Details

analyze213.0ms (1.6%)

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)

sample231.0ms (1.7%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify248.0ms (1.8%)

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)

series382.0ms (2.8%)

Counts

3 → 69

Calls

3 calls:

229.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
148.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite8.0ms (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:

5.0ms	(-.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))

simplify119.0ms (0.9%)

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

prune75.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Error

0.0b

Counts

94 → 4

Alt Table

Status	Error	Program
	15.8b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (+.f64 (.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)))
	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))
	15.8b	(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))

Compiler

Compiled 1712 to 646 computations (62.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
✓	0.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
✓	0.3b	(*.f64 (log.f64 z) y)
✓	0.3b	(+.f64 (*.f64 (log.f64 z) y) y)

series1.1s (8.2%)

Counts

4 → 85

Calls

4 calls:

549.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
255.0ms	(*.f64 (log.f64 z) y)
204.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
88.0ms	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))

rewrite39.0ms (0.3%)

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:

27.0ms	(+.f64 (*.f64 (log.f64 z) y) y)
6.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z))
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)))

simplify81.0ms (0.6%)

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	2224
1	359	1880
2	1046	1687
3	3564	1685
4	5040	1685

prune134.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	129	5	134
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Error

0.0b

Counts

138 → 7

Alt Table

Status	Error	Program
	15.8b	(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))
	0.4b	(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)))
	14.3b	(fma.f64 x 1/2 (-.f64 (/.f64 (-.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (.f64 y y)) (-.f64 (.f64 (log.f64 z) y) y)) (.f64 y z)))
	35.0b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (sqrt.f64 y)) (sqrt.f64 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))
	0.4b	(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)))
	28.2b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (log.f64 z) y)) (sqrt.f64 (.f64 (log.f64 z) y))) y) (.f64 y z)))

Compiler

Compiled 2768 to 944 computations (65.9% saved)

localize13.0ms (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)
✓	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series1.9s (14%)

Counts

4 → 60

Calls

4 calls:

1.6s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
254.0ms	(+.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))
32.0ms	(cbrt.f64 z)

rewrite29.0ms (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))
6.0ms	(*.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)

simplify88.0ms (0.7%)

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

prune309.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	225	6	231

Error

0.0b

Counts

231 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 (cbrt.f64 z))) z)) y))
▶	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))))
	15.8b	(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 (fma.f64 y (-.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 z))) 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)))
	28.2b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (log.f64 z) y)) (sqrt.f64 (.f64 (log.f64 z) y))) y) (.f64 y z)))

Compiler

Compiled 5366 to 1890 computations (64.8% saved)

localize23.0ms (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))
✓	0.2b	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)
✓	0.6b	(cbrt.f64 (neg.f64 z))
✓	5.9b	(pow.f64 z 2/3)

series5.5s (40.8%)

Counts

4 → 72

Calls

4 calls:

3.4s	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)
2.1s	(.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))
38.0ms	(cbrt.f64 (neg.f64 z))
25.0ms	(pow.f64 z 2/3)

rewrite22.0ms (0.2%)

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))
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)

simplify134.0ms (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

prune236.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	160	6	166

Error

0.0b

Counts

166 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 (cbrt.f64 z))) z)) y))
✓	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))))
	15.8b	(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 (fma.f64 y (-.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 z))) 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)))
	28.2b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (log.f64 z) y)) (sqrt.f64 (.f64 (log.f64 z) y))) y) (.f64 y z)))

Compiler

Compiled 5975 to 3777 computations (36.8% saved)

regimes1.6s (11.6%)

Accuracy

Total 0.1b remaining (83.6%)

Threshold costs 0.1b (83.6%)

Counts

187 → 1

Compiler

Compiled 25774 to 16312 computations (36.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	22
2	43	22
3	53	22
4	59	22
5	60	22
6	59	22

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.0s (7.5%)

Algorithm

1×

intervals

Results

579.0ms	8000×	body	128	valid
16.0ms	287×	body	128	invalid
4.0ms	81×	body	128	nan

Compiler

Compiled 185 to 120 computations (35.1% saved)

Details

analyze213.0ms (1.6%)

sample231.0ms (1.7%)

simplify248.0ms (1.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series382.0ms (2.8%)

rewrite8.0ms (0.1%)

simplify119.0ms (0.9%)

prune75.0ms (0.6%)

localize9.0ms (0.1%)

series1.1s (8.2%)

rewrite39.0ms (0.3%)

simplify81.0ms (0.6%)

prune134.0ms (1%)

localize13.0ms (0.1%)

series1.9s (14%)

rewrite29.0ms (0.2%)

simplify88.0ms (0.7%)

prune309.0ms (2.3%)

localize23.0ms (0.2%)

series5.5s (40.8%)

rewrite22.0ms (0.2%)

simplify134.0ms (1%)

prune236.0ms (1.8%)

regimes1.6s (11.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.0s (7.5%)

Profiling