Details

analyze313.0ms (3.3%)

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
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample118.0ms (1.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 34 to 20 computations (41.2% saved)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series95.0ms (1%)

Counts

3 → 84

Calls

3 calls:

72.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
18.0ms	(/.f64 v (+.f64 t1 u))
5.0ms	(-.f64 -1 (/.f64 u t1))

rewrite54.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
229×	`add-sqr-sqrt_binary64`
219×	`*-un-lft-identity_binary64`
129×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`

Counts

3 → 257

Calls

3 calls:

13.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
7.0ms	(-.f64 -1 (/.f64 u t1))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify262.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
310×	`associate-/l/_binary64`
233×	`associate-/l*_binary64`
223×	`div-sub_binary64`
212×	`fma-neg_binary64`

Counts

341 → 303

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	465	9966
1	1202	8417
2	3569	8323
3	4946	8323
4	5008	8323

prune422.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	297	6	303
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	298	7	305

Error

Counts

305 → 7

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
	0.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
	4.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	14.1b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
	2.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 8214 to 2941 computations (64.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.2b	(*.f64 (neg.f64 u) (/.f64 1 t1))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))

series131.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

72.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
53.0ms	(*.f64 (neg.f64 u) (/.f64 1 t1))
5.0ms	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`times-frac_binary64`
90×	`*-un-lft-identity_binary64`
72×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
18×	`associate-/l*_binary64`

Counts

3 → 157

Calls

3 calls:

8.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
7.0ms	(*.f64 (neg.f64 u) (/.f64 1 t1))
3.0ms	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))

simplify189.0ms (2%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
214×	`div-sub_binary64`
200×	`distribute-rgt-neg-out_binary64`
191×	`distribute-lft-neg-out_binary64`
188×	`fma-neg_binary64`

Counts

241 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	5266
1	807	4702
2	2560	4682
3	4533	4682
4	4986	4682
5	4935	4682

prune356.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	320	7	327

Error

Counts

327 → 7

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
▶	0.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
	4.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	14.1b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
	2.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 7937 to 3492 computations (56% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
✓	12.6b	(cbrt.f64 (/.f64 u t1))

series1.3s (13.7%)

Counts

4 → 108

Calls

4 calls:

747.0ms	(*.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))
434.0ms	(cbrt.f64 (/.f64 u t1))
85.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
36.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))

rewrite70.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`times-frac_binary64`
134×	`add-sqr-sqrt_binary64`
127×	`*-un-lft-identity_binary64`
103×	`add-cube-cbrt_binary64`
92×	`cbrt-prod_binary64`

Counts

4 → 244

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))
12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
8.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))
2.0ms	(cbrt.f64 (/.f64 u t1))

simplify236.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
293×	`associate-l_binary64`
273×	`associate-r_binary64`
196×	`associate-/l/_binary64`
188×	`*-commutative_binary64`

Counts

352 → 404

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	466	8357
1	1090	7769
2	3375	7430
3	4808	7430
4	4964	7430

prune493.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	476	0	476
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	476	7	483

Error

Counts

483 → 7

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	1.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
✓	0.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
	4.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	14.1b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
	2.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 15368 to 4230 computations (72.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.7b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))
✓	1.0b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))

series101.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

73.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
27.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

rewrite490.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

1342×	`times-frac_binary64`
914×	`add-sqr-sqrt_binary64`
827×	`*-un-lft-identity_binary64`
459×	`add-cube-cbrt_binary64`
182×	`difference-of-squares_binary64`

Counts

2 → 634

Calls

2 calls:

26.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
16.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

simplify756.0ms (8%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-/r/_binary64`
484×	`fma-def_binary64`
318×	`associate-*l/_binary64`
311×	`*-commutative_binary64`
244×	`associate-*r/_binary64`

Counts

706 → 720

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	491	25016
1	1250	23497
2	4397	23441
3	4990	23441
4	4969	23441

prune795.0ms (8.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	851	1	852
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	852	7	859

Error

Counts

859 → 7

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	1.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
✓	0.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 u t1)) (cbrt.f64 (/.f64 u t1)))) (cbrt.f64 (/.f64 u t1)))))
	4.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	14.1b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
	2.4b	(/.f64 1 (*.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) v) (+.f64 t1 u)))

Compiler

Compiled 26003 to 10659 computations (59% saved)

regimes1.8s (19.5%)

Accuracy

Total 1.2b remaining (90.4%)

Threshold costs 0b (0%)

Counts

246 → 1

Compiler

Compiled 20934 to 13174 computations (37.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	23	16
3	27	16
4	30	16
5	31	16
6	30	16

end1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample1.3s (13.5%)

Algorithm

1×

intervals

Results

641.0ms	8000×	body	128	valid
19.0ms	235×	body	128	invalid

Compiler

Compiled 164 to 100 computations (39% saved)

Details

analyze313.0ms (3.3%)

sample118.0ms (1.3%)

simplify80.0ms (0.8%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series95.0ms (1%)

rewrite54.0ms (0.6%)

simplify262.0ms (2.8%)

prune422.0ms (4.4%)

localize9.0ms (0.1%)

series131.0ms (1.4%)

rewrite36.0ms (0.4%)

simplify189.0ms (2%)

prune356.0ms (3.8%)

localize13.0ms (0.1%)

series1.3s (13.7%)

rewrite70.0ms (0.7%)

simplify236.0ms (2.5%)

prune493.0ms (5.2%)

localize8.0ms (0.1%)

series101.0ms (1.1%)

rewrite490.0ms (5.2%)

simplify756.0ms (8%)

prune795.0ms (8.4%)

regimes1.8s (19.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.3s (13.5%)

Profiling