Details

analyze232.0ms (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)

sample272.0ms (3.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify289.0ms (3.7%)

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 (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series213.0ms (2.7%)

Counts

1 → 24

Calls

1 calls:

213.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

590×	`unsub-neg_binary64`
528×	`distribute-rgt-in_binary64`
517×	`fma-neg_binary64`
485×	`distribute-lft-in_binary64`
434×	`times-frac_binary64`

Counts

34 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	424
1	100	361
2	244	361
3	688	361
4	3027	361
5	4224	361
6	5405	361

prune17.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Error

0.0b

Counts

22 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
▶	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	0.6b	(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))))

Compiler

Compiled 398 to 157 computations (60.6% saved)

localize14.0ms (0.2%)

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)

series676.0ms (8.6%)

Counts

3 → 49

Calls

3 calls:

269.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
204.0ms	(*.f64 (log.f64 z) y)
204.0ms	(+.f64 (*.f64 (log.f64 z) y) y)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`

Counts

3 → 64

Calls

3 calls:

5.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
3.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
3.0ms	(*.f64 (log.f64 z) y)

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
470×	`unsub-neg_binary64`
466×	`fma-neg_binary64`
320×	`cancel-sign-sub-inv_binary64`
258×	`distribute-rgt-in_binary64`

Counts

113 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1449
1	311	1190
2	918	1077
3	3003	1074
4	4579	1074
5	4981	1074
6	4891	1074

prune484.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

0.0b

Counts

117 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y) (.f64 y z)))
▶	0.3b	(fma.f64 x 1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (*.f64 y z)))

Compiler

Compiled 2236 to 730 computations (67.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series2.4s (31.1%)

Counts

4 → 96

Calls

4 calls:

1.1s	(*.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y)))
887.0ms	(cbrt.f64 (fma.f64 y (log.f64 z) y))
260.0ms	(fma.f64 y (log.f64 z) y)
217.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (cbrt.f64 (fma.f64 y (log.f64 z) y)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (cbrt.f64 (fma.f64 y (log.f64 z) y)))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y)))
1.0ms	(cbrt.f64 (fma.f64 y (log.f64 z) y))
0.0ms	(fma.f64 y (log.f64 z) y)

simplify158.0ms (2%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
686×	`unswap-sqr_binary64`
498×	`log-prod_binary64`
421×	`exp-prod_binary64`
201×	`*-commutative_binary64`

Counts

199 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	3284
1	276	2524
2	692	2229
3	1756	2021
4	4078	1988
5	4883	1988
6	4882	1988
7	4972	1988

prune184.0ms (2.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	232	4	236

Error

0.0b

Counts

236 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
▶	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y) (.f64 y z)))
✓	0.3b	(fma.f64 x 1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (*.f64 y z)))

Compiler

Compiled 7366 to 1667 computations (77.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series831.0ms (10.6%)

Counts

4 → 72

Calls

4 calls:

489.0ms	(.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y)))
270.0ms	(.f64 (.f64 (log.f64 z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(.f64 (.f64 (log.f64 z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
6.0ms	(.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

629×	`unswap-sqr_binary64`
466×	`distribute-rgt-in_binary64`
441×	`distribute-lft-in_binary64`
413×	`*-commutative_binary64`
385×	`log-prod_binary64`

Counts

175 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1805
1	244	1524
2	875	1413
3	1401	1385
4	4717	1385
5	4991	1385

prune175.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	33.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 y))) (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 y))))) (cbrt.f64 y)) y) (.f64 y z)))
	0.4b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 5) (cbrt.f64 (cbrt.f64 y)))) (cbrt.f64 y)) y) (.f64 y z)))
	33.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 (sqrt.f64 y))) y) (*.f64 y z)))
✓	0.3b	(fma.f64 x 1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (log.f64 z) y)) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (cbrt.f64 (fma.f64 y (log.f64 z) y))) (*.f64 y z)))

Compiler

Compiled 4727 to 1671 computations (64.6% saved)

regimes631.0ms (8.1%)

Accuracy

Total 0.0b remaining (51.1%)

Threshold costs 0.0b (51.1%)

Counts

83 → 1

Compiler

Compiled 13707 to 8074 computations (41.1% saved)

simplify3.0ms (0%)

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
5	19	14

end0.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

sample849.0ms (10.9%)

Algorithm

1×

intervals

Results

479.0ms	8000×	body	128	valid
17.0ms	278×	body	128	invalid
4.0ms	64×	body	128	nan

Compiler

Compiled 179 to 100 computations (44.1% saved)

Details

analyze232.0ms (3%)

sample272.0ms (3.5%)

simplify289.0ms (3.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series213.0ms (2.7%)

rewrite1.0ms (0%)

simplify67.0ms (0.9%)

prune17.0ms (0.2%)

localize14.0ms (0.2%)

series676.0ms (8.6%)

rewrite15.0ms (0.2%)

simplify102.0ms (1.3%)

prune484.0ms (6.2%)

localize13.0ms (0.2%)

series2.4s (31.1%)

rewrite19.0ms (0.2%)

simplify158.0ms (2%)

prune184.0ms (2.4%)

localize12.0ms (0.2%)

series831.0ms (10.6%)

rewrite24.0ms (0.3%)

simplify97.0ms (1.2%)

prune175.0ms (2.2%)

regimes631.0ms (8.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample849.0ms (10.9%)

Profiling