Details

analyze246.0ms (4.2%)

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 (19%)

Results

1.0s	8256×	body	128	valid
42.0ms	372×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify40.0ms (0.7%)

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%)

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 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) y)

series174.0ms (3%)

Counts

2 → 33

Calls

2 calls:

168.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
6.0ms	(-.f64 (log.f64 z) z)

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

669×	`log1p-expm1-u_binary64`
669×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
72×	`egg-rr`
67×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	128	16
2	1740	16

Stop Event

1×	node limit

Counts

2 → 72

Calls

2 calls:

42.0ms	(-.f64 (log.f64 z) z)
42.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-neg_binary64`
487×	`sub-neg_binary64`
324×	`unsub-neg_binary64`
290×	`associate--r-_binary64`
276×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	340
1	101	316
2	258	274
3	729	274
4	2137	274
5	4282	274

Stop Event

1×	node limit

Counts

105 → 88

prune75.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Error

0.0b

Counts

89 → 7

Alt Table

Status	Error	Program
	13.2b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) (/.f64 1 (+.f64 z (log.f64 z)))) y))
▶	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	18.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (/.f64 1 (+.f64 (pow.f64 (log.f64 z) 2) (.f64 z (+.f64 z (log.f64 z)))))) y))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
	18.5b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	34.7b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	19.2b	(fma.f64 x 1/2 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 2))))

Compiler

Compiled 1726 to 759 computations (56% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

series498.0ms (8.5%)

Counts

3 → 49

Calls

3 calls:

172.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
170.0ms	(*.f64 (log.f64 z) y)
156.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))

rewrite68.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`fma-def_binary64`
516×	`log-prod_binary64`
311×	`fma-neg_binary64`
243×	`egg-rr`
174×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	185	25
2	2821	25

Stop Event

1×	node limit

Counts

3 → 243

Calls

3 calls:

62.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
62.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
62.0ms	(*.f64 (log.f64 z) y)

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
509×	`sub-neg_binary64`
434×	`fma-def_binary64`
334×	`associate--r-_binary64`
293×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	593
1	117	423
2	271	387
3	878	387
4	2407	387
5	4649	387

Stop Event

1×	node limit

Counts

292 → 257

prune383.0ms (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	257	7	264

Error

Counts

264 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x 1/2 (-.f64 (fma.f64 (.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) y) (.f64 y z)))
	18.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (/.f64 1 (+.f64 (pow.f64 (log.f64 z) 2) (.f64 z (+.f64 z (log.f64 z)))))) y))
	17.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 z) y) 3)) y) (.f64 y z)))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
▶	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
	18.5b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	19.2b	(fma.f64 x 1/2 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 2))))

Compiler

Compiled 5419 to 2247 computations (58.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y)
✓	0.2b	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z))
✓	0.5b	(cbrt.f64 (log.f64 z))
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 z)) 2)

series691.0ms (11.8%)

Counts

4 → 60

Calls

4 calls:

449.0ms	(fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y)
101.0ms	(cbrt.f64 (log.f64 z))
72.0ms	(pow.f64 (cbrt.f64 (log.f64 z)) 2)
68.0ms	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z))

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

722×	`log1p-expm1-u_binary64`
722×	`expm1-log1p-u_binary64`
238×	`prod-diff_binary64`
174×	`egg-rr`
96×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	201	29
2	2307	29

Stop Event

1×	node limit

Counts

4 → 174

Calls

4 calls:

63.0ms	(fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y)
63.0ms	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z))
63.0ms	(cbrt.f64 (log.f64 z))
63.0ms	(pow.f64 (cbrt.f64 (log.f64 z)) 2)

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

486×	`unswap-sqr_binary64`
352×	`fma-def_binary64`
342×	`associate-l_binary64`
319×	`associate-r_binary64`
222×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	558
1	154	550
2	362	508
3	1139	508
4	3956	508

Stop Event

1×	node limit

Counts

234 → 197

prune239.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	224	7	231

Error

Counts

231 → 7

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 x 1/2 (-.f64 (fma.f64 (.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) y) (.f64 y z)))
	18.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (/.f64 1 (+.f64 (pow.f64 (log.f64 z) 2) (.f64 z (+.f64 z (log.f64 z)))))) y))
	17.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 z) y) 3)) y) (.f64 y z)))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
✓	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
	18.5b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	19.2b	(fma.f64 x 1/2 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 2))))

Compiler

Compiled 5468 to 2397 computations (56.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2))
✓	0.3b	(fma.f64 (*.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) y)
✓	0.5b	(pow.f64 (cbrt.f64 y) 2)
✓	0.6b	(cbrt.f64 y)

series199.0ms (3.4%)

Counts

4 → 27

Calls

4 calls:

98.0ms	(fma.f64 (*.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) y)
67.0ms	(*.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2))
24.0ms	(pow.f64 (cbrt.f64 y) 2)
10.0ms	(cbrt.f64 y)

rewrite46.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`log1p-expm1-u_binary64`
693×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
116×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	177	29
2	1990	29

Stop Event

1×	node limit

Counts

4 → 80

Calls

4 calls:

45.0ms	(*.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2))
45.0ms	(fma.f64 (*.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) y)
45.0ms	(pow.f64 (cbrt.f64 y) 2)
45.0ms	(cbrt.f64 y)

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

285×	`cancel-sign-sub-inv_binary64`
273×	`unsub-neg_binary64`
230×	`fma-neg_binary64`
197×	`sub-neg_binary64`
181×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	219
1	72	219
2	152	219
3	465	219
4	1892	219
5	4421	219

Stop Event

1×	node limit

Counts

107 → 88

prune110.0ms (1.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	111	7	118

Error

Counts

118 → 7

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 x 1/2 (-.f64 (fma.f64 (.f64 (log.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) y) (.f64 y z)))
	18.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (/.f64 1 (+.f64 (pow.f64 (log.f64 z) 2) (.f64 z (+.f64 z (log.f64 z)))))) y))
	17.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 z) y) 3)) y) (.f64 y z)))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
✓	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
	18.5b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	19.2b	(fma.f64 x 1/2 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 2))))

Compiler

Compiled 2419 to 1060 computations (56.2% saved)

regimes1.5s (26.1%)

Accuracy

Total 0.0b remaining (58.2%)

Threshold costs 0.0b (58.2%)

Counts

194 → 1

Compiler

Compiled 26125 to 16691 computations (36.1% 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	21	17
2	28	17
3	29	17

Stop Event

1×

saturated

end117.0ms (2%)

Compiler: Compiled 178 to 110 computations (38.2% saved)

Details

analyze246.0ms (4.2%)

sample1.1s (19%)

simplify40.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series174.0ms (3%)

rewrite44.0ms (0.7%)

simplify35.0ms (0.6%)

prune75.0ms (1.3%)

localize9.0ms (0.1%)

series498.0ms (8.5%)

rewrite68.0ms (1.2%)

simplify44.0ms (0.8%)

prune383.0ms (6.6%)

localize11.0ms (0.2%)

series691.0ms (11.8%)

rewrite66.0ms (1.1%)

simplify43.0ms (0.7%)

prune239.0ms (4.1%)

localize13.0ms (0.2%)

series199.0ms (3.4%)

rewrite46.0ms (0.8%)

simplify36.0ms (0.6%)

prune110.0ms (1.9%)

regimes1.5s (26.1%)

simplify2.0ms (0%)

end117.0ms (2%)

Profiling