Details

analyze37.0ms (1.2%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample836.0ms (27.4%)

Results

745.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series10.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 47

Calls

1 calls:

5.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

simplify77.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
387×	`distribute-rgt-in_binary64`
223×	`fma-def_binary64`
161×	`associate-/l*_binary64`

Counts

71 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1282
1	280	1222
2	785	1160
3	2516	1148
4	4566	1139
5	5172	1139

prune41.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
	30.5b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
▶	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 1023 to 331 computations (67.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.5b	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

series27.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
10.0ms	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

simplify66.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-neg_binary64`
534×	`cancel-sign-sub-inv_binary64`
437×	`times-frac_binary64`
306×	`associate-/l*_binary64`
245×	`fma-def_binary64`

Counts

70 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1427
1	268	1315
2	845	1204
3	3551	1195
4	5024	1195

prune96.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	117	4	121

Error

Counts

121 → 4

Alt Table

Status	Error	Program
	30.5b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
▶	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 2037 to 813 computations (60.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
✓	0.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
✓	0.0b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series68.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

28.0ms

(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

25.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

15.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

rewrite160.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

278×	`*-un-lft-identity_binary64`
214×	`cbrt-prod_binary64`
171×	`times-frac_binary64`
160×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`

Counts

3 → 247

Calls

3 calls:

84.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

25.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

5.0ms

(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

simplify269.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

764×	`associate-/l*_binary64`
580×	`fma-def_binary64`
261×	`associate-l_binary64`
253×	`associate-r_binary64`
167×	`associate-/r/_binary64`

Counts

319 → 306

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	9475
1	709	9094
2	2322	8282
3	4867	8282
4	4956	8282

prune397.0ms (13%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	591	0	591
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	591	4	595

Error

Counts

595 → 4

Alt Table

Status	Error	Program
	30.5b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
▶	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
✓	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 20588 to 3762 computations (81.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (+.f64 x y))
✓	0.5b	(cbrt.f64 (-.f64 x y))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))

series126.0ms (4.1%)

Counts

4 → 96

Calls

4 calls:

41.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
33.0ms	(cbrt.f64 (-.f64 x y))
28.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
24.0ms	(cbrt.f64 (+.f64 x y))

rewrite33.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`cbrt-prod_binary64`
54×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
28×	`cbrt-div_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
8.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
2.0ms	(cbrt.f64 (-.f64 x y))
2.0ms	(cbrt.f64 (+.f64 x y))

simplify176.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

514×	`times-frac_binary64`
407×	`fma-neg_binary64`
320×	`associate-r_binary64`
299×	`unswap-sqr_binary64`
235×	`associate-l_binary64`

Counts

242 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	358	5947
1	950	5705
2	3056	5366
3	4966	5366
4	5083	5366

prune317.0ms (10.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	513	0	513
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	513	4	517

Error

Counts

517 → 4

Alt Table

Status	Error	Program
	30.5b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
✓	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
✓	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 22060 to 6443 computations (70.8% saved)

regimes140.0ms (4.6%)

Accuracy

Total 0.0b remaining (44.6%)

Threshold costs 0.0b (44.6%)

Counts

57 → 1

Compiler

Compiled 2955 to 1590 computations (46.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	11	14
2	16	14
3	18	14
4	19	14
5	19	14

end59.0ms (1.9%)

Compiler: Compiled 107 to 47 computations (56.1% saved)

Details

analyze37.0ms (1.2%)

sample836.0ms (27.4%)

simplify70.0ms (2.3%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series10.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify77.0ms (2.5%)

prune41.0ms (1.3%)

localize9.0ms (0.3%)

series27.0ms (0.9%)

rewrite1.0ms (0%)

simplify66.0ms (2.2%)

prune96.0ms (3.1%)

localize10.0ms (0.3%)

series68.0ms (2.2%)

rewrite160.0ms (5.3%)

simplify269.0ms (8.8%)

prune397.0ms (13%)

localize10.0ms (0.3%)

series126.0ms (4.1%)

rewrite33.0ms (1.1%)

simplify176.0ms (5.8%)

prune317.0ms (10.4%)

regimes140.0ms (4.6%)

simplify2.0ms (0.1%)

end59.0ms (1.9%)

Profiling