Details

analyze492.0ms (7.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
0%	31.2%	68.8%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	28.1%	71.9%	10
4.7%	21.8%	73.5%	11
4.7%	21.8%	73.5%	12
7%	19.5%	73.5%	13
8.2%	17.5%	74.3%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample2.6s (37.6%)

Results

1.0s	5891×	body	128	valid
613.0ms	768×	body	1024	valid
449.0ms	927×	body	512	valid
213.0ms	650×	body	256	valid
45.0ms	282×	body	128	invalid
19.0ms	20×	body	2048	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-neg_binary64`
326×	`fma-def_binary64`
173×	`distribute-rgt-in_binary64`
134×	`unsub-neg_binary64`
124×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	25	17
2	46	17
3	71	17
4	112	17
5	173	17
6	293	17
7	437	17
8	681	17
9	1080	17
10	1312	17
11	1523	17
12	1539	17
13	1539	17
14	1492	17

prune6.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
✓	0.0b	(*.f64 z (log1p.f64 (neg.f64 y)))
✓	0.2b	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

series716.0ms (10.4%)

Counts

3 → 108

Calls

3 calls:

280.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
248.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))
187.0ms	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

rewrite135.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

714×	`prod-diff_binary64`
470×	`fma-udef_binary64`
320×	`fma-def_binary64`
207×	`fma-neg_binary64`
195×	`expm1-udef_binary64`

Counts

3 → 144

Calls

3 calls:

132.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
132.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))
132.0ms	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	226	33
2	2572	33
3	4693	33
4	4716	33
5	4954	33
0	0	0
1	0	0

simplify119.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
580×	`associate--r+_binary64`
405×	`unsub-neg_binary64`
368×	`distribute-neg-in_binary64`
243×	`sub-neg_binary64`

Counts

252 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1970
1	471	1834
2	1472	1770
3	4706	1770
4	4990	1770
5	4999	1770
6	4970	1770

prune159.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	218	6	224

Error

0.0b

Counts

224 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
	36.3b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
▶	0.3b	(-.f64 (fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z))))))) t)
	36.7b	(.f64 (-.f64 (pow.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 y))) 2) (*.f64 t t)) (/.f64 1 (fma.f64 x (log.f64 y) (fma.f64 z (log1p.f64 y) t))))
	37.4b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)
	9.9b	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))

Compiler

Compiled 4574 to 1636 computations (64.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z)))))))
✓	2.9b	(*.f64 (pow.f64 y 4) z)
✓	4.9b	(*.f64 (pow.f64 y 3) z)
✓	6.7b	(*.f64 (pow.f64 y 2) z)

series178.0ms (2.6%)

Counts

4 → 36

Calls

4 calls:

141.0ms	(fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z)))))))
16.0ms	(*.f64 (pow.f64 y 3) z)
12.0ms	(*.f64 (pow.f64 y 4) z)
9.0ms	(*.f64 (pow.f64 y 2) z)

rewrite74.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

482×	`log1p-udef_binary64`
263×	`log1p-expm1-u_binary64`
263×	`expm1-log1p-u_binary64`
253×	`add-exp-log_binary64`
253×	`add-log-exp_binary64`

Counts

4 → 52

Calls

4 calls:

72.0ms	(fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z)))))))
72.0ms	(*.f64 (pow.f64 y 4) z)
72.0ms	(*.f64 (pow.f64 y 3) z)
72.0ms	(*.f64 (pow.f64 y 2) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	63
1	573	63
2	4880	63
3	5590	63
0	0	0
1	0	0

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

620×	`distribute-rgt-neg-in_binary64`
573×	`sub-neg_binary64`
552×	`distribute-lft-neg-in_binary64`
421×	`fma-def_binary64`
405×	`neg-mul-1_binary64`

Counts

88 → 71

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	1154
1	174	975
2	509	918
3	1693	887
4	3299	886
5	4460	886
6	4967	886

prune110.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Error

0.0b

Counts

77 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
	36.3b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
✓	0.3b	(-.f64 (fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z))))))) t)
	36.7b	(.f64 (-.f64 (pow.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 y))) 2) (*.f64 t t)) (/.f64 1 (fma.f64 x (log.f64 y) (fma.f64 z (log1p.f64 y) t))))
	37.4b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)
▶	9.9b	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))

Compiler

Compiled 2520 to 1525 computations (39.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (log1p.f64 y))
✓	0.0b	(-.f64 (*.f64 z (log1p.f64 y)) t)
✓	0.1b	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))

series620.0ms (9%)

Counts

3 → 108

Calls

3 calls:

