Details

analyze357.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample37.0ms

Algorithm

intervals

Results

12.0ms	194×	body	80	valid
7.0ms	24×	body	2560	valid
5.0ms	20×	body	1280	valid
4.0ms	10×	body	5120	valid
1.0ms	5×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune5.0ms

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: 36.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`pow1_binary64` `add-cube-cbrt_binary64`
3×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

3 → 38

Calls

3 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5042	458

prune74.0ms

Filtered

38 candidates to 47 candidates (-23.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	41	6	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	6	48

Merged error: 19.3b

Counts

48 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
8.1b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
17.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
8.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune95.0ms

Filtered

71 candidates to 136 candidates (-91.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Merged error: 19.3b

Counts

142 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

6.0b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
15.2b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))) re)
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `exp-sum_binary64` `sqrt-div_binary64` `exp-prod_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `log-pow_binary64` `sqrt-pow1_binary64`
2×	`exp-diff_binary64` `rem-sqrt-square_binary64` `log-div_binary64`
1×	`rem-exp-log_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 63

Calls

4 calls:

7.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
19.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
8.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4887	706
1	4887	706

prune79.0ms

Filtered

57 candidates to 75 candidates (-31.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	75	6	81

Merged error: 19.3b

Counts

81 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

14.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

33.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4879	612
1	4879	612

prune74.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	68	6	74

Merged error: 19.3b

Counts

74 → 6

regimes219.0ms

Accuracy

58.8% (8.9b remaining)

Error of 26.7b against oracle of 17.8b and baseline of 39.4b

bsearch36.0ms

Steps

Iters	Range		Point
9	1.750560446780778e+125	1.3619909583452352e+130	5.0878830972405194e+128
10	-6.1389577482358635e-286	-1.299719363882134e-301	-1.3234464689827902e-301

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	61
1	47	61

end0.0ms

sample972.0ms

Algorithm

intervals

Results

313.0ms	6073×	body	80	valid
207.0ms	689×	body	2560	valid
119.0ms	488×	body	1280	valid
98.0ms	271×	body	5120	valid
56.0ms	270×	body	640	valid
20.0ms	140×	body	320	valid
7.0ms	69×	body	160	valid

Details

analyze357.0ms

sample37.0ms

simplify6.0ms

prune5.0ms

localize10.0ms

rewrite18.0ms

series21.0ms

simplify41.0ms

prune74.0ms

localize12.0ms

rewrite49.0ms

series30.0ms

simplify68.0ms

prune95.0ms

localize17.0ms

rewrite37.0ms

series27.0ms

simplify71.0ms

prune79.0ms

localize22.0ms

rewrite49.0ms

series28.0ms

simplify40.0ms

prune74.0ms

regimes219.0ms

bsearch36.0ms

simplify2.0ms

end0.0ms

sample972.0ms

Profiling