Details

analyze563.0ms

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
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample46.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
8.0ms	21×	body	1280	valid
5.0ms	27×	body	640	valid
4.0ms	24×	body	1280	nan
4.0ms	29×	body	640	nan
2.0ms	14×	body	320	nan
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	6×	body	160	nan
0.0ms	9×	body	80	nan

simplify216.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (212.0ms)

Iter	Nodes	Cost
0	4867	12
1	4867	12

prune3.0ms

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: 16.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
3.0b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
4.4b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
67×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
33×	`difference-of-squares_binary64`
19×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
16×	`log-prod_binary64`
8×	`associate--r+_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
5×	`associate-/l*_binary64`
4×	`log-div_binary64`
3×	`associate--r-_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `associate-/r/_binary64` `div-sub_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 119

Calls

4 calls:

23.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
9.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))
17.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
17.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
7.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))
10.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
14.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify71.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5453	1839

prune193.0ms

Filtered

93 candidates to 131 candidates (-40.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	7	132

Merged error: 0.1b

Counts

132 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (-.f64 1 y))
0.2b	(cbrt.f64 (-.f64 1 y))
4.4b	(log.f64 (-.f64 1 (/.f64 (/.f64 (-.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))))
11.3b	(-.f64 1 (/.f64 (/.f64 (-.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`difference-of-squares_binary64` `times-frac_binary64`
20×	`cbrt-prod_binary64`
14×	`log-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`pow1/3_binary64` `div-sub_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `log-pow_binary64`

Counts

4 → 80

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 1 y))
4.0ms	(cbrt.f64 (-.f64 1 y))
53.0ms	(log.f64 (-.f64 1 (/.f64 (/.f64 (-.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))))
52.0ms	(-.f64 1 (/.f64 (/.f64 (-.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cbrt.f64 (-.f64 1 y))
5.0ms	(cbrt.f64 (-.f64 1 y))
14.0ms	(log.f64 (-.f64 1 (/.f64 (/.f64 (-.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))))
10.0ms	(-.f64 1 (/.f64 (/.f64 (-.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y))))

simplify69.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4916	1527
1	4916	1527

prune127.0ms

Filtered

70 candidates to 92 candidates (-31.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Merged error: 0.1b

Counts

99 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (pow.f64 (-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))) 3))
0.3b	(pow.f64 (-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))) 3)
3.0b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
4.4b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
20×	`cbrt-prod_binary64`
16×	`difference-of-squares_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `distribute-lft-out--_binary64`
8×	`log-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
5×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`flip3--_binary64` `cube-div_binary64` `times-frac_binary64` `flip--_binary64`
3×	`pow-unpow_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `log-div_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 100

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))) 3))
6.0ms	(pow.f64 (-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))) 3)
17.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
17.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))) 3))
74.0ms	(pow.f64 (-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))) 3)
10.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
14.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify66.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5021	2291

prune125.0ms

Filtered

65 candidates to 112 candidates (-72.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	112	7	119

Merged error: 0.1b

Counts

119 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
4.4b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
4.4b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
4.4b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
24×	`log-prod_binary64`
23×	`*-un-lft-identity_binary64`
16×	`difference-of-squares_binary64`
8×	`times-frac_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `log-div_binary64`
4×	`flip3--_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
3×	`rem-log-exp_binary64` `log-pow_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate--r-_binary64` `div-sub_binary64`

Counts

4 → 74

Calls

4 calls:

17.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
17.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
18.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
20.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
13.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
17.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
14.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify69.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4919	1363
1	4919	1363

prune139.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	86	7	93

Merged error: 0.1b

Counts

93 → 7

regimes337.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 17.3b

bsearch122.0ms

Steps

Iters	Range		Point
10	0.17897871674741597	25296299292772.46	36548376.49439328
7	-2166294307462215.8	-122752156327699.7	-123901047790978.4

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	161	48
1	161	48

end0.0ms

sample1.3s

Algorithm

intervals

Results

282.0ms	5643×	body	80	valid
215.0ms	861×	body	1280	valid
145.0ms	816×	body	640	valid
124.0ms	655×	body	1280	nan
107.0ms	727×	body	640	nan
62.0ms	438×	body	320	valid
56.0ms	473×	body	320	nan
21.0ms	242×	body	160	valid
16.0ms	217×	body	160	nan
12.0ms	324×	body	80	nan

Details

analyze563.0ms

sample46.0ms

simplify216.0ms

prune3.0ms

localize10.0ms

rewrite71.0ms

series44.0ms

simplify71.0ms

prune193.0ms

localize14.0ms

rewrite116.0ms

series35.0ms

simplify69.0ms

prune127.0ms

localize12.0ms

rewrite52.0ms

series113.0ms

simplify66.0ms

prune125.0ms

localize14.0ms

rewrite74.0ms

series55.0ms

simplify69.0ms

prune139.0ms

regimes337.0ms

bsearch122.0ms

simplify5.0ms

end0.0ms

sample1.3s

Profiling