Details

analyze229.0ms

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
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample73.0ms

Algorithm

intervals

Results

30.0ms	56×	body	1280	valid
15.0ms	45×	body	640	valid
9.0ms	119×	body	80	valid
7.0ms	23×	body	320	valid
2.0ms	13×	body	160	valid
0.0ms	6×	body	80	invalid
0.0ms	1×	body	640	invalid
0.0ms	5×	body	80	overflowed

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5391	41

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.6b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(*.f64 (-.f64 1 eps) x)
0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
3.7b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64` `frac-times_binary64`
60×	`neg-sub0_binary64` `exp-diff_binary64`
42×	`associate-*l/_binary64`
40×	`associate-*r/_binary64`
34×	`add-sqr-sqrt_binary64`
32×	`flip3--_binary64` `flip--_binary64`
30×	`flip3-+_binary64` `flip-+_binary64`
25×	`-un-lft-identity_binary64` `associate-l*_binary64`
20×	`un-div-inv_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`add-exp-log_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64` `times-frac_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
2×	`distribute-lft-out_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `diff-log_binary64`

Counts

4 → 182

Calls

4 calls:

13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
7.0ms	(*.f64 (-.f64 1 eps) x)
15.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
20.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
17.0ms	(*.f64 (-.f64 1 eps) x)
34.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
132.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5005	9341

prune309.0ms

Filtered

104 candidates to 194 candidates (-86.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	3	195

Merged error: 0.3b

Counts

195 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
5.2b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 x 3) 2/3)
8.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

series45.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(*.f64 (pow.f64 x 3) 2/3)
21.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify69.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4859	681
1	4859	681

prune46.0ms

Filtered

32 candidates to 51 candidates (-59.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	49	5	54

Merged error: 0.3b

Counts

54 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

5.2b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
46.4b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
46.4b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
46.4b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 41

Calls

4 calls:

13.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

series103.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
25.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
22.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
25.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

simplify80.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4811	701
1	4811	701

prune66.0ms

Filtered

39 candidates to 53 candidates (-35.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Merged error: 0.3b

Counts

58 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (*.f64 (pow.f64 x 3) 2/3))
0.1b	(*.f64 (pow.f64 x 3) 2/3)
1.1b	(log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 2/3)))
5.2b	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
11×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `log-prod_binary64` `log-pow_binary64` `prod-exp_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `exp-to-pow_binary64` `exp-prod_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 69

Calls

4 calls:

2.0ms	(exp.f64 (*.f64 (pow.f64 x 3) 2/3))
6.0ms	(*.f64 (pow.f64 x 3) 2/3)
2.0ms	(log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 2/3)))
8.0ms	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))

series80.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(exp.f64 (*.f64 (pow.f64 x 3) 2/3))
24.0ms	(*.f64 (pow.f64 x 3) 2/3)
24.0ms	(log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 2/3)))
19.0ms	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))

simplify77.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4985	980
1	4985	980

prune55.0ms

Filtered

50 candidates to 81 candidates (-62.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	81	5	86

Merged error: 0.3b

Counts

86 → 5

regimes38.0ms

Accuracy

97.2% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 16.2b

bsearch84.0ms

Steps

Iters	Range		Point
9	6.812020401843318	3131560.010487294	10.174801829828485

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	74
1	70	74

end0.0ms

sample2.1s

Algorithm

intervals

Results

937.0ms	1734×	body	1280	valid
426.0ms	1255×	body	640	valid
315.0ms	4056×	body	80	valid
150.0ms	664×	body	320	valid
43.0ms	291×	body	160	valid
19.0ms	237×	body	80	invalid
13.0ms	177×	body	80	overflowed
10.0ms	18×	body	1280	invalid
4.0ms	11×	body	640	invalid
1.0ms	2×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze229.0ms

sample73.0ms

simplify81.0ms

prune4.0ms

localize18.0ms

rewrite68.0ms

series209.0ms

simplify143.0ms

prune309.0ms

localize8.0ms

rewrite16.0ms

series45.0ms

simplify69.0ms

prune46.0ms

localize12.0ms

rewrite24.0ms

series103.0ms

simplify80.0ms

prune66.0ms

localize10.0ms

rewrite19.0ms

series80.0ms

simplify77.0ms

prune55.0ms

regimes38.0ms

bsearch84.0ms

simplify4.0ms

end0.0ms

sample2.1s

Profiling