Details

analyze489.0ms (6.2%)

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
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)

sample1.0s (12.6%)

Results

864.0ms	8256×	body	128	valid
28.0ms	276×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify74.0ms (0.9%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.9b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series82.0ms (1%)

Counts

2 → 60

Calls

2 calls:

66.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
15.0ms	(/.f64 v (+.f64 t1 u))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
3.0ms	(/.f64 v (+.f64 t1 u))

simplify190.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
383×	`fma-def_binary64`
336×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
286×	`distribute-rgt-in_binary64`

Counts

246 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7288
1	848	7129
2	2435	7053
3	4601	7053
4	5003	7053

prune182.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	214	7	221

Error

0.3b

Counts

221 → 7

Alt Table

Status	Error	Program
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	23.7b	(*.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))
	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
▶	1.0b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	3.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.8b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))

Compiler

Compiled 5671 to 2137 computations (62.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 t1 u))
✓	0.2b	(*.f64 v (/.f64 1 (+.f64 t1 u)))
✓	0.9b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

series91.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

66.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
16.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
8.0ms	(/.f64 1 (+.f64 t1 u))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
31×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 119

Calls

3 calls:

11.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
7.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
4.0ms	(/.f64 1 (+.f64 t1 u))

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-/r*_binary64`
449×	`associate-/r/_binary64`
415×	`associate-/l/_binary64`
366×	`fma-neg_binary64`
338×	`fma-def_binary64`

Counts

215 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3908
1	577	3653
2	2003	3521
3	4793	3521
4	5013	3521

prune210.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	201	7	208

Error

0.3b

Counts

208 → 7

Alt Table

Status	Error	Program
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	23.7b	(.f64 (sqrt.f64 (/.f64 (.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))))
▶	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	3.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.8b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))

Compiler

Compiled 4452 to 2159 computations (51.5% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
✓	0.6b	(cbrt.f64 v)
✓	1.6b	(/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	8.6b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

series1.1s (14%)

Counts

4 → 84

Calls

4 calls:

1.0s	(/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
45.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
37.0ms	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
34.0ms	(cbrt.f64 v)

rewrite77.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
25×	`cbrt-prod_binary64`
18×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`
14×	`cbrt-div_binary64`

Counts

4 → 104

Calls

4 calls:

18.0ms	(/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
4.0ms	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
4.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
1.0ms	(cbrt.f64 v)

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-def_binary64`
381×	`unswap-sqr_binary64`
308×	`times-frac_binary64`
268×	`associate-/l*_binary64`
247×	`associate-r_binary64`

Counts

188 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	5663
1	1000	4654
2	3428	4230
3	5017	4230

prune427.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	353	7	360

Error

0.3b

Counts

360 → 7

Alt Table

Status	Error	Program
▶	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	23.7b	(.f64 (sqrt.f64 (/.f64 (.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))))
✓	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	3.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.8b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))

Compiler

Compiled 17083 to 8610 computations (49.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u))))
	8.6b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
✓	11.2b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

series1.9s (24%)

Counts

3 → 108

Calls

3 calls:

1.0s

(/.f64 (*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

559.0ms

(*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u))))

328.0ms

(cbrt.f64 (/.f64 v (+.f64 t1 u)))

rewrite65.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`cbrt-prod_binary64`
99×	`*-un-lft-identity_binary64`
79×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`

Counts

3 → 164

Calls

3 calls:

22.0ms

(/.f64 (*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

17.0ms

(*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u))))

4.0ms

(cbrt.f64 (/.f64 v (+.f64 t1 u)))

simplify169.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

331×	`times-frac_binary64`
320×	`associate-/l*_binary64`
275×	`associate-l_binary64`
270×	`fma-def_binary64`
253×	`associate-/r*_binary64`

Counts

272 → 340

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	632	11208
1	1727	10154
2	4978	10154

prune894.0ms (11.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	659	0	659
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	659	7	666

Error

0.3b

Counts

666 → 7

Alt Table

Status	Error	Program
✓	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	23.7b	(.f64 (sqrt.f64 (/.f64 (.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))))
✓	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	3.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.8b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))

Compiler

Compiled 39645 to 18191 computations (54.1% saved)

regimes482.0ms (6.1%)

Accuracy

Total 1.1b remaining (83.1%)

Threshold costs 0b (0%)

Counts

109 → 1

Compiler

Compiled 11254 to 6646 computations (40.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	28	18
3	33	18
4	35	18
5	34	18

end110.0ms (1.4%)

Compiler: Compiled 204 to 121 computations (40.7% saved)

Details

analyze489.0ms (6.2%)

sample1.0s (12.6%)

simplify74.0ms (0.9%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series82.0ms (1%)

rewrite38.0ms (0.5%)

simplify190.0ms (2.4%)

prune182.0ms (2.3%)

localize8.0ms (0.1%)

series91.0ms (1.1%)

rewrite29.0ms (0.4%)

simplify120.0ms (1.5%)

prune210.0ms (2.6%)

localize36.0ms (0.4%)

series1.1s (14%)

rewrite77.0ms (1%)

simplify126.0ms (1.6%)

prune427.0ms (5.4%)

localize15.0ms (0.2%)

series1.9s (24%)

rewrite65.0ms (0.8%)

simplify169.0ms (2.1%)

prune894.0ms (11.2%)

regimes482.0ms (6.1%)

simplify2.0ms (0%)

end110.0ms (1.4%)

Profiling