Details

analyze236.0ms (3%)

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%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample1.3s (16.2%)

Results

973.0ms	8256×	body	128	valid
40.0ms	358×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify282.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
806×	`fma-neg_binary64`
746×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	59	16
3	115	16
4	270	14
5	514	14
6	792	14
7	1191	14
8	1435	14
9	1716	14
10	2343	14
11	2639	14
12	2704	14
13	3251	14
14	3766	14
15	3977	14
16	4124	14
17	4234	14
18	4260	14
19	4085	14
20	4111	14
21	4149	14
22	4189	14
23	4189	14
24	4189	14
25	4871	14
26	4999	14
27	4907	14

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 51 to 31 computations (39.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.0b	(-.f64 (log.f64 z) z)
✓	0.2b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series243.0ms (3.1%)

Counts

3 → 69

Calls

3 calls:

168.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
70.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
4.0ms	(-.f64 (log.f64 z) z)

rewrite90.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
425×	`log-prod_binary64`
221×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Counts

3 → 168

Calls

3 calls:

87.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
87.0ms	(-.f64 (log.f64 z) z)
87.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	188	30
2	2293	30
3	4933	30
4	4973	30

simplify295.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1274×	`unsub-neg_binary64`
805×	`distribute-neg-in_binary64`
676×	`sub-neg_binary64`
489×	`fma-def_binary64`
419×	`+-commutative_binary64`

Counts

237 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	926
1	139	819
2	345	717
3	759	717
4	2015	717
5	2532	717
6	3132	717
7	3501	717
8	3593	717
9	3688	717
10	3727	717
11	3735	717
12	3740	717
13	3967	717
14	4012	717
15	4054	717
16	4066	717
17	4084	717
18	4090	717
19	4108	717
20	4630	717
21	4712	717
22	5057	717

prune157.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	185	6	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	6	192

Error

0.0b

Counts

192 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (fma.f64 1/3 (*.f64 3 (log.f64 z)) (neg.f64 z)) (+.f64 (neg.f64 z) z)) y))
	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	24.3b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	37.7b	(fma.f64 x 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3) (pow.f64 y 3)) (fma.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z)) (-.f64 (.f64 y y) (.f64 (.f64 y (-.f64 (log.f64 z) z)) y)))))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))

Compiler

Compiled 3536 to 1385 computations (60.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log.f64 z) z)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

series193.0ms (2.5%)

Counts

1 → 36

Calls

1 calls:

192.0ms

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

rewrite72.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
425×	`log-prod_binary64`
224×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Counts

1 → 31

Calls

1 calls:

72.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	188	14
2	2294	14
3	4937	14
4	4976	14

simplify152.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-neg_binary64`
847×	`sub-neg_binary64`
705×	`unsub-neg_binary64`
450×	`fma-def_binary64`
382×	`neg-sub0_binary64`

Counts

67 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	107	530
2	281	503
3	656	443
4	1675	443
5	3078	443
6	3726	443
7	4162	443
8	4502	443
9	4718	443
10	4687	443
11	4687	443
12	4911	443

prune250.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	155	6	161

Error

0.0b

Counts

161 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	0.1b	(+.f64 (fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x)) y)
▶	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	24.3b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	37.7b	(fma.f64 x 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3) (pow.f64 y 3)) (fma.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z)) (-.f64 (.f64 y y) (.f64 (.f64 y (-.f64 (log.f64 z) z)) y)))))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))

Compiler

Compiled 2938 to 1200 computations (59.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
✓	0.0b	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
✓	0.3b	(+.f64 (*.f64 (log.f64 z) y) y)
✓	0.3b	(*.f64 (log.f64 z) y)

series841.0ms (10.7%)

Counts

4 → 85

Calls

4 calls:

315.0ms	(*.f64 (log.f64 z) y)
286.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
162.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
78.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

rewrite95.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

646×	`fma-def_binary64`
336×	`fma-neg_binary64`
242×	`egg-rr`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`

Counts

4 → 242

Calls

4 calls:

78.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
78.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
78.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
78.0ms	(*.f64 (log.f64 z) y)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	245	41
2	3222	41
3	4941	41

simplify377.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1103×	`unsub-neg_binary64`
821×	`fma-def_binary64`
673×	`sub-neg_binary64`
537×	`distribute-neg-in_binary64`
412×	`+-commutative_binary64`

