Details

analyze811.0ms

Algorithm

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
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample198.0ms

Algorithm

intervals

Results

85.0ms	102×	body	1280	valid
59.0ms	27×	body	2560	valid
19.0ms	46×	body	640	valid
5.0ms	10×	body	640	invalid
5.0ms	26×	body	320	valid
3.0ms	49×	body	80	valid
3.0ms	4×	body	1280	invalid
1.0ms	14×	body	80	invalid
1.0ms	6×	body	160	invalid
1.0ms	6×	body	160	valid
1.0ms	2×	body	320	invalid
0.0ms	8×	body	80	nan

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4961	22
1	4961	22

prune9.0ms

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

Merged error: 46.8b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
0.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac_binary64_2495`
485×	`add-sqr-sqrt_binary64_2485`
366×	`*-un-lft-identity_binary64_2500`
224×	`add-cube-cbrt_binary64_2471`
174×	`associate-r_binary64_2559`
168×	`difference-of-squares_binary64_2529`
88×	`unpow-prod-down_binary64_2435`
85×	`sqr-pow_binary64_2532`
84×	`difference-of-sqr-1_binary64_2530`
29×	`div-inv_binary64_2501`
28×	`distribute-lft-out--_binary64_2545`
19×	`add-exp-log_binary64_2464`
18×	`add-cbrt-cube_binary64_2472`
13×	`associate-/l_binary64_2564` `associate-/r_binary64_2563`
7×	`pow1_binary64_2446`
6×	`div-exp_binary64_2453` `add-log-exp_binary64_2465` `cbrt-undiv_binary64_2470`
3×	`associate-l_binary64_2560` `pow-unpow_binary64_2433` `prod-exp_binary64_2451` `unswap-sqr_binary64_2528` `cbrt-unprod_binary64_2469`
2×	`associate-/l/_binary64_2566` `associate-/r/_binary64_2565` `flip--_binary64_2526` `flip3--_binary64_2499`
1×	`div-sub_binary64_2494` `diff-log_binary64_2416` `pow-exp_binary64_2424` `frac-2neg_binary64_2493` `sub-neg_binary64_2504` `pow-to-exp_binary64_2425` `pow-prod-down_binary64_2427` `pow-pow_binary64_2428` `-commutative_binary64_2568` `clear-num_binary64_2503` `distribute-lft-out_binary64_2544` `associate-r/_binary64_2561`

Counts

4 → 448

Calls

4 calls:

50.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
10.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
18.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series910.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
169.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
147.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
289.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify186.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5144	14782

prune993.0ms

Filtered

269 candidates to 460 candidates (-71.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	452	8	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	453	8	461

Merged error: 19.4b

Counts

461 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.4b	(*.f64 1/6 i)
16.8b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64_2495`
97×	`add-sqr-sqrt_binary64_2485`
85×	`add-cube-cbrt_binary64_2471` `*-un-lft-identity_binary64_2500`
50×	`associate-r_binary64_2559`
25×	`add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472`
13×	`pow1_binary64_2446` `associate-/r*_binary64_2563`
9×	`div-inv_binary64_2501`
7×	`associate-l_binary64_2560` `prod-exp_binary64_2451` `cbrt-unprod_binary64_2469`
6×	`div-exp_binary64_2453` `cbrt-undiv_binary64_2470`
5×	`pow-prod-down_binary64_2427` `unswap-sqr_binary64_2528`
4×	`add-log-exp_binary64_2465`
3×	`associate-/l_binary64_2564` `-commutative_binary64_2568` `associate-*r/_binary64_2561`
2×	`associate-/l/_binary64_2566` `flip3-+_binary64_2498` `associate-/r/_binary64_2565` `flip-+_binary64_2525`
1×	`distribute-rgt-in_binary64_2543` `frac-2neg_binary64_2493` `distribute-lft-in_binary64_2542` `clear-num_binary64_2503`

Counts

4 → 179

Calls

4 calls:

7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
19.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
3.0ms	(*.f64 1/6 i)
8.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

series146.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
46.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
10.0ms	(*.f64 1/6 i)
45.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

simplify82.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5024	5503

prune756.0ms

Filtered

151 candidates to 191 candidates (-26.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	177	14	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	178	21	199

