Details

analyze462.0ms (2.4%)

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)

sample28.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify316.0ms (1.6%)

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)

localize8.0ms (0%)

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)

series340.0ms (1.8%)

Counts

3 → 69

Calls

3 calls:

240.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
89.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
10.0ms	(-.f64 (log.f64 z) z)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 58

Calls

3 calls:

11.0ms	(-.f64 (log.f64 z) z)
0.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
0.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

simplify134.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
513×	`fma-def_binary64`
353×	`associate-l_binary64`
311×	`exp-prod_binary64`
278×	`associate-r_binary64`

Counts

127 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1706
1	274	1350
2	803	1312
3	3226	1312
4	4661	1312
5	4985	1312
6	4989	1312
7	4905	1312

prune79.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Error

0.0b

Counts

94 → 6

Alt Table

Status	Error	Program
	0.7b	(fma.f64 x 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
	26.6b	(fma.f64 x 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 3)))
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	14.8b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

Compiler

Compiled 1772 to 676 computations (61.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
✓	0.2b	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.7b	(cbrt.f64 z)

series3.1s (16.2%)

Counts

4 → 60

Calls

4 calls:

2.5s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
514.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)

rewrite60.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
34×	`pow1_binary64`
33×	`add-sqr-sqrt_binary64`
25×	`associate-+r+_binary64`
25×	`add-cube-cbrt_binary64`

Counts

4 → 127

Calls

4 calls:

29.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
9.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)
1.0ms	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)

simplify208.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

669×	`distribute-rgt-in_binary64`
601×	`distribute-lft-in_binary64`
521×	`fma-neg_binary64`
322×	`cancel-sign-sub-inv_binary64`
273×	`log-prod_binary64`

Counts

187 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	2646
1	390	1654
2	1365	1572
3	4136	1562
4	5098	1562

prune390.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	225	5	230

Error

0.0b

Counts

230 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	26.6b	(fma.f64 x 1/2 (cbrt.f64 (.f64 (.f64 (fma.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y) (fma.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)) (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
	0.1b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

Compiler

Compiled 5352 to 1844 computations (65.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))
✓	0.3b	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)
✓	0.7b	(cbrt.f64 (neg.f64 z))
✓	5.9b	(pow.f64 z 2/3)

series7.6s (39.7%)

Counts

4 → 72

Calls

4 calls:

4.9s	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)
2.7s	(.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))
36.0ms	(cbrt.f64 (neg.f64 z))
25.0ms	(pow.f64 z 2/3)

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`prod-diff_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
28×	`pow1_binary64`

Counts

4 → 121

Calls

4 calls:

9.0ms	(.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))
2.0ms	(pow.f64 z 2/3)
1.0ms	(cbrt.f64 (neg.f64 z))
0.0ms	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)

simplify145.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-neg_binary64`
521×	`log-prod_binary64`
403×	`fma-def_binary64`
299×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`

Counts

193 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	3483
1	361	3153
2	1097	2957
3	3332	2954
4	4450	2954
5	4955	2954

prune242.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	159	6	165

Error

0.0b

Counts

165 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.6b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z)))))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

Compiler

Compiled 6109 to 3869 computations (36.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (cbrt.f64 z))
✓	0.2b	(fma.f64 y (fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
✓	0.2b	(fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z))
	0.7b	(cbrt.f64 z)

series3.0s (15.7%)

Counts

3 → 48

Calls

3 calls:

2.1s	(fma.f64 y (fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
652.0ms	(log.f64 (cbrt.f64 z))
276.0ms	(fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 38

Calls

3 calls:

1.0ms	(log.f64 (cbrt.f64 z))
0.0ms	(fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z))
0.0ms	(fma.f64 y (fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

814×	`distribute-rgt-in_binary64`
778×	`distribute-lft-in_binary64`
649×	`fma-def_binary64`
262×	`fma-neg_binary64`
101×	`associate-l_binary64`

Counts

86 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1309
1	179	1160
2	426	820
3	1168	806
4	4924	806
5	4978	806

prune168.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Error

0.0b

Counts

152 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.6b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z)))))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 2 (log.f64 (cbrt.f64 z)) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

Compiler

Compiled 2965 to 1250 computations (57.8% saved)

regimes1.3s (6.6%)

Accuracy

Total 0.1b remaining (82.6%)

Threshold costs 0.1b (82.6%)

Counts

118 → 1

Compiler

Compiled 16550 to 10673 computations (35.5% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	11	23
1	14	23
2	19	23
3	21	23
4	22	23
5	22	23

end1.0ms (0%)

Compiler: Compiled 18 to 10 computations (44.4% saved)

sample1.4s (7.5%)

Algorithm

1×

intervals

Results

746.0ms	8000×	body	128	valid
27.0ms	298×	body	128	invalid
5.0ms	80×	body	128	nan

Compiler

Compiled 193 to 129 computations (33.2% saved)

Details

analyze462.0ms (2.4%)

sample28.0ms (0.1%)

simplify316.0ms (1.6%)

prune3.0ms (0%)

localize8.0ms (0%)

series340.0ms (1.8%)

rewrite14.0ms (0.1%)

simplify134.0ms (0.7%)

prune79.0ms (0.4%)

localize14.0ms (0.1%)

series3.1s (16.2%)

rewrite60.0ms (0.3%)

simplify208.0ms (1.1%)

prune390.0ms (2%)

localize26.0ms (0.1%)

series7.6s (39.7%)

rewrite23.0ms (0.1%)

simplify145.0ms (0.8%)

prune242.0ms (1.3%)

localize11.0ms (0.1%)

series3.0s (15.7%)

rewrite3.0ms (0%)

simplify74.0ms (0.4%)

prune168.0ms (0.9%)

regimes1.3s (6.6%)

simplify6.0ms (0%)

end1.0ms (0%)

sample1.4s (7.5%)

Profiling