Counts

327 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	1188
1	151	926
2	338	830
3	905	830
4	2308	830
5	2762	830
6	3490	830
7	3737	830
8	3823	830
9	3879	830
10	3897	830
11	3900	830
12	4189	830
13	4233	830
14	4257	830
15	4261	830
16	4267	830
17	4269	830
18	4275	830
19	4257	830
20	4745	830
21	4589	830
22	4550	830
23	4698	830
24	4888	830

prune274.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	266	5	271

Error

0.0b

Counts

271 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x)) y)
	24.3b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	0.4b	(fma.f64 x 1/2 (fma.f64 (.f64 y (pow.f64 (cbrt.f64 (log.f64 z)) 2)) (cbrt.f64 (log.f64 z)) (-.f64 y (.f64 z y))))
	37.7b	(fma.f64 x 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3) (pow.f64 y 3)) (fma.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z)) (-.f64 (.f64 y y) (.f64 (.f64 y (-.f64 (log.f64 z) z)) y)))))
	19.5b	(fma.f64 x 1/2 (.f64 (-.f64 (pow.f64 (fma.f64 (log.f64 z) y y) 2) (pow.f64 (.f64 z y) 2)) (/.f64 1 (fma.f64 z y (fma.f64 (log.f64 z) y y)))))

Compiler

Compiled 5442 to 2111 computations (61.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log.f64 z) z)
✓	0.1b	(+.f64 (fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x)) y)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x))

series141.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

71.0ms	(+.f64 (fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x)) y)
70.0ms	(fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x))

rewrite63.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`log-prod_binary64`
389×	`fma-def_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
197×	`fma-neg_binary64`

Counts

2 → 85

Calls

2 calls:

61.0ms	(+.f64 (fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x)) y)
60.0ms	(fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	217	29
2	2797	27
3	5384	27

simplify221.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

918×	`unsub-neg_binary64`
753×	`sub-neg_binary64`
576×	`fma-neg_binary64`
520×	`fma-def_binary64`
420×	`neg-sub0_binary64`

Counts

157 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	1079
1	140	969
2	329	861
3	727	855
4	1716	855
5	2872	855
6	3528	855
7	4202	855
8	4722	855
9	4821	855
10	4859	855
11	4826	855
12	4826	855
13	4993	855

prune189.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	218	5	223

Error

0.0b

Counts

223 → 5

Alt Table

Status	Error	Program
	30.9b	(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (-.f64 (log.f64 z) z)) (fma.f64 1/2 x y))
✓	0.1b	(+.f64 (fma.f64 y (-.f64 (log.f64 z) z) (*.f64 1/2 x)) y)
	24.3b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	0.4b	(fma.f64 x 1/2 (fma.f64 (.f64 y (pow.f64 (cbrt.f64 (log.f64 z)) 2)) (cbrt.f64 (log.f64 z)) (-.f64 y (.f64 z y))))
	19.5b	(fma.f64 x 1/2 (.f64 (-.f64 (pow.f64 (fma.f64 (log.f64 z) y y) 2) (pow.f64 (.f64 z y) 2)) (/.f64 1 (fma.f64 z y (fma.f64 (log.f64 z) y y)))))

Compiler

Compiled 4119 to 1774 computations (56.9% saved)

regimes2.3s (29.1%)

Accuracy

Total 0.1b remaining (59.6%)

Threshold costs 0.1b (59.6%)

Counts

270 → 1

Compiler

Compiled 37638 to 23767 computations (36.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`*-rgt-identity_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	20	17
2	23	17
3	24	17
4	22	17

end84.0ms (1.1%)

Compiler: Compiled 141 to 80 computations (43.3% saved)

Details

analyze236.0ms (3%)

sample1.3s (16.2%)

simplify282.0ms (3.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series243.0ms (3.1%)

rewrite90.0ms (1.1%)

simplify295.0ms (3.8%)

prune157.0ms (2%)

localize7.0ms (0.1%)

series193.0ms (2.5%)

rewrite72.0ms (0.9%)

simplify152.0ms (1.9%)

prune250.0ms (3.2%)

localize10.0ms (0.1%)

series841.0ms (10.7%)

rewrite95.0ms (1.2%)

simplify377.0ms (4.8%)

prune274.0ms (3.5%)

localize9.0ms (0.1%)

series141.0ms (1.8%)

rewrite63.0ms (0.8%)

simplify221.0ms (2.8%)

prune189.0ms (2.4%)

regimes2.3s (29.1%)

simplify2.0ms (0%)

end84.0ms (1.1%)

Profiling