Merged error: 9.9b

Counts

199 → 21

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 i n) 50)
0.3b	(.f64 (.f64 i i) 50/3)
2.4b	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
3.7b	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1_binary64_2446` `add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472`
11×	`add-sqr-sqrt_binary64_2485`
9×	`associate-r_binary64_2559`
8×	`add-cube-cbrt_binary64_2471` `*-un-lft-identity_binary64_2500`
7×	`pow-prod-down_binary64_2427` `prod-exp_binary64_2451` `cbrt-unprod_binary64_2469`
6×	`add-log-exp_binary64_2465`
5×	`associate-l_binary64_2560`
3×	`*-commutative_binary64_2568`
2×	`flip3-+_binary64_2498` `distribute-rgt-in_binary64_2543` `associate-+r+_binary64_2551` `distribute-lft-in_binary64_2542` `unswap-sqr_binary64_2528` `flip-+_binary64_2525` `associate-*r/_binary64_2561`
1×	`+-commutative_binary64_2567` `sum-log_binary64_2415`

Counts

4 → 72

Calls

4 calls:

5.0ms	(.f64 (.f64 i n) 50)
5.0ms	(.f64 (.f64 i i) 50/3)
5.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
6.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (.f64 i n) 50)
20.0ms	(.f64 (.f64 i i) 50/3)
49.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
30.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

simplify67.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5112	1133

prune360.0ms

Filtered

53 candidates to 84 candidates (-58.5%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	83	22	105

Merged error: 9.9b

Counts

105 → 22

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
10.5b	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))
10.5b	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))
10.5b	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-cube-cbrt_binary64_2471` `add-sqr-sqrt_binary64_2485` `*-un-lft-identity_binary64_2500`
9×	`times-frac_binary64_2495`
6×	`add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472`
4×	`pow1_binary64_2446` `add-log-exp_binary64_2465`
3×	`pow1/3_binary64_2438` `cbrt-prod_binary64_2467` `associate-/l_binary64_2564` `associate-/r_binary64_2563` `cbrt-div_binary64_2468` `associate-*r/_binary64_2561`
2×	`associate-/l/_binary64_2566`
1×	`flip3-+_binary64_2498` `div-exp_binary64_2453` `frac-2neg_binary64_2493` `div-inv_binary64_2501` `cbrt-undiv_binary64_2470` `clear-num_binary64_2503` `flip-+_binary64_2525`

Counts

4 → 59

Calls

4 calls:

6.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
5.0ms	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))
5.0ms	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))
5.0ms	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
155.0ms	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))
153.0ms	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))
160.0ms	(cbrt.f64 (.f64 n (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i)))

simplify92.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5131	2203

prune337.0ms

Filtered

61 candidates to 71 candidates (-16.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	2	18	20
Picked	1	0	1
Done	0	1	1
Total	70	23	93

Merged error: 9.9b

Counts

93 → 23

regimes653.0ms

Accuracy

65.6% (6.2b remaining)

Error of 16.8b against oracle of 10.7b and baseline of 28.6b

bsearch351.0ms

Steps

Iters	Range	Point
10	8724534181933599/4398046511104	4980367391359067/4	2003.3137174584608
9	-8879371147982719/22835963083295358096932575511191922182123945984	-772589255412701/6129982163463555433433388108601236734474956488734408704	-3.827469972222611e-31

Iters

Range

Point

8724534181933599/4398046511104

4980367391359067/4

2003.3137174584608

-8879371147982719/22835963083295358096932575511191922182123945984

-772589255412701/6129982163463555433433388108601236734474956488734408704

-3.827469972222611e-31

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	75
1	45	75

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	2856×	body	1280	valid
2.0s	954×	body	2560	valid
601.0ms	1530×	body	640	valid
174.0ms	700×	body	320	valid
119.0ms	244×	body	640	invalid
108.0ms	1621×	body	80	valid
94.0ms	118×	body	1280	invalid
58.0ms	184×	body	320	invalid
49.0ms	329×	body	160	valid
39.0ms	426×	body	80	invalid
38.0ms	10×	body	5120	valid
34.0ms	18×	body	2560	invalid
19.0ms	103×	body	160	invalid
13.0ms	303×	body	80	nan

Details

analyze811.0ms

sample198.0ms

simplify57.0ms

prune9.0ms

localize15.0ms

rewrite115.0ms

series910.0ms

simplify186.0ms

prune993.0ms

localize17.0ms

rewrite46.0ms

series146.0ms

simplify82.0ms

prune756.0ms

localize16.0ms

rewrite23.0ms

series114.0ms

simplify67.0ms

prune360.0ms

localize25.0ms

rewrite23.0ms

series491.0ms

simplify92.0ms

prune337.0ms

regimes653.0ms

bsearch351.0ms

simplify3.0ms

end0.0ms

sample6.1s

Profiling