Details

analyze1.1s

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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample231.0ms

Algorithm

intervals

Results

59.0ms	108×	body	1280	valid
48.0ms	44×	body	1280	nan
30.0ms	60×	body	640	valid
22.0ms	33×	body	640	nan
19.0ms	113×	body	80	overflowed
9.0ms	28×	body	320	valid
7.0ms	17×	body	320	nan
6.0ms	9×	body	640	invalid
4.0ms	50×	body	80	valid
4.0ms	3×	body	1280	invalid
2.0ms	5×	body	320	invalid
2.0ms	10×	body	160	valid
2.0ms	8×	body	160	nan
1.0ms	18×	body	80	nan
1.0ms	3×	body	160	invalid
1.0ms	5×	body	80	invalid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

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: 32.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
2.5b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`pow-unpow_binary64` `unpow-prod-down_binary64`
10×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64` `times-frac_binary64`
7×	`sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(pow.f64 x (/.f64 1 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(pow.f64 x (/.f64 1 n))
37.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4913	797
1	4913	797

prune73.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Merged error: 24.0b

Counts

57 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
0.1b	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
2.5b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
33×	`unpow-prod-down_binary64`
30×	`log-prod_binary64`
27×	`difference-of-squares_binary64`
19×	`sqr-pow_binary64`
15×	`add-cube-cbrt_binary64` `exp-sum_binary64`
13×	`pow-unpow_binary64`
9×	`distribute-lft-out--_binary64` `times-frac_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `log-div_binary64` `exp-prod_binary64`
3×	`flip3--_binary64` `distribute-lft-out_binary64` `flip--_binary64`
2×	`log-pow_binary64` `exp-diff_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `rem-exp-log_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 105

Calls

4 calls:

4.0ms	(pow.f64 x (/.f64 1 n))
12.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
11.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
13.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow.f64 x (/.f64 1 n))
30.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
52.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
31.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify62.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4969	2107
1	4969	2107

prune145.0ms

Filtered

89 candidates to 117 candidates (-31.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	115	6	121

Merged error: 23.9b

Counts

121 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))) 3)))
0.1b	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
2.5b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`unpow-prod-down_binary64`
18×	`difference-of-squares_binary64`
17×	`add-cube-cbrt_binary64` `exp-prod_binary64`
15×	`log-prod_binary64`
14×	`sqr-pow_binary64` `cbrt-prod_binary64`
13×	`pow-unpow_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64`
7×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`add-cbrt-cube_binary64` `cube-prod_binary64`
3×	`log-pow_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `log-div_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `rem-exp-log_binary64` `div-inv_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 101

Calls

4 calls:

4.0ms	(pow.f64 x (/.f64 1 n))
5.0ms	(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))) 3)))
13.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow.f64 x (/.f64 1 n))
33.0ms	(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))) 3)))
48.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
31.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5072	1840

prune154.0ms

Filtered

86 candidates to 113 candidates (-31.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	113	6	119

Merged error: 23.9b

Counts

119 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 E.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))) 3)))
0.1b	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
2.5b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
30×	`pow-unpow_binary64` `unpow-prod-down_binary64`
18×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
15×	`log-prod_binary64` `sqr-pow_binary64`
14×	`cbrt-prod_binary64`
9×	`pow1_binary64` `times-frac_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
4×	`add-cbrt-cube_binary64` `cube-prod_binary64`
3×	`log-pow_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `log-div_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `e-exp-1_binary64` `div-inv_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 108

Calls

4 calls:

4.0ms	(pow.f64 x (/.f64 1 n))
7.0ms	(pow.f64 E.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))) 3)))
11.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow.f64 x (/.f64 1 n))
54.0ms	(pow.f64 E.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))) 3)))
49.0ms	(log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))
30.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify51.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5016	2039

prune149.0ms

Filtered

91 candidates to 120 candidates (-31.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Merged error: 23.9b

Counts

126 → 6

regimes254.0ms

Accuracy

81.3% (1.9b remaining)

Error of 24.3b against oracle of 22.4b and baseline of 32.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	66
1	62	66

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.0s	3735×	body	1280	valid
1.3s	1140×	body	1280	nan
704.0ms	1579×	body	640	valid
650.0ms	925×	body	640	nan
487.0ms	2788×	body	80	overflowed
215.0ms	701×	body	320	valid
187.0ms	269×	body	640	invalid
185.0ms	432×	body	320	nan
144.0ms	1614×	body	80	valid
121.0ms	100×	body	1280	invalid
71.0ms	371×	body	160	valid
67.0ms	168×	body	320	invalid
49.0ms	220×	body	160	nan
34.0ms	549×	body	80	nan
28.0ms	230×	body	80	invalid
24.0ms	98×	body	160	invalid

Details

analyze1.1s

sample231.0ms

simplify58.0ms

prune3.0ms

localize8.0ms

rewrite16.0ms

series47.0ms

simplify66.0ms

prune73.0ms

localize10.0ms

rewrite44.0ms

series124.0ms

simplify62.0ms

prune145.0ms

localize13.0ms

rewrite37.0ms

series122.0ms

simplify46.0ms

prune154.0ms

localize13.0ms

rewrite37.0ms

series143.0ms

simplify51.0ms

prune149.0ms

regimes254.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.6s

Profiling