Details

analyze582.0ms (7.1%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.3s (15.6%)

Results

1.1s	8255×	body	128	valid
3.0ms	26×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 56 to 35 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
✓	0.0b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
✓	0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
✓	0.2b	(*.f64 (+.f64 y 1/2) (log.f64 y))

series331.0ms (4.1%)

Counts

4 → 96

Calls

4 calls:

154.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
86.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
81.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
10.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
20×	`add-log-exp_binary64`
18×	`prod-diff_binary64`

Counts

4 → 119

Calls

4 calls:

7.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
7.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
5.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
3.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify121.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

374×	`fma-neg_binary64`
307×	`associate--l+_binary64`
299×	`cancel-sign-sub-inv_binary64`
275×	`exp-sum_binary64`
242×	`exp-diff_binary64`

Counts

215 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	3418
1	609	3074
2	2022	2997
3	4350	2997
4	4873	2997

prune197.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	215	5	220

Error

0.0b

Counts

220 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (sqrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (cbrt.f64 (+.f64 y 1/2)) (cbrt.f64 (+.f64 y 1/2))) (*.f64 (cbrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
	29.8b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (sqrt.f64 (+.f64 y 1/2)) (sqrt.f64 (log.f64 y))) (*.f64 (sqrt.f64 (+.f64 y 1/2)) (sqrt.f64 (log.f64 y))))) y) z)

Compiler

Compiled 4587 to 2465 computations (46.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
✓	0.0b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
✓	0.1b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series139.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

81.0ms	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
46.0ms	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
8.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 65

Calls

3 calls:

5.0ms	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
2.0ms	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-neg_binary64`
603×	`fma-def_binary64`
350×	`distribute-rgt-in_binary64`
341×	`associate-l_binary64`
318×	`distribute-lft-in_binary64`

Counts

137 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	2390
1	363	2232
2	1108	2071
3	4562	2071
4	5037	2071

prune89.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	111	5	116

Error

0.0b

Counts

116 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (sqrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (cbrt.f64 (+.f64 y 1/2)) (cbrt.f64 (+.f64 y 1/2))) (*.f64 (cbrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
▶	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
	29.8b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (sqrt.f64 (+.f64 y 1/2)) (sqrt.f64 (log.f64 y))) (*.f64 (sqrt.f64 (+.f64 y 1/2)) (sqrt.f64 (log.f64 y))))) y) z)

Compiler

Compiled 2421 to 1263 computations (47.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
✓	0.1b	(.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y))))
✓	0.3b	(+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
✓	0.5b	(cbrt.f64 y)

series588.0ms (7.2%)

Counts

4 → 48

Calls

4 calls:

263.0ms	(+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
149.0ms	(.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y))))
142.0ms	(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
34.0ms	(cbrt.f64 y)

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`log-prod_binary64`
60×	`distribute-lft-in_binary64`
60×	`distribute-rgt-in_binary64`
39×	`cbrt-prod_binary64`
36×	`*-un-lft-identity_binary64`

Counts

4 → 152

Calls

4 calls:

20.0ms	(+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
6.0ms	(.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y))))
6.0ms	(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-neg_binary64`
346×	`associate-l_binary64`
337×	`associate-r_binary64`
279×	`distribute-rgt-out_binary64`
242×	`fma-def_binary64`

Counts

200 → 275

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3870
1	648	3338
2	2606	3114
3	4519	3114
4	4899	3114

prune336.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	292	6	298

Error

Counts

298 → 6

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 (log.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) (+.f64 1/2 y))) (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 y))) (+.f64 1/2 y)))) y) z)
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (sqrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (cbrt.f64 (+.f64 y 1/2)) (cbrt.f64 (+.f64 y 1/2))) (*.f64 (cbrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
✓	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
▶	0.2b	(-.f64 (+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y) z)

Compiler

Compiled 9092 to 5072 computations (44.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
✓	0.1b	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
✓	0.3b	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
✓	0.5b	(cbrt.f64 (neg.f64 y))

series2.9s (35.6%)

Counts

4 → 60

Calls

4 calls:

1.3s	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
1.2s	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
333.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
40.0ms	(cbrt.f64 (neg.f64 y))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cube-cbrt_binary64`
10×	`cbrt-prod_binary64`

Counts

4 → 86

Calls

4 calls:

7.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
5.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
3.0ms	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
1.0ms	(cbrt.f64 (neg.f64 y))

simplify131.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-def_binary64`
325×	`unsub-neg_binary64`
314×	`*-commutative_binary64`
273×	`exp-sum_binary64`
270×	`sub-neg_binary64`

Counts

146 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	3335
1	398	2651
2	1381	2558
3	3439	2492
4	4504	2492
5	4805	2492

prune182.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	155	6	161

Error

Counts

161 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	0.3b	(-.f64 (+.f64 (-.f64 x (.f64 1/3 (.f64 (fma.f64 y 3 3/2) (log.f64 y)))) y) z)
	0.2b	(-.f64 (+.f64 x (fma.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 y)))) (fma.f64 y -3 -3/2) y)) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (cbrt.f64 (+.f64 y 1/2)) (cbrt.f64 (+.f64 y 1/2))) (*.f64 (cbrt.f64 (+.f64 y 1/2)) (log.f64 y)))) y) z)
✓	0.2b	(-.f64 (+.f64 (-.f64 x (+.f64 (.f64 (+.f64 1/2 y) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
✓	0.2b	(-.f64 (+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y) z)

Compiler

Compiled 4198 to 2816 computations (32.9% saved)

regimes674.0ms (8.3%)

Accuracy

Total 0.1b remaining (87%)

Threshold costs 0.1b (87%)

Counts

132 → 1

Compiler

Compiled 12225 to 8499 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	23	16
3	27	16
4	29	16
5	29	16

end115.0ms (1.4%)

Compiler: Compiled 154 to 108 computations (29.9% saved)

Details

analyze582.0ms (7.1%)

sample1.3s (15.6%)

simplify120.0ms (1.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series331.0ms (4.1%)

rewrite27.0ms (0.3%)

simplify121.0ms (1.5%)

prune197.0ms (2.4%)

localize8.0ms (0.1%)

series139.0ms (1.7%)

rewrite11.0ms (0.1%)

simplify91.0ms (1.1%)

prune89.0ms (1.1%)

localize13.0ms (0.2%)

series588.0ms (7.2%)

rewrite43.0ms (0.5%)

simplify140.0ms (1.7%)

prune336.0ms (4.1%)

localize13.0ms (0.2%)

series2.9s (35.6%)

rewrite20.0ms (0.2%)

simplify131.0ms (1.6%)

prune182.0ms (2.2%)

regimes674.0ms (8.3%)

simplify2.0ms (0%)

end115.0ms (1.4%)

Profiling