Details

analyze721.0ms (11.6%)

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%	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)

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 34 to 20 computations (41.2% saved)

simplify77.0ms (1.2%)

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

prune3.0ms (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	15.8b	(/.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))
✓	1.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series194.0ms (3.1%)

Counts

3 → 84

Calls

3 calls:

171.0ms	(/.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))

rewrite78.0ms (1.3%)

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:

11.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
6.0ms	(-.f64 -1 (/.f64 u t1))
3.0ms	(/.f64 v (+.f64 t1 u))

simplify269.0ms (4.3%)

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

prune250.0ms (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

0.2b

Counts

305 → 7

Alt Table

Status	Error	Program
	15.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	7.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (pow.f64 (-.f64 -1 (/.f64 u t1)) 3)))
▶	1.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	6.1b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
	1.9b	(.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))))
	30.8b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	2.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 8186 to 2939 computations (64.1% saved)

localize10.0ms (0.2%)

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))
✓	1.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))

series82.0ms (1.3%)

Counts

3 → 84

Calls

3 calls:

70.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
7.0ms	(*.f64 (neg.f64 u) (/.f64 1 t1))
5.0ms	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))

rewrite53.0ms (0.9%)

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:

29.0ms	(*.f64 (neg.f64 u) (/.f64 1 t1))
8.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
2.0ms	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))

simplify174.0ms (2.8%)

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

prune300.0ms (4.8%)

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

0.2b

Counts

327 → 7

Alt Table

Status	Error	Program
	15.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	7.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (pow.f64 (-.f64 -1 (/.f64 u t1)) 3)))
✓	1.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	6.1b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
▶	1.9b	(.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))))
	30.8b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	2.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 7909 to 3490 computations (55.9% saved)

localize46.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 v (cbrt.f64 (+.f64 t1 u)))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
✓	0.6b	(cbrt.f64 (+.f64 t1 u))
✓	3.1b	(/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

series831.0ms (13.4%)

Counts

4 → 120

Calls

4 calls:

438.0ms	(/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
346.0ms	(/.f64 v (cbrt.f64 (+.f64 t1 u)))
26.0ms	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
21.0ms	(cbrt.f64 (+.f64 t1 u))

rewrite75.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

358×	`times-frac_binary64`
303×	`add-sqr-sqrt_binary64`
277×	`*-un-lft-identity_binary64`
155×	`add-cube-cbrt_binary64`
128×	`cbrt-prod_binary64`

Counts

4 → 332

Calls

4 calls:

14.0ms	(/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
9.0ms	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
4.0ms	(/.f64 v (cbrt.f64 (+.f64 t1 u)))
2.0ms	(cbrt.f64 (+.f64 t1 u))

simplify361.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

410×	`associate-r_binary64`
402×	`associate-/l/_binary64`
277×	`associate-/r*_binary64`
239×	`associate-l_binary64`
212×	`fma-def_binary64`

Counts

452 → 455

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	655	15001
1	1745	14721
2	4958	14721
3	5018	14721

prune446.0ms (7.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	549	0	549
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	549	7	556

Error

0.2b

Counts

556 → 7

Alt Table

Status	Error	Program
	15.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	7.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (pow.f64 (-.f64 -1 (/.f64 u t1)) 3)))
✓	1.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	6.1b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
✓	1.9b	(.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))))
	30.8b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
▶	2.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 22824 to 9543 computations (58.2% 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 1 (+.f64 t1 u))
✓	0.1b	(/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	2.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

series128.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

72.0ms	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
46.0ms	(/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
9.0ms	(/.f64 1 (+.f64 t1 u))

rewrite98.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

426×	`times-frac_binary64`
352×	`add-sqr-sqrt_binary64`
316×	`*-un-lft-identity_binary64`
155×	`add-cube-cbrt_binary64`
114×	`associate-r_binary64`

Counts

3 → 333

Calls

3 calls:

32.0ms	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
13.0ms	(/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
4.0ms	(/.f64 1 (+.f64 t1 u))

simplify258.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

404×	`fma-def_binary64`
347×	`associate-/r/_binary64`
308×	`fma-neg_binary64`
265×	`distribute-rgt-in_binary64`
241×	`distribute-lft-in_binary64`

Counts

417 → 403

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	10438
1	887	9926
2	2949	9862
3	4825	9850
4	4967	9850

prune369.0ms (5.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	486	0	486
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	486	7	493

Error

0.2b

Counts

493 → 7

Alt Table

Status	Error	Program
	15.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	7.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (pow.f64 (-.f64 -1 (/.f64 u t1)) 3)))
✓	1.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	6.1b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
✓	1.9b	(.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))))
	30.8b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	2.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 13628 to 6410 computations (53% saved)

regimes350.0ms (5.6%)

Accuracy

Total 1.3b remaining (86.3%)

Threshold costs 0b (0%)

Counts

98 → 1

Compiler

Compiled 7446 to 4702 computations (36.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	22	19
2	30	19
3	38	19
4	41	19
5	42	19
6	40	19

end1.0ms (0%)

Compiler: Compiled 16 to 11 computations (31.3% saved)

sample1.0s (16.1%)

Algorithm

1×

intervals

Results

588.0ms	8000×	body	128	valid
10.0ms	247×	body	128	invalid

Compiler

Compiled 163 to 104 computations (36.2% saved)

Details

analyze721.0ms (11.6%)

sample26.0ms (0.4%)

simplify77.0ms (1.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series194.0ms (3.1%)

rewrite78.0ms (1.3%)

simplify269.0ms (4.3%)

prune250.0ms (4%)

localize10.0ms (0.2%)

series82.0ms (1.3%)

rewrite53.0ms (0.9%)

simplify174.0ms (2.8%)

prune300.0ms (4.8%)

localize46.0ms (0.7%)

series831.0ms (13.4%)

rewrite75.0ms (1.2%)

simplify361.0ms (5.8%)

prune446.0ms (7.2%)

localize8.0ms (0.1%)

series128.0ms (2.1%)

rewrite98.0ms (1.6%)

simplify258.0ms (4.2%)

prune369.0ms (5.9%)

regimes350.0ms (5.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.0s (16.1%)

Profiling