Details

analyze401.0ms (5.7%)

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)

sample4.0s (57.4%)

Results

2.5s	2563×	body	8192	exit
1.1s	7625×	body	128	valid
153.0ms	234×	body	1024	valid
96.0ms	243×	body	512	valid
38.0ms	152×	body	256	valid
9.0ms	71×	body	128	invalid
3.0ms	2×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify101.0ms (1.4%)

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	0.9b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(log1p.f64 (exp.f64 x))

series153.0ms (2.2%)

Counts

1 → 12

Calls

1 calls:

153.0ms

(log1p.f64 (exp.f64 x))

rewrite72.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

291×	`expm1-log1p-u_binary64`
290×	`log1p-expm1-u_binary64`
269×	`add-cbrt-cube_binary64`
261×	`add-log-exp_binary64`
259×	`add-exp-log_binary64`

Counts

1 → 34

Calls

1 calls:

71.0ms

(log1p.f64 (exp.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	73	5
2	786	5
3	4890	5
4	4923	5
0	0	0
1	0	0

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
663×	`fma-neg_binary64`
607×	`distribute-rgt-neg-in_binary64`
528×	`cancel-sign-sub-inv_binary64`
420×	`sub-neg_binary64`

Counts

46 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	93
1	48	91
2	95	85
3	262	79
4	810	79
5	1769	79
6	2958	79
7	4128	79
8	4491	79
9	4808	79
10	4953	79
11	4821	79
12	4827	79

prune32.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

0.2b

Counts

44 → 4

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	0.5b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
	0.9b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	11.0b	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))

Compiler

Compiled 628 to 305 computations (51.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.5b	(log1p.f64 (exp.f64 x))
✓	0.7b	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

series527.0ms (7.5%)

Counts

2 → 24

Calls

2 calls:

289.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
238.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

rewrite81.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

835×	`log1p-udef_binary64`
459×	`expm1-log1p-u_binary64`
458×	`log1p-expm1-u_binary64`
341×	`unpow-prod-down_binary64`
233×	`log-prod_binary64`

Counts

2 → 74

Calls

2 calls:

80.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
80.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	120	13
2	1231	13
3	4761	13
4	6177	13
0	0	0
1	0	0

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

904×	`fma-neg_binary64`
507×	`associate-+l+_binary64`
493×	`*-commutative_binary64`
434×	`cancel-sign-sub-inv_binary64`
394×	`unswap-sqr_binary64`

Counts

98 → 90

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	47	296
1	132	292
2	352	272
3	1209	256
4	2220	256
5	3260	255
6	3914	254
7	4810	248
8	4988	248
9	4858	248

prune118.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Error

0.2b

Counts

136 → 4

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.5b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
▶	0.9b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	14.8b	(-.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (.f64 x 3/8))))))) (.f64 x y))

Compiler

Compiled 2219 to 1174 computations (47.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	1.0b	(log.f64 (+.f64 1 (exp.f64 x)))

series145.0ms (2.1%)

Counts

2 → 8

Calls

2 calls:

143.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite82.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

505×	`prod-diff_binary64`
494×	`log1p-expm1-u_binary64`
494×	`expm1-log1p-u_binary64`
295×	`unpow-prod-down_binary64`
230×	`log-prod_binary64`

Counts

2 → 96

Calls

2 calls:

80.0ms	(+.f64 1 (exp.f64 x))
80.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	112	11
2	1274	11
3	4868	11
4	5598	11
0	0	0
1	0	0

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary64`
804×	`unswap-sqr_binary64`
666×	`cancel-sign-sub-inv_binary64`
419×	`fma-def_binary64`
350×	`distribute-rgt-neg-in_binary64`

Counts

104 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	89
1	72	85
2	163	79
3	448	68
4	1312	68
5	2363	68
6	4864	68
7	5005	68

prune85.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Error

0.2b

Counts

113 → 4

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.5b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
✓	0.9b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	14.8b	(-.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (.f64 x 3/8))))))) (.f64 x y))

Compiler

Compiled 1768 to 936 computations (47.1% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8)))))
✓	1.0b	(pow.f64 (log.f64 2) 2)
✓	8.0b	(+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8))))))
✓	10.6b	(cbrt.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8)))))))

series79.0ms (1.1%)

Counts

4 → 36

Calls

4 calls:

51.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8)))))))
17.0ms	(.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8)))))
10.0ms	(+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8))))))
0.0ms	(pow.f64 (log.f64 2) 2)

rewrite79.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

410×	`log1p-udef_binary64`
231×	`add-sqr-sqrt_binary64`
225×	`log1p-expm1-u_binary64`
225×	`expm1-log1p-u_binary64`
219×	`add-log-exp_binary64`

Counts

4 → 85

Calls

4 calls:

77.0ms	(.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8)))))
77.0ms	(pow.f64 (log.f64 2) 2)
77.0ms	(+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8))))))
77.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (+.f64 3/2 (.f64 x 3/8)) (log.f64 2))) (.f64 (.f64 x x) (+.f64 (.f64 x 1/8) (.f64 (log.f64 2) (+.f64 3/4 (*.f64 x 3/8)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	116
1	475	106
2	4714	106
3	5313	106
0	0	0
1	0	0

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

271×	`cancel-sign-sub-inv_binary64`
241×	`times-frac_binary64`
210×	`fma-def_binary64`
209×	`associate-/r*_binary64`
201×	`associate-/l*_binary64`

Counts

121 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	3486
1	705	3176
2	3195	2612
3	4878	2536
4	4996	2536
5	4957	2536

prune220.0ms (3.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	125	4	129

Error

0.2b

Counts

129 → 4

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.5b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
✓	0.9b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	18.7b	(-.f64 (exp.f64 (log.f64 (cbrt.f64 (fma.f64 (pow.f64 (log.f64 2) 2) (fma.f64 x (fma.f64 x 3/8 3/2) (log.f64 2)) (.f64 (.f64 x x) (fma.f64 (log.f64 2) (fma.f64 x 3/8 3/4) (.f64 x 1/8))))))) (.f64 x y))

Compiler

Compiled 7147 to 5795 computations (18.9% saved)

regimes286.0ms (4.1%)

Accuracy

Total 0.3b remaining (60.3%)

Threshold costs 0.3b (60.3%)

Counts

65 → 1

Compiler

Compiled 6340 to 5181 computations (18.3% 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	10	16
1	16	16
2	26	16
3	32	16
4	36	16
5	37	16
6	37	16

end76.0ms (1.1%)

Compiler: Compiled 92 to 69 computations (25% saved)

Details

analyze401.0ms (5.7%)

sample4.0s (57.4%)

simplify101.0ms (1.4%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series153.0ms (2.2%)

rewrite72.0ms (1%)

simplify129.0ms (1.8%)

prune32.0ms (0.5%)

localize8.0ms (0.1%)

series527.0ms (7.5%)

rewrite81.0ms (1.2%)

simplify106.0ms (1.5%)

prune118.0ms (1.7%)

localize6.0ms (0.1%)

series145.0ms (2.1%)

rewrite82.0ms (1.2%)

simplify52.0ms (0.7%)

prune85.0ms (1.2%)

localize27.0ms (0.4%)

series79.0ms (1.1%)

rewrite79.0ms (1.1%)

simplify120.0ms (1.7%)

prune220.0ms (3.1%)

regimes286.0ms (4.1%)

simplify3.0ms (0%)

end76.0ms (1.1%)

Profiling