Details

analyze3.0ms (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)

sample4.8s (73.2%)

Results

3.0s	2229×	body	8192	exit
1.3s	7700×	body	128	valid
148.0ms	189×	body	1024	valid
111.0ms	216×	body	512	valid
48.0ms	150×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify136.0ms (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

prune5.0ms (0.1%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.2b	(log1p.f64 (exp.f64 x))

series335.0ms (5.1%)

Counts

2 → 36

Calls

2 calls:

250.0ms	(log1p.f64 (exp.f64 x))
85.0ms	(-.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:

3.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
0.0ms	(log1p.f64 (exp.f64 x))

simplify93.0ms (1.4%)

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

prune36.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

Counts

57 → 3

Alt Table

Status	Error	Program
▶	12.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
	22.5b	(fma.f64 x (+.f64 (-.f64 1/2 y) (.f64 x 1/8)) (-.f64 (log.f64 2) (.f64 1/192 (pow.f64 x 4))))
✓	0.2b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 815 to 310 computations (62% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	0.2b	(log1p.f64 (exp.f64 x))
✓	1.0b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	1.9b	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

series139.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

95.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
44.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
0.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
354×	`distribute-neg-in_binary64`
303×	`sub-neg_binary64`
271×	`associate-+r+_binary64`
222×	`fma-neg_binary64`

Counts

70 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	2386
1	654	2314
2	2649	2270
3	4934	2268
4	5053	2268

prune169.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
✓	12.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
▶	22.5b	(fma.f64 x (+.f64 (-.f64 1/2 y) (.f64 x 1/8)) (-.f64 (log.f64 2) (.f64 1/192 (pow.f64 x 4))))
✓	0.2b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 3910 to 2045 computations (47.7% saved)

localize25.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log.f64 2) (*.f64 1/192 (pow.f64 x 4)))
✓	0.1b	(*.f64 1/192 (pow.f64 x 4))
✓	0.3b	(fma.f64 x (+.f64 (-.f64 1/2 y) (.f64 x 1/8)) (-.f64 (log.f64 2) (.f64 1/192 (pow.f64 x 4))))

series57.0ms (0.9%)

Counts

3 → 27

Calls

3 calls:

35.0ms	(fma.f64 x (+.f64 (-.f64 1/2 y) (.f64 x 1/8)) (-.f64 (log.f64 2) (.f64 1/192 (pow.f64 x 4))))
16.0ms	(-.f64 (log.f64 2) (*.f64 1/192 (pow.f64 x 4)))
6.0ms	(*.f64 1/192 (pow.f64 x 4))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`

Counts

3 → 62

Calls

3 calls:

8.0ms	(*.f64 1/192 (pow.f64 x 4))
7.0ms	(-.f64 (log.f64 2) (*.f64 1/192 (pow.f64 x 4)))
1.0ms	(fma.f64 x (+.f64 (-.f64 1/2 y) (.f64 x 1/8)) (-.f64 (log.f64 2) (.f64 1/192 (pow.f64 x 4))))

simplify159.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-neg_binary64`
495×	`cancel-sign-sub-inv_binary64`
331×	`associate-l_binary64`
309×	`associate-r_binary64`
300×	`fma-def_binary64`

Counts

89 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1603
1	272	1369
2	647	1231
3	2582	1229
4	4403	1229
5	4863	1229

prune176.0ms (2.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
✓	12.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	22.5b	(fma.f64 x (+.f64 (-.f64 1/2 y) (.f64 x 1/8)) (-.f64 (log.f64 2) (.f64 1/192 (pow.f64 x 4))))
✓	0.2b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 2418 to 1898 computations (21.5% saved)

regimes174.0ms (2.7%)

Accuracy

Total 0.2b remaining (48.9%)

Threshold costs 0.2b (48.9%)

Counts

27 → 1

Compiler

Compiled 950 to 730 computations (23.2% saved)

simplify5.0ms (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

end105.0ms (1.6%)

Compiler: Compiled 57 to 41 computations (28.1% saved)

Details

analyze3.0ms (0%)

sample4.8s (73.2%)

simplify136.0ms (2.1%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

series335.0ms (5.1%)

rewrite4.0ms (0.1%)

simplify93.0ms (1.4%)

prune36.0ms (0.6%)

localize11.0ms (0.2%)

series139.0ms (2.1%)

rewrite2.0ms (0%)

simplify91.0ms (1.4%)

prune169.0ms (2.6%)

localize25.0ms (0.4%)

series57.0ms (0.9%)

rewrite20.0ms (0.3%)

simplify159.0ms (2.4%)

prune176.0ms (2.7%)

regimes174.0ms (2.7%)

simplify5.0ms (0.1%)

end105.0ms (1.6%)

Profiling