Details

analyze254.0ms (6.3%)

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)

sample1.1s (28.2%)

Results

1.0s	8256×	body	128	valid
52.0ms	399×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

982×	`fma-def_binary64`
790×	`fma-neg_binary64`
274×	`sub-neg_binary64`
221×	`associate--r+_binary64`
216×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	65	16
3	143	16
4	336	14
5	718	14
6	1240	14
7	1881	14
8	2833	14
9	3323	14
10	4425	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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	(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 (0.2%)

Local error

Found 3 expressions with local error:

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

series228.0ms (5.7%)

Counts

3 → 69

Calls

3 calls:

156.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
67.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
4.0ms	(-.f64 (log.f64 z) z)

rewrite50.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	189	30
2	2401	30

Stop Event

1×	node limit

Counts

3 → 150

Calls

3 calls:

48.0ms	(-.f64 (log.f64 z) z)
48.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
48.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

535×	`sub-neg_binary64`
489×	`fma-def_binary64`
365×	`unsub-neg_binary64`
256×	`associate--l-_binary64`
206×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	926
1	152	819
2	386	717
3	1065	717
4	3043	717
5	4451	717

Stop Event

1×	node limit

Counts

219 → 175

prune119.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	6	176

Error

0.0b

Counts

176 → 6

Alt Table

Status	Error	Program
	28.3b	(fma.f64 x 1/2 (fma.f64 y (log.f64 (/.f64 z (exp.f64 z))) y))
▶	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y))
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	0.7b	(fma.f64 x 1/2 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2)))
	0.1b	(fma.f64 x 1/2 (+.f64 y (*.f64 y (-.f64 (log.f64 z) z))))

Compiler

Compiled 3144 to 1277 computations (59.4% saved)

localize11.0ms (0.3%)

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))

series68.0ms (1.7%)

Counts

1 → 36

Calls

1 calls:

68.0ms

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

rewrite38.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	189	14
2	2402	14

Stop Event

1×	node limit

Counts

1 → 30

Calls

1 calls:

37.0ms

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

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-neg_binary64`
448×	`fma-def_binary64`
324×	`associate-+l-_binary64`
275×	`associate--l+_binary64`
251×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	108	530
2	301	503
3	830	443
4	2325	443

Stop Event

1×	node limit

Counts

66 → 43

prune97.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Error

0.0b

Counts

146 → 6

Alt Table

Status	Error	Program
	28.3b	(fma.f64 x 1/2 (fma.f64 y (log.f64 (/.f64 z (exp.f64 z))) y))
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y))
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	0.7b	(fma.f64 x 1/2 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2)))
▶	0.1b	(fma.f64 x 1/2 (+.f64 y (*.f64 y (-.f64 (log.f64 z) z))))

Compiler

Compiled 2572 to 1104 computations (57.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series380.0ms (9.4%)

Counts

3 → 72

Calls

3 calls:

158.0ms	(+.f64 y (*.f64 y (-.f64 (log.f64 z) z)))
151.0ms	(*.f64 y (-.f64 (log.f64 z) z))
71.0ms	(fma.f64 x 1/2 (+.f64 y (*.f64 y (-.f64 (log.f64 z) z))))

rewrite56.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
423×	`fma-def_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
199×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	218	33
2	2978	33

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

54.0ms	(fma.f64 x 1/2 (+.f64 y (*.f64 y (-.f64 (log.f64 z) z))))
54.0ms	(*.f64 y (-.f64 (log.f64 z) z))
54.0ms	(+.f64 y (*.f64 y (-.f64 (log.f64 z) z)))

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
533×	`unsub-neg_binary64`
330×	`sub-neg_binary64`
274×	`distribute-rgt-in_binary64`
187×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	983
1	149	873
2	387	873
3	1038	771
4	2989	771
5	4815	771

Stop Event

1×	node limit

Counts

185 → 137

prune205.0ms (5.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	228	6	234
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	232	8	240

