Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample3.0s (62.2%)

Results

1.8s	2234×	body	8192	exit
830.0ms	7693×	body	128	valid
109.0ms	204×	body	1024	valid
74.0ms	217×	body	512	valid
29.0ms	141×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 x))
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

series298.0ms (6.2%)

Counts

2 → 36

Calls

2 calls:

205.0ms	(log1p.f64 (exp.f64 x))
93.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
0.0ms	(log1p.f64 (exp.f64 x))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

620×	`cancel-sign-sub-inv_binary64`
339×	`unswap-sqr_binary64`
285×	`*-commutative_binary64`
285×	`unsub-neg_binary64`
252×	`distribute-rgt-in_binary64`

Counts

68 → 56

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	73	789
1	167	742
2	426	710
3	1507	707
4	3171	707
5	4588	701
6	4872	701

prune34.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	1.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
	23.4b	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
	8.3b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 839 to 310 computations (63.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.3b	(.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	0.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	5.1b	(cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

series204.0ms (4.3%)

Counts

3 → 72

Calls

3 calls:

89.0ms

(*.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

60.0ms

(*.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

54.0ms

(cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`
29×	`pow1_binary64`

Counts

3 → 129

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

7.0ms

(*.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

2.0ms

(cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

simplify158.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-r_binary64`
436×	`associate-l_binary64`
392×	`times-frac_binary64`
336×	`fma-def_binary64`
310×	`associate-/r*_binary64`

Counts

201 → 263

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	494	9159
1	1450	8574
2	5488	8574

prune348.0ms (7.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	508	0	508
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	508	4	512

Error

Counts

512 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	1.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
	23.4b	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
▶	8.3b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 24738 to 8705 computations (64.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series13.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
478×	`neg-sub0_binary64`
433×	`neg-mul-1_binary64`
375×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	459
1	52	346
2	104	346
3	328	346
4	1670	346
5	2981	346
6	4467	346
7	4969	346

prune16.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	22	4	26

Error

Counts

26 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	1.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
▶	23.4b	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	8.3b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 274 to 192 computations (29.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 x))
	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.1b	(exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
✓	1.3b	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

series99.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

89.0ms	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
10.0ms	(exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`exp-sum_binary64`
8×	`log-prod_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
3.0ms	(exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
544×	`associate-l_binary64`
446×	`associate-r_binary64`
359×	`associate--l+_binary64`
274×	`cancel-sign-sub-inv_binary64`

Counts

92 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	1475
1	366	1378
2	1192	1312
3	4705	1306
4	4991	1306
5	4973	1306

prune71.0ms (1.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	1.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	23.4b	(log.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	8.3b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 2365 to 830 computations (64.9% saved)

regimes70.0ms (1.5%)

Accuracy

Total 0.1b remaining (55%)

Threshold costs 0.1b (55%)

Counts

23 → 1

Compiler

Compiled 800 to 529 computations (33.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	23	11
3	29	11
4	33	11
5	34	11
6	34	11

end58.0ms (1.2%)

Compiler: Compiled 75 to 42 computations (44% saved)

Details

analyze1.0ms (0%)

sample3.0s (62.2%)

simplify100.0ms (2.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series298.0ms (6.2%)

rewrite4.0ms (0.1%)

simplify77.0ms (1.6%)

prune34.0ms (0.7%)

localize9.0ms (0.2%)

series204.0ms (4.3%)

rewrite44.0ms (0.9%)

simplify158.0ms (3.3%)

prune348.0ms (7.3%)

localize6.0ms (0.1%)

series13.0ms (0.3%)

rewrite1.0ms (0%)

simplify67.0ms (1.4%)

prune16.0ms (0.3%)

localize8.0ms (0.2%)

series99.0ms (2.1%)

rewrite8.0ms (0.2%)

simplify98.0ms (2.1%)

prune71.0ms (1.5%)

regimes70.0ms (1.5%)

simplify3.0ms (0.1%)

end58.0ms (1.2%)

Profiling