Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

sample94.0ms

Algorithm

intervals

Results

34.0ms	57×	body	1280	valid
18.0ms	55×	body	640	valid
7.0ms	105×	body	80	valid
7.0ms	4×	body	2560	valid
5.0ms	24×	body	320	valid
2.0ms	11×	body	640	nan
2.0ms	6×	body	1280	nan
2.0ms	42×	body	80	nan
1.0ms	28×	body	80	overflowed
1.0ms	11×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan
0.0ms	3×	body	80	invalid

simplify340.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (327.0ms)

Iter	Nodes	Cost
0	5255	20

prune1.0ms

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: 23.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
2.0b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
2.3b	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
6×	`add-exp-log_binary64`
5×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `associate-/r*_binary64` `log-prod_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

3 → 61

Calls

3 calls:

9.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
7.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
7.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))

series281.0ms

Counts

3 → 9

Calls

3 calls:

187.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
27.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
67.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))

simplify91.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4981	1791
1	4981	1791

prune77.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Merged error: 5.8b

Counts

71 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z))))) t)
1.6b	(-.f64 y (*.f64 y (exp.f64 z)))
2.1b	(log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

7.0ms	(/.f64 (log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z))))) t)
3.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
5.0ms	(log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))

series279.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(/.f64 (log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z))))) t)
27.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
64.0ms	(log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4989	1766
1	4989	1766

prune61.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Merged error: 5.8b

Counts

76 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 y (*.f64 y (exp.f64 z)))
1.6b	(-.f64 y (*.f64 y (exp.f64 z)))
3.9b	(log.f64 (-.f64 1 (pow.f64 (-.f64 y (*.f64 y (exp.f64 z))) 3)))
5.0b	(log.f64 (+.f64 1 (.f64 (-.f64 y (.f64 y (exp.f64 z))) (+.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`log-prod_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `difference-of-squares_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `log-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
1×	`flip3-+_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`

Counts

4 → 59

Calls

4 calls:

3.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
3.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
8.0ms	(log.f64 (-.f64 1 (pow.f64 (-.f64 y (*.f64 y (exp.f64 z))) 3)))
3.0ms	(log.f64 (+.f64 1 (.f64 (-.f64 y (.f64 y (exp.f64 z))) (+.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
29.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
322.0ms	(log.f64 (-.f64 1 (pow.f64 (-.f64 y (*.f64 y (exp.f64 z))) 3)))
320.0ms	(log.f64 (+.f64 1 (.f64 (-.f64 y (.f64 y (exp.f64 z))) (+.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5009	2228

prune99.0ms

Filtered

53 candidates to 71 candidates (-34.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Merged error: 5.8b

Counts

76 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/6 (pow.f64 z 3))
3.6b	(.f64 y (+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (.f64 1/6 (pow.f64 z 3)))))
7.5b	(log.f64 (-.f64 1 (neg.f64 (.f64 y (+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (.f64 1/6 (pow.f64 z 3))))))))
8.5b	(+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (*.f64 1/6 (pow.f64 z 3))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-exp-log_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`log-prod_binary64` `associate-l_binary64`
5×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64`
3×	`sum-log_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `log-div_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `associate-+r+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 83

Calls

4 calls:

7.0ms	(*.f64 1/6 (pow.f64 z 3))
11.0ms	(.f64 y (+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (.f64 1/6 (pow.f64 z 3)))))
4.0ms	(log.f64 (-.f64 1 (neg.f64 (.f64 y (+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (.f64 1/6 (pow.f64 z 3))))))))
10.0ms	(+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (*.f64 1/6 (pow.f64 z 3))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(*.f64 1/6 (pow.f64 z 3))
61.0ms	(.f64 y (+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (.f64 1/6 (pow.f64 z 3)))))
106.0ms	(log.f64 (-.f64 1 (neg.f64 (.f64 y (+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (.f64 1/6 (pow.f64 z 3))))))))
16.0ms	(+.f64 (.f64 1/2 (.f64 z z)) (+.f64 z (*.f64 1/6 (pow.f64 z 3))))

simplify56.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5076	1959

prune101.0ms

Filtered

68 candidates to 95 candidates (-39.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	88	7	95
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	89	13	102

Merged error: 5.7b

Counts

102 → 13

regimes264.0ms

Accuracy

27.2% (6.9b remaining)

Error of 12.3b against oracle of 5.4b and baseline of 14.8b

bsearch246.0ms

Steps

Iters	Range		Point
9	1.682766884961365e+113	1.452050925131856e+118	1.3278686628389493e+114
10	6.028638700029601e-24	2.520417719987038e-13	6.199663690275312e-24
7	-5.289929946142908e-130	-4.183883088826554e-132	-2.093658234288246e-131
8	-6.137718933286439e-34	-1.9252326498444865e-36	-2.5849067727820856e-36

simplify28.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	719	193
1	719	193

end0.0ms

sample2.6s

Algorithm

intervals

Results

847.0ms	1454×	body	1280	valid
523.0ms	1581×	body	640	valid
242.0ms	3471×	body	80	valid
191.0ms	907×	body	320	valid
109.0ms	83×	body	2560	valid
71.0ms	1474×	body	80	nan
67.0ms	504×	body	160	valid
63.0ms	263×	body	640	nan
49.0ms	864×	body	80	overflowed
40.0ms	119×	body	1280	nan
35.0ms	206×	body	320	nan
11.0ms	104×	body	160	nan
1.0ms	21×	body	80	invalid
1.0ms	2×	body	1280	invalid
0.0ms	1×	body	320	invalid

Details

analyze1.1s

sample94.0ms

simplify340.0ms

prune1.0ms

localize10.0ms

rewrite25.0ms

series281.0ms

simplify91.0ms

prune77.0ms

localize10.0ms

rewrite19.0ms

series279.0ms

simplify73.0ms

prune61.0ms

localize19.0ms

rewrite19.0ms

series702.0ms

simplify52.0ms

prune99.0ms

localize16.0ms

rewrite34.0ms

series206.0ms

simplify56.0ms

prune101.0ms

regimes264.0ms

bsearch246.0ms

simplify28.0ms

end0.0ms

sample2.6s

Profiling