Error

0.0b

Counts

240 → 8

Alt Table

Status	Error	Program
	0.8b	(fma.f64 x 1/2 (fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (-.f64 (log.f64 z) z)) y))
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	19.0b	(fma.f64 x 1/2 (+.f64 y (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) y) (fma.f64 z (+.f64 z (log.f64 z)) (pow.f64 (log.f64 z) 2)))))
✓	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 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) (*.f64 y (-.f64 (log.f64 z) z))))
	20.5b	(fma.f64 x 1/2 (/.f64 1 (/.f64 (-.f64 y (.f64 y (-.f64 (log.f64 z) z))) (-.f64 (.f64 y y) (pow.f64 (*.f64 y (-.f64 (log.f64 z) z)) 2)))))
	20.4b	(fma.f64 x 1/2 (-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 y (-.f64 (log.f64 z) z)))) (/.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 2) (-.f64 y (.f64 y (-.f64 (log.f64 z) z))))))
	13.2b	(fma.f64 x 1/2 (+.f64 y (/.f64 (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) y) (+.f64 z (log.f64 z)))))

Compiler

Compiled 4420 to 1827 computations (58.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 y (-.f64 (log.f64 z) z))
✓	0.1b	(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) (*.f64 y (-.f64 (log.f64 z) z)))
✓	0.5b	(pow.f64 (cbrt.f64 y) 2)
✓	0.6b	(cbrt.f64 y)

series207.0ms (5.2%)

Counts

3 → 48

Calls

3 calls:

134.0ms	(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) (*.f64 y (-.f64 (log.f64 z) z)))
39.0ms	(pow.f64 (cbrt.f64 y) 2)
34.0ms	(cbrt.f64 y)

rewrite45.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`prod-diff_binary64`
243×	`fma-def_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
159×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	209	21
2	2574	19

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

44.0ms	(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) (*.f64 y (-.f64 (log.f64 z) z)))
44.0ms	(pow.f64 (cbrt.f64 y) 2)
44.0ms	(cbrt.f64 y)

simplify33.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-neg_binary64`
416×	`unswap-sqr_binary64`
273×	`fma-def_binary64`
264×	`associate-l_binary64`
214×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	440
1	109	422
2	257	386
3	739	386
4	2866	386

Stop Event

1×	node limit

Counts

118 → 87

prune138.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	143	8	151

Error

0.0b

Counts

151 → 8

Alt Table

Status	Error	Program
	0.8b	(fma.f64 x 1/2 (fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (-.f64 (log.f64 z) z)) y))
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	19.0b	(fma.f64 x 1/2 (+.f64 y (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) y) (fma.f64 z (+.f64 z (log.f64 z)) (pow.f64 (log.f64 z) 2)))))
✓	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 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) (*.f64 y (-.f64 (log.f64 z) z))))
	20.5b	(fma.f64 x 1/2 (/.f64 1 (/.f64 (-.f64 y (.f64 y (-.f64 (log.f64 z) z))) (-.f64 (.f64 y y) (pow.f64 (*.f64 y (-.f64 (log.f64 z) z)) 2)))))
	20.4b	(fma.f64 x 1/2 (-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 y (-.f64 (log.f64 z) z)))) (/.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 2) (-.f64 y (.f64 y (-.f64 (log.f64 z) z))))))
	13.2b	(fma.f64 x 1/2 (+.f64 y (/.f64 (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) y) (+.f64 z (log.f64 z)))))

Compiler

Compiled 2801 to 1128 computations (59.7% saved)

regimes618.0ms (15.4%)

Accuracy

Total 0.1b remaining (78.7%)

Threshold costs 0.1b (78.7%)

Counts

93 → 1

Compiler

Compiled 10579 to 6803 computations (35.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14
2	16	14
3	18	14
4	19	14

Stop Event

1×

saturated

end132.0ms (3.3%)

Compiler: Compiled 210 to 122 computations (41.9% saved)

Details

analyze254.0ms (6.3%)

sample1.1s (28.2%)

simplify42.0ms (1.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series228.0ms (5.7%)

rewrite50.0ms (1.3%)

simplify51.0ms (1.3%)

prune119.0ms (3%)

localize11.0ms (0.3%)

series68.0ms (1.7%)

rewrite38.0ms (0.9%)

simplify30.0ms (0.8%)

prune97.0ms (2.4%)

localize8.0ms (0.2%)

series380.0ms (9.4%)

rewrite56.0ms (1.4%)

simplify53.0ms (1.3%)

prune205.0ms (5.1%)

localize11.0ms (0.3%)

series207.0ms (5.2%)

rewrite45.0ms (1.1%)

simplify33.0ms (0.8%)

prune138.0ms (3.4%)

regimes618.0ms (15.4%)

simplify2.0ms (0.1%)

end132.0ms (3.3%)

Profiling