Details

analyze417.0ms (6.7%)

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
25%	74.9%	0.1%	5
43.7%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample3.9s (63.5%)

Results

2.5s	2566×	body	8192	exit
987.0ms	7664×	body	128	valid
121.0ms	196×	body	1024	valid
110.0ms	262×	body	512	valid
32.0ms	133×	body	256	valid
15.0ms	78×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify101.0ms (1.6%)

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

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series228.0ms (3.7%)

Counts

2 → 36

Calls

2 calls:

158.0ms	(log1p.f64 (exp.f64 x))
70.0ms	(-.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))

simplify75.0ms (1.2%)

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

prune31.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	55	3	58

Error

0.2b

Counts

58 → 3

Alt Table

Status	Error	Program
	13.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
▶	10.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 795 to 294 computations (63% 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))

series10.0ms (0.2%)

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))

simplify73.0ms (1.2%)

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

prune19.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	21	4	25

Error

0.2b

Counts

25 → 4

Alt Table

Status	Error	Program
	13.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	12.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
	28.3b	(log.f64 (.f64 2 (exp.f64 (.f64 x (-.f64 1/2 y)))))

Compiler

Compiled 315 to 238 computations (24.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	0.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	1.1b	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

series126.0ms (2%)

Counts

3 → 72

Calls

3 calls:

81.0ms

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

35.0ms

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

10.0ms

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

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

4.0ms

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

1.0ms

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

simplify147.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
597×	`fma-def_binary64`
506×	`associate-/l*_binary64`
250×	`*-commutative_binary64`
137×	`+-commutative_binary64`

Counts

165 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	669	9535
1	2330	8681
2	5361	8681

prune516.0ms (8.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	393	4	397

Error

0.2b

Counts

397 → 4

Alt Table

Status	Error	Program
▶	13.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	28.3b	(log.f64 (.f64 2 (exp.f64 (.f64 x (-.f64 1/2 y)))))
	60.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))))

Compiler

Compiled 24231 to 18870 computations (22.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.0b	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
	0.2b	(log1p.f64 (exp.f64 x))
✓	1.1b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

series111.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

70.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
40.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite3.0ms (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:

1.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
1.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

simplify104.0ms (1.7%)

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

prune88.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	145	4	149

Error

0.2b

Counts

149 → 4

Alt Table

Status	Error	Program
✓	13.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	28.3b	(log.f64 (.f64 2 (exp.f64 (.f64 x (-.f64 1/2 y)))))
	60.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))))

Compiler

Compiled 3934 to 2063 computations (47.6% saved)

regimes85.0ms (1.4%)

Accuracy

Total 0.2b remaining (37.1%)

Threshold costs 0.2b (37.1%)

Counts

29 → 1

Compiler

Compiled 1129 to 885 computations (21.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-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	9	14
1	18	14
2	27	14
3	33	14
4	37	14
5	38	14
6	37	14

end76.0ms (1.2%)

Compiler: Compiled 104 to 79 computations (24% saved)

Details

analyze417.0ms (6.7%)

sample3.9s (63.5%)

simplify101.0ms (1.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series228.0ms (3.7%)

rewrite4.0ms (0.1%)

simplify75.0ms (1.2%)

prune31.0ms (0.5%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify73.0ms (1.2%)

prune19.0ms (0.3%)

localize9.0ms (0.1%)

series126.0ms (2%)

rewrite17.0ms (0.3%)

simplify147.0ms (2.4%)

prune516.0ms (8.3%)

localize8.0ms (0.1%)

series111.0ms (1.8%)

rewrite3.0ms (0%)

simplify104.0ms (1.7%)

prune88.0ms (1.4%)

regimes85.0ms (1.4%)

simplify3.0ms (0%)

end76.0ms (1.2%)

Profiling