Details

analyze236.0ms (3.6%)

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)

sample1.3s (20.5%)

Results

1.0s	8256×	body	128	valid
49.0ms	411×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify284.0ms (4.3%)

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)

localize7.0ms (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)

series288.0ms (4.4%)

Counts

3 → 69

Calls

3 calls:

213.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
69.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite6.0ms (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:

3.0ms	(-.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))

simplify130.0ms (2%)

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

prune71.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	6	94

Error

0.0b

Counts

94 → 6

Alt Table

Status	Error	Program
	17.5b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
▶	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z))) (cbrt.f64 (-.f64 (log.f64 z) z))) y))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
	35.4b	(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))))
	0.1b	(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))

Compiler

Compiled 1743 to 660 computations (62.1% 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 (*.f64 (log.f64 z) y) y)
✓	0.3b	(*.f64 (log.f64 z) y)

series644.0ms (9.8%)

Counts

4 → 85

Calls

4 calls:

242.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
172.0ms	(*.f64 (log.f64 z) y)
158.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
72.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

rewrite15.0ms (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))
3.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
3.0ms	(*.f64 (log.f64 z) y)
0.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

simplify92.0ms (1.4%)

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 → 141

Iterations

Useful iterations: 3 (0.0ms)

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

prune124.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	140	7	147

Error

0.0b

Counts

147 → 7

Alt Table

Status	Error	Program
	17.5b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
✓	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 (-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y) (.f64 y z)))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z))) (cbrt.f64 (-.f64 (log.f64 z) z))) y))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
	34.9b	(fma.f64 x 1/2 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (log.f64 z) y) 3) (pow.f64 y 3)) (+.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (-.f64 (.f64 y y) (.f64 (.f64 (log.f64 z) y) y)))) (.f64 y z)))
▶	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))

Compiler

Compiled 2839 to 954 computations (66.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.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))
✓	0.5b	(cbrt.f64 z)

series1.5s (23.4%)

Counts

4 → 60

Calls

4 calls:

1.2s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
216.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
44.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
31.0ms	(cbrt.f64 z)

rewrite28.0ms (0.4%)

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))
8.0ms	(*.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)

simplify96.0ms (1.5%)

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	2690
1	390	1698
2	1365	1634
3	4136	1624
4	5098	1624

prune206.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	226	5	231

Error

0.0b

Counts

231 → 5

Alt Table

Status	Error	Program
▶	0.4b	(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)))
	17.6b	(fma.f64 x 1/2 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z))) (cbrt.f64 (-.f64 (log.f64 z) z))) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 5256 to 1796 computations (65.8% 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))
✓	0.4b	(.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)

series665.0ms (10.1%)

Counts

4 → 72

Calls

4 calls:

411.0ms	(.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y)))
188.0ms	(.f64 (.f64 (log.f64 z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
31.0ms	(cbrt.f64 y)

rewrite24.0ms (0.4%)

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:

10.0ms	(.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)

simplify104.0ms (1.6%)

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	1632
2	875	1561
3	1401	1525
4	4717	1525
5	4991	1525

prune151.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	190	5	195

Error

0.0b

Counts

195 → 5

Alt Table

Status	Error	Program
✓	0.4b	(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)))
	17.6b	(fma.f64 x 1/2 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z))) (cbrt.f64 (-.f64 (log.f64 z) z))) y))
✓	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 4713 to 1550 computations (67.1% saved)

regimes399.0ms (6.1%)

Accuracy

Total 0.1b remaining (66.6%)

Threshold costs 0.1b (66.6%)

Counts

53 → 1

Compiler

Compiled 7505 to 4463 computations (40.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	16	17
2	26	17
3	32	17
4	36	17
5	37	17
6	37	17

end81.0ms (1.2%)

Compiler: Compiled 129 to 75 computations (41.9% saved)

Details

analyze236.0ms (3.6%)

sample1.3s (20.5%)

simplify284.0ms (4.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series288.0ms (4.4%)

rewrite6.0ms (0.1%)

simplify130.0ms (2%)

prune71.0ms (1.1%)

localize9.0ms (0.1%)

series644.0ms (9.8%)

rewrite15.0ms (0.2%)

simplify92.0ms (1.4%)

prune124.0ms (1.9%)

localize12.0ms (0.2%)

series1.5s (23.4%)

rewrite28.0ms (0.4%)

simplify96.0ms (1.5%)

prune206.0ms (3.1%)

localize12.0ms (0.2%)

series665.0ms (10.1%)

rewrite24.0ms (0.4%)

simplify104.0ms (1.6%)

prune151.0ms (2.3%)

regimes399.0ms (6.1%)

simplify3.0ms (0%)

end81.0ms (1.2%)

Profiling