Details

analyze615.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 23 to 18 computations (21.7% saved)

sample48.0ms (0.1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
11.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify693.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (289.0ms)

Iter	Nodes	Cost
0	4924	19
1	4924	19

prune54.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize41.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 m (-.f64 1 m))
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)

rewrite164.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
10×	`associate-l_binary64`
8×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`
7×	`pow1_binary64`
6×	`associate-*r/_binary64` `difference-of-squares_binary64`
4×	`sub-neg_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

3 → 95

Calls

3 calls:

74.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
29.0ms	(*.f64 m (-.f64 1 m))
28.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series334.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

146.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
101.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
86.0ms	(*.f64 m (-.f64 1 m))

simplify154.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5029	1776

prune963.0ms (1.7%)

Pruning

49 alts after pruning (48 fresh and 1 done)

	Pruned	Kept	Total
New	56	48	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	49	105

Merged error: 0b

Counts

105 → 49

Compiler

Compiled 3136 to 2239 computations (28.6% saved)

localize22.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 m (*.f64 m (neg.f64 m)))
0.1b	(.f64 (-.f64 (/.f64 (+.f64 m (.f64 m (neg.f64 m))) v) 1) (-.f64 1 m))
0.1b	(/.f64 (+.f64 m (*.f64 m (neg.f64 m))) v)

rewrite62.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`associate-l_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `cancel-sign-sub-inv_binary64` `difference-of-squares_binary64` `flip--_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `distribute-rgt-neg-out_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `unsub-neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 86

Calls

3 calls:

32.0ms	(.f64 (-.f64 (/.f64 (+.f64 m (.f64 m (neg.f64 m))) v) 1) (-.f64 1 m))
10.0ms	(/.f64 (+.f64 m (*.f64 m (neg.f64 m))) v)
6.0ms	(+.f64 m (*.f64 m (neg.f64 m)))

series267.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

113.0ms	(+.f64 m (*.f64 m (neg.f64 m)))
101.0ms	(.f64 (-.f64 (/.f64 (+.f64 m (.f64 m (neg.f64 m))) v) 1) (-.f64 1 m))
52.0ms	(/.f64 (+.f64 m (*.f64 m (neg.f64 m))) v)

simplify257.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	4955	1941
1	4955	1941

prune1.2s (2.1%)

Pruning

79 alts after pruning (78 fresh and 1 done)

	Pruned	Kept	Total
New	51	44	95
Fresh	13	34	47
Picked	0	1	1
Done	1	0	1
Total	65	79	144

Merged error: 0b

Counts

144 → 79

Compiler

Compiled 4032 to 2595 computations (35.6% saved)

localize15.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 m (*.f64 m m))
0.1b	(.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (-.f64 1 m))
0.1b	(/.f64 (-.f64 m (*.f64 m m)) v)

rewrite64.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
11×	`difference-of-squares_binary64`
10×	`associate-l_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
6×	`associate-r_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64`
2×	`associate-/l/_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 96

Calls

3 calls:

33.0ms	(.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (-.f64 1 m))
9.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
5.0ms	(-.f64 m (*.f64 m m))

series139.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
50.0ms	(-.f64 m (*.f64 m m))
37.0ms	(.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (-.f64 1 m))

simplify106.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4991	2089
1	4991	2089

prune2.0s (3.5%)

Pruning

85 alts after pruning (83 fresh and 2 done)

	Pruned	Kept	Total
New	79	26	105
Fresh	20	57	77
Picked	0	1	1
Done	0	1	1
Total	99	85	184

Merged error: 0b

Counts

184 → 85

Compiler

Compiled 4322 to 2343 computations (45.8% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (.f64 (-.f64 (/.f64 (-.f64 m (*.f64 m m)) v) 1) (neg.f64 m)))
0.1b	(/.f64 (-.f64 m (*.f64 m m)) v)
0.1b	(/.f64 (-.f64 m (*.f64 m m)) v)
0.2b	(.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (neg.f64 m))

rewrite128.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `associate-/l*_binary64`
9×	`add-log-exp_binary64`
8×	`distribute-rgt-out--_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-/r_binary64` `pow1_binary64` `associate-l/_binary64`
4×	`associate-/l/_binary64` `frac-add_binary64` `associate-+l+_binary64`
3×	`distribute-lft-neg-in_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
2×	`distribute-rgt-neg-out_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-mul-1_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `unsub-neg_binary64` `*-commutative_binary64`

Counts

4 → 133

Calls

4 calls:

41.0ms	(+.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (.f64 (-.f64 (/.f64 (-.f64 m (*.f64 m m)) v) 1) (neg.f64 m)))
38.0ms	(.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (neg.f64 m))
12.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
11.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)

series226.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
57.0ms	(+.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (.f64 (-.f64 (/.f64 (-.f64 m (*.f64 m m)) v) 1) (neg.f64 m)))
53.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
52.0ms	(.f64 (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) 1) (neg.f64 m))

simplify172.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	5623	3001

prune3.5s (6.1%)

Pruning

114 alts after pruning (111 fresh and 3 done)

	Pruned	Kept	Total
New	96	49	145
Fresh	20	62	82
Picked	0	1	1
Done	0	2	2
Total	116	114	230

Merged error: 0b

Counts

230 → 114

Compiler

Compiled 4207 to 1273 computations (69.7% saved)

regimes4.9s (8.7%)

Compiler: Compiled 23340 to 14885 computations (36.2% saved)

bsearch17.8s (31.2%)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	224	31
1	224	31

end0.0ms (0%)

sample23.1s (40.4%)

Algorithm

1×

intervals

Results

536.0ms	8000×	body	128	valid
292.0ms	8049×	pre	128	true
3.0ms	49×	body	128	invalid

Compiler

Compiled 8004 to 5098 computations (36.3% saved)

Pareto

0.000950836947593826

Details

analyze615.0ms (1.1%)

sample48.0ms (0.1%)

simplify693.0ms (1.2%)

prune54.0ms (0.1%)

localize41.0ms (0.1%)

rewrite164.0ms (0.3%)

series334.0ms (0.6%)

simplify154.0ms (0.3%)

prune963.0ms (1.7%)

localize22.0ms (0%)

rewrite62.0ms (0.1%)

series267.0ms (0.5%)

simplify257.0ms (0.4%)

prune1.2s (2.1%)

localize15.0ms (0%)

rewrite64.0ms (0.1%)

series139.0ms (0.2%)

simplify106.0ms (0.2%)

prune2.0s (3.5%)

localize44.0ms (0.1%)

rewrite128.0ms (0.2%)

series226.0ms (0.4%)

simplify172.0ms (0.3%)

prune3.5s (6.1%)

regimes4.9s (8.7%)

bsearch17.8s (31.2%)

simplify48.0ms (0.1%)

end0.0ms (0%)

sample23.1s (40.4%)

Profiling