261.0ms	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))
261.0ms	(*.f64 z (log1p.f64 y))
99.0ms	(-.f64 (*.f64 z (log1p.f64 y)) t)

rewrite130.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
498×	`fma-udef_binary64`
287×	`fma-def_binary64`
226×	`fma-neg_binary64`
191×	`expm1-udef_binary64`

Counts

3 → 151

Calls

3 calls:

126.0ms	(*.f64 z (log1p.f64 y))
126.0ms	(-.f64 (*.f64 z (log1p.f64 y)) t)
126.0ms	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	204	30
2	2495	30
3	4823	30
4	4705	30
5	4986	30
0	0	0
1	0	0

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-def_binary64`
428×	`associate--r+_binary64`
395×	`associate--l+_binary64`
367×	`times-frac_binary64`
281×	`sub-neg_binary64`

Counts

259 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	1524
1	379	1474
2	1177	1394
3	3778	1386
4	4667	1386
5	5072	1386

prune176.0ms (2.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	217	6	223

Error

0.0b

Counts

223 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
▶	36.3b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
✓	0.3b	(-.f64 (fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z))))))) t)
	36.7b	(.f64 (-.f64 (pow.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 y))) 2) (*.f64 t t)) (/.f64 1 (fma.f64 x (log.f64 y) (fma.f64 z (log1p.f64 y) t))))
	37.4b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)
✓	9.9b	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))

Compiler

Compiled 4077 to 1465 computations (64.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (log1p.f64 y))
	0.0b	(-.f64 (*.f64 z (log1p.f64 y)) t)
✓	0.1b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
✓	0.2b	(*.f64 (sqrt.f64 x) (log.f64 y))

series233.0ms (3.4%)

Counts

2 → 49

Calls

2 calls:

198.0ms	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
35.0ms	(*.f64 (sqrt.f64 x) (log.f64 y))

rewrite59.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

760×	`prod-diff_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
123×	`add-sqr-sqrt_binary64`
117×	`expm1-log1p-u_binary64`

Counts

2 → 40

Calls

2 calls:

57.0ms	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
57.0ms	(*.f64 (sqrt.f64 x) (log.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	243	25
2	2934	25
3	5024	25
0	0	0
1	0	0

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
649×	`sub-neg_binary64`
309×	`associate--r+_binary64`
290×	`fma-def_binary64`
263×	`times-frac_binary64`

Counts

89 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	732
1	252	704
2	776	682
3	2642	679
4	4703	679
5	4980	679

prune135.0ms (2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	226	7	233

Error

0.0b

Counts

233 → 7

Alt Table

Status	Error	Program
	36.5b	(fma.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (log.f64 y))) 3) (-.f64 (.f64 z (log1p.f64 y)) t))
✓	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
✓	36.3b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
✓	0.3b	(-.f64 (fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z))))))) t)
	36.7b	(.f64 (-.f64 (pow.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 y))) 2) (*.f64 t t)) (/.f64 1 (fma.f64 x (log.f64 y) (fma.f64 z (log1p.f64 y) t))))
	37.4b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)
✓	9.9b	(fma.f64 x (log.f64 y) (-.f64 (*.f64 z (log1p.f64 y)) t))

Compiler

Compiled 4866 to 1479 computations (69.6% saved)

regimes441.0ms (6.4%)

Accuracy

Total 0.0b remaining (38.3%)

Threshold costs 0.0b (38.3%)

Counts

66 → 1

Compiler

Compiled 8174 to 5223 computations (36.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	18	17
2	23	17
3	26	17
4	27	17
5	27	17

end120.0ms (1.8%)

Compiler: Compiled 183 to 120 computations (34.4% saved)

Details

analyze492.0ms (7.2%)

sample2.6s (37.6%)

simplify57.0ms (0.8%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

series716.0ms (10.4%)

rewrite135.0ms (2%)

simplify119.0ms (1.7%)

prune159.0ms (2.3%)

localize20.0ms (0.3%)

series178.0ms (2.6%)

rewrite74.0ms (1.1%)

simplify100.0ms (1.5%)

prune110.0ms (1.6%)

localize8.0ms (0.1%)

series620.0ms (9%)

rewrite130.0ms (1.9%)

simplify95.0ms (1.4%)

prune176.0ms (2.6%)

localize12.0ms (0.2%)

series233.0ms (3.4%)

rewrite59.0ms (0.9%)

simplify69.0ms (1%)

prune135.0ms (2%)

regimes441.0ms (6.4%)

simplify2.0ms (0%)

end120.0ms (1.8%)

Profiling