Details

analyze1.2s (11.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
12.5%	85.9%	1.7%	7
21.9%	76.5%	1.7%	8
23.4%	74.1%	2.4%	9
28.9%	68.7%	2.4%	10
30%	67.1%	2.8%	11
33%	64.2%	2.8%	12
33.7%	63.3%	3%	13
33.7%	63.3%	3%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample7.1s (63.8%)

Results

5.4s	3276×	body	8192	exit
1.2s	7607×	body	128	valid
175.0ms	255×	body	1024	valid
113.0ms	250×	body	512	valid
41.0ms	144×	body	256	valid
5.0ms	29×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify100.0ms (0.9%)

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%)

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.7b	(log1p.f64 (exp.f64 x))

series300.0ms (2.7%)

Counts

2 → 36

Calls

2 calls:

208.0ms	(log1p.f64 (exp.f64 x))
92.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite6.0ms (0%)

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))

simplify80.0ms (0.7%)

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

prune39.0ms (0.3%)

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

0.4b

Counts

57 → 3

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	0.8b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
	11.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 797 to 296 computations (62.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
	0.7b	(log1p.f64 (exp.f64 x))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	0.7b	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))

series513.0ms (4.6%)

Counts

3 → 48

Calls

3 calls:

211.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
207.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
95.0ms	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
15×	`fma-neg_binary64`

Counts

3 → 92

Calls

3 calls:

7.0ms	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
2.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
2.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-l_binary64`
532×	`fma-def_binary64`
437×	`fma-neg_binary64`
300×	`log-prod_binary64`
245×	`cancel-sign-sub-inv_binary64`

Counts

140 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1758
1	310	1614
2	942	1481
3	3073	1474
4	4605	1474
5	4887	1474

prune141.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	147	3	150

Error

0.4b

Counts

150 → 3

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	11.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
	14.0b	(-.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8))))) (*.f64 x y))

Compiler

Compiled 2623 to 1274 computations (51.4% saved)

localize7.0ms (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))

series11.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(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))

simplify64.0ms (0.6%)

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

prune21.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	22	3	25

Error

0.4b

Counts

25 → 3

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	11.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
▶	14.0b	(-.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8))))) (*.f64 x y))

Compiler

Compiled 310 to 241 computations (22.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (log.f64 2) (.f64 x x))
✓	1.0b	(pow.f64 (log.f64 2) 2)
✓	7.8b	(+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8))))
✓	10.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8)))))

series107.0ms (1%)

Counts

4 → 36

Calls

4 calls:

73.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8)))))
21.0ms	(.f64 (log.f64 2) (.f64 x x))
12.0ms	(+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8))))
0.0ms	(pow.f64 (log.f64 2) 2)

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`associate-*r/_binary64`
40×	`frac-add_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
14×	`cbrt-div_binary64`

Counts

4 → 102

Calls

4 calls:

11.0ms	(+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8))))
11.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8)))))
4.0ms	(.f64 (log.f64 2) (.f64 x x))
2.0ms	(pow.f64 (log.f64 2) 2)

simplify165.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

462×	`fma-def_binary64`
362×	`distribute-rgt-in_binary64`
352×	`distribute-lft-in_binary64`
247×	`times-frac_binary64`
211×	`associate-/r*_binary64`

Counts

138 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	11195
1	1491	10172
2	5029	10172

prune464.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	192	4	196

Error

0.4b

Counts

196 → 4

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	15.7b	(-.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 (log.f64 2) (.f64 x x)) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))) (.f64 (pow.f64 x 3) (+.f64 1/8 (.f64 (log.f64 2) 3/8))))))) (*.f64 x y))
	59.5b	(-.f64 (-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (log.f64 2) 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x))))))) (.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2))) x))) (+.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x)))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (log.f64 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x))))))) (.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2))) x))) (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 2) 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x))))))) (.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2))) (pow.f64 x 2))))))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (log.f64 2) 3) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x))))))) (.f64 (pow.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2))) 2) (pow.f64 x 2)))) (+.f64 (.f64 1/64 (/.f64 (.f64 (pow.f64 (log.f64 2) 4) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x))))))) (.f64 (pow.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2))) 2) (pow.f64 x 2)))) (.f64 1/16 (/.f64 (.f64 (pow.f64 (log.f64 2) 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2)))) (.f64 3 (log.f64 (/.f64 1 x))))))) (.f64 (pow.f64 (+.f64 1/8 (.f64 3/8 (log.f64 2))) 2) (pow.f64 x 2))))))) (.f64 x y))
✓	11.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 17785 to 15410 computations (13.4% saved)

regimes374.0ms (3.4%)

Accuracy

Total 0.3b remaining (62.8%)

Threshold costs 0.3b (62.8%)

Counts

103 → 1

Compiler

Compiled 7670 to 6049 computations (21.1% saved)

simplify3.0ms (0%)

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

end197.0ms (1.8%)

Compiler: Compiled 320 to 288 computations (10% saved)

Details

analyze1.2s (11.1%)

sample7.1s (63.8%)

simplify100.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series300.0ms (2.7%)

rewrite6.0ms (0%)

simplify80.0ms (0.7%)

prune39.0ms (0.3%)

localize8.0ms (0.1%)

series513.0ms (4.6%)

rewrite16.0ms (0.1%)

simplify100.0ms (0.9%)

prune141.0ms (1.3%)

localize7.0ms (0.1%)

series11.0ms (0.1%)

rewrite1.0ms (0%)

simplify64.0ms (0.6%)

prune21.0ms (0.2%)

localize22.0ms (0.2%)

series107.0ms (1%)

rewrite44.0ms (0.4%)

simplify165.0ms (1.5%)

prune464.0ms (4.2%)

regimes374.0ms (3.4%)

simplify3.0ms (0%)

end197.0ms (1.8%)

Profiling