Details

analyze237.0ms (2.9%)

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)

sample266.0ms (3.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify288.0ms (3.5%)

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 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)

series305.0ms (3.7%)

Counts

3 → 69

Calls

3 calls:

212.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
88.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite7.0ms (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:

4.0ms	(-.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 (1.6%)

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

prune86.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
	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))
	32.0b	(fma.f64 x 1/2 (*.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
	0.8b	(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))))
	11.4b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (.f64 (log.f64 z) (log.f64 z)) (.f64 z z)) (+.f64 (log.f64 z) z)) y))
	15.9b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (fma.f64 z z (*.f64 (log.f64 z) (+.f64 z (log.f64 z))))) y))
	16.0b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (.f64 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (-.f64 (log.f64 z) z))) y))
	0.3b	(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 1904 to 730 computations (61.7% saved)

localize9.0ms (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))
✓	0.2b	(*.f64 (log.f64 z) y)
✓	0.2b	(+.f64 (*.f64 (log.f64 z) y) y)

series1.1s (13.7%)

Counts

4 → 85

Calls

4 calls:

538.0ms	(*.f64 (log.f64 z) y)
254.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
214.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
118.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

5.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
4.0ms	(*.f64 (log.f64 z) y)
3.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
0.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
554×	`fma-neg_binary64`
487×	`unsub-neg_binary64`
334×	`distribute-rgt-in_binary64`
312×	`distribute-lft-in_binary64`

Counts

159 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2276
1	359	1880
2	1046	1687
3	3564	1685
4	5040	1685

prune142.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
▶	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))
	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 (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (.f64 (cbrt.f64 (log.f64 z)) y)) y) (.f64 y z)))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (.f64 (log.f64 z) y))) (cbrt.f64 (.f64 (log.f64 z) y))) y) (.f64 y z)))
	16.0b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (.f64 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (-.f64 (log.f64 z) z))) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

Compiler

Compiled 2696 to 912 computations (66.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
✓	0.2b	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series2.0s (23.9%)

Counts

4 → 60

Calls

4 calls:

1.5s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
305.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
81.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
32.0ms	(cbrt.f64 z)

rewrite28.0ms (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:

11.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
5.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)
0.0ms	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

664×	`distribute-rgt-in_binary64`
592×	`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	1359	1572
3	4136	1562
4	5098	1562

prune295.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	224	6	230

Error

0.0b

Counts

230 → 6

Alt Table

Status	Error	Program
✓	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))
▶	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 (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (.f64 (cbrt.f64 (log.f64 z)) y)) y) (.f64 y z)))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (.f64 (log.f64 z) y))) (cbrt.f64 (.f64 (log.f64 z) y))) y) (.f64 y z)))
	16.0b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (.f64 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (-.f64 (log.f64 z) z))) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

Compiler

Compiled 5309 to 1827 computations (65.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.4b	(.f64 (.f64 (log.f64 z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)

series836.0ms (10.2%)

Counts

4 → 72

Calls

4 calls:

524.0ms	(.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y)))
240.0ms	(.f64 (.f64 (log.f64 z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
39.0ms	(*.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:

9.0ms	(.f64 (.f64 (log.f64 z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
5.0ms	(.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)

simplify101.0ms (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

prune193.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	190	6	196

Error

0.0b

Counts

196 → 6

Alt Table

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

Compiler

Compiled 4717 to 1668 computations (64.6% saved)

regimes1.1s (13.1%)

Accuracy

Total 0.0b remaining (56.8%)

Threshold costs 0.0b (56.8%)

Counts

138 → 1

Compiler

Compiled 18585 to 11755 computations (36.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	31	19
3	36	19
4	38	19
5	37	19

end1.0ms (0%)

Compiler: Compiled 16 to 11 computations (31.3% saved)

sample868.0ms (10.6%)

Algorithm

1×

intervals

Results

495.0ms	8000×	body	128	valid
18.0ms	308×	body	128	invalid
5.0ms	72×	body	128	nan

Compiler

Compiled 172 to 100 computations (41.9% saved)

Details

analyze237.0ms (2.9%)

sample266.0ms (3.2%)

simplify288.0ms (3.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series305.0ms (3.7%)

rewrite7.0ms (0.1%)

simplify134.0ms (1.6%)

prune86.0ms (1%)

localize9.0ms (0.1%)

series1.1s (13.7%)

rewrite16.0ms (0.2%)

simplify79.0ms (1%)

prune142.0ms (1.7%)

localize13.0ms (0.2%)

series2.0s (23.9%)

rewrite28.0ms (0.3%)

simplify91.0ms (1.1%)

prune295.0ms (3.6%)

localize13.0ms (0.2%)

series836.0ms (10.2%)

rewrite24.0ms (0.3%)

simplify101.0ms (1.2%)

prune193.0ms (2.4%)

regimes1.1s (13.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample868.0ms (10.6%)

Profiling