b remaining (-681.8%)

Threshold costs -0.2b (-681.8%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 15 to 9 computations (40% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	23	42

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (.f64 (.f64 x x) x))))))
(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (.f64 (.f64 x x) x))))))
(log.f64 (+.f64 x (+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (.f64 x (.f64 x x)))))))
(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
(log.f64 (+.f64 x x))

Compiler

Compiled 31 to 20 computations (35.5% saved)

soundness80.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

674×	`associate-/l*_binary64`
564×	`unswap-sqr_binary64`
452×	`associate-/r*_binary64`
394×	`fma-def_binary64`
389×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	204
1	143	193
2	378	187
3	1227	185
4	6039	185

Stop Event

1×	node limit

Compiler

Compiled 258 to 210 computations (18.6% saved)

end27.0ms (0.8%)

Compiler: Compiled 29 to 18 computations (37.9% saved)

Iter	Nodes	Cost
0	11	102
1	23	84
2	37	84
3	54	84
4	79	84
5	116	84
6	184	84
7	253	84
8	334	84
9	448	84
10	569	84
11	579	84

Iter	Nodes	Cost
0	11	102
1	23	84
2	37	84
3	54	84
4	79	84
5	116	84
6	184	84
7	253	84
8	334	84
9	448	84
10	569	84
11	579	84

Details

analyze118.0ms (3.7%)

sample2.0s (62%)

preprocess149.0ms (4.7%)

simplify134.0ms (4.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize14.0ms (0.5%)

series2.0ms (0.1%)

rewrite48.0ms (1.5%)

simplify46.0ms (1.5%)

eval15.0ms (0.5%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

localize28.0ms (0.9%)

series4.0ms (0.1%)

rewrite59.0ms (1.9%)

simplify7.0ms (0.2%)

localize14.0ms (0.4%)

series2.0ms (0.1%)

rewrite60.0ms (1.9%)

simplify24.0ms (0.7%)

eval28.0ms (0.9%)

prune29.0ms (0.9%)

localize26.0ms (0.8%)

series3.0ms (0.1%)

rewrite51.0ms (1.6%)

simplify170.0ms (5.4%)

eval12.0ms (0.4%)

prune7.0ms (0.2%)

regimes14.0ms (0.5%)

regimes5.0ms (0.2%)

simplify5.0ms (0.2%)

soundness80.0ms (2.5%)

end27.0ms (0.8%)

Profiling

Iter	Nodes	Cost
0	11	102
1	23	84
2	37	84
3	54	84
4	79	84
5	116	84
6	184	84
7	253	84
8	334	84
9	448	84
10	569	84
11	579	84