Details

analyze888.0ms (5.8%)

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
0%	56.2%	43.8%	7
0%	56.2%	43.8%	8
0%	53%	47%	9
0%	49.9%	50.1%	10
0%	49.9%	50.1%	11
0%	49.1%	50.9%	12
0%	48%	52%	13
0%	48%	52%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample2.2s (14.3%)

Results

1.1s	8256×	body	128	valid
804.0ms	591×	body	8192	exit
38.0ms	244×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify285.0ms (1.9%)

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)

series294.0ms (1.9%)

Counts

3 → 69

Calls

3 calls:

203.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
86.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite7.0ms (0%)

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)
1.0ms	(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))

simplify129.0ms (0.8%)

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

prune82.0ms (0.5%)

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
	26.6b	(fma.f64 x 1/2 (cbrt.f64 (.f64 (.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) (fma.f64 y (-.f64 (log.f64 z) z) y)) (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))
	17.2b	(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)))
	27.4b	(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))))
	0.8b	(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))))

Compiler

Compiled 1802 to 674 computations (62.6% saved)

localize13.0ms (0.1%)

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)

series2.1s (13.5%)

Counts

4 → 60

Calls

4 calls:

1.7s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
260.0ms	(+.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)

rewrite30.0ms (0.2%)

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:

12.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
4.0ms	(*.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)

simplify97.0ms (0.6%)

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

prune282.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
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 (pow.f64 z 1/3)) z)) y))
	0.2b	(fma.f64 x 1/2 (-.f64 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))) (*.f64 y z)))
	11.1b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (*.f64 (-.f64 (log.f64 z) z) (fma.f64 1/3 (log.f64 z) z)) (fma.f64 1/3 (log.f64 z) z)) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	17.2b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	27.4b	(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))))

Compiler

Compiled 5352 to 1883 computations (64.8% saved)

localize19.0ms (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 (pow.f64 z 1/3)) z))
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)
✓	5.0b	(pow.f64 z 1/3)

series233.0ms (1.5%)

Counts

2 → 16

Calls

2 calls:

208.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (pow.f64 z 1/3)) z))
24.0ms	(pow.f64 z 1/3)

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
23×	`associate-+r+_binary64`
17×	`pow1_binary64`
16×	`log-pow_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 77

Calls

2 calls:

12.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (pow.f64 z 1/3)) z))
1.0ms	(pow.f64 z 1/3)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
529×	`distribute-rgt-in_binary64`
510×	`fma-neg_binary64`
480×	`distribute-lft-in_binary64`
474×	`associate-l_binary64`

Counts

93 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1212
1	295	722
2	942	555
3	4673	555
4	4832	555

prune258.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	207	6	213

Error

0.0b

Counts

213 → 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 (pow.f64 z 1/3)) z)) y))
	0.2b	(fma.f64 x 1/2 (-.f64 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))) (*.f64 y z)))
	11.1b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (*.f64 (-.f64 (log.f64 z) z) (fma.f64 1/3 (log.f64 z) z)) (fma.f64 1/3 (log.f64 z) z)) y))
▶	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	17.2b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	27.4b	(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))))

Compiler

Compiled 5178 to 2518 computations (51.4% saved)

localize24.0ms (0.2%)

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 (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y)
✓	0.6b	(cbrt.f64 (neg.f64 z))
✓	6.0b	(pow.f64 z 2/3)

series6.5s (42.6%)

Counts

4 → 72

Calls

4 calls:

4.5s	(fma.f64 (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y)
2.0s	(.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)

rewrite21.0ms (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:

10.0ms	(.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))
1.0ms	(pow.f64 z 2/3)
1.0ms	(cbrt.f64 (neg.f64 z))
0.0ms	(fma.f64 (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y)

simplify150.0ms (1%)

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

prune226.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	160	6	166

Error

0.0b

Counts

166 → 6

Alt Table

Status	Error	Program
	11.1b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (*.f64 (-.f64 (log.f64 z) z) (fma.f64 1/3 (log.f64 z) z)) (fma.f64 1/3 (log.f64 z) z)) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 (log.f64 (.f64 (pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y y) (.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 (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	17.2b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	0.2b	(fma.f64 x 1/2 (-.f64 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))) (*.f64 y z)))
	27.4b	(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))))

Compiler

Compiled 5980 to 3786 computations (36.7% saved)

regimes1.3s (8.3%)

Accuracy

Total 0.1b remaining (79.6%)

Threshold costs 0.1b (79.6%)

Counts

142 → 1

Compiler

Compiled 20098 to 13224 computations (34.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	21	16
3	23	16
4	24	16
5	23	16

end138.0ms (0.9%)

Compiler: Compiled 181 to 122 computations (32.6% saved)

Details

analyze888.0ms (5.8%)

sample2.2s (14.3%)

simplify285.0ms (1.9%)

prune3.0ms (0%)

localize8.0ms (0%)

series294.0ms (1.9%)

rewrite7.0ms (0%)

simplify129.0ms (0.8%)

prune82.0ms (0.5%)

localize13.0ms (0.1%)

series2.1s (13.5%)

rewrite30.0ms (0.2%)

simplify97.0ms (0.6%)

prune282.0ms (1.8%)

localize19.0ms (0.1%)

series233.0ms (1.5%)

rewrite19.0ms (0.1%)

simplify72.0ms (0.5%)

prune258.0ms (1.7%)

localize24.0ms (0.2%)

series6.5s (42.6%)

rewrite21.0ms (0.1%)

simplify150.0ms (1%)

prune226.0ms (1.5%)

regimes1.3s (8.3%)

simplify3.0ms (0%)

end138.0ms (0.9%)

Profiling