Details

analyze463.0ms

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%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample40.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
3.0ms	35×	body	80	nan

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5536	12

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.1b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
29.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`log-pow_binary64`
20×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64`
4×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `div-sub_binary64` `log-div_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series31.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5798	1032

prune108.0ms

Filtered

45 candidates to 69 candidates (-53.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	58	13	71

Merged error: 7.2b

Counts

71 → 13

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.3b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
30.9b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac_binary64`
71×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
46×	`pow1_binary64`
43×	`log-pow_binary64`
24×	`associate-/r*_binary64`
11×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
7×	`associate-/l*_binary64`
6×	`div-inv_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `log-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `rem-log-exp_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

3 → 148

Calls

3 calls:

8.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series73.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
35.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
9.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5409	2944

prune151.0ms

Filtered

99 candidates to 157 candidates (-58.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	148	9	157
Fresh	6	5	11
Picked	1	0	1
Done	0	1	1
Total	155	15	170

Merged error: 7.2b

Counts

170 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
0.3b	(/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
30.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac_binary64`
66×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`associate-/r*_binary64`
20×	`pow1_binary64`
16×	`log-pow_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
6×	`div-inv_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`pow1/3_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 149

Calls

4 calls:

11.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
7.0ms	(/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
58.0ms	(/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
22.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5236	3614

prune200.0ms

Filtered

127 candidates to 161 candidates (-26.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	11	13
Picked	1	0	1
Done	1	0	1
Total	162	14	176

Merged error: 7.2b

Counts

176 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.2b	(.f64 3/2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
0.3b	(/.f64 (.f64 3/2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
30.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`add-exp-log_binary64` `cbrt-prod_binary64`
11×	`add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`associate-r_binary64`
4×	`cbrt-div_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
3×	`pow1/3_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `log-div_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

5.0ms	(log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
8.0ms	(.f64 3/2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.0ms	(/.f64 (.f64 3/2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
24.0ms	(.f64 3/2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
36.0ms	(/.f64 (.f64 3/2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
20.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5222	1319

prune84.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	97	15	112

Merged error: 7.2b

Counts

112 → 15

regimes413.0ms

Accuracy

57.3% (10.5b remaining)

Error of 17.9b against oracle of 7.3b and baseline of 32.0b

bsearch152.0ms

Steps

Iters	Range		Point
9	3.110799702491798e+52	8.227313667400087e+57	8.116903149692801e+57
9	2.2933253215131948e-278	1.4554737512185619e-270	2.4998168956729745e-273
5	-4.2637357093888454e-274	-1.3614568465908693e-274	-1.9933387775564622e-274
8	-8.793087884432578e+128	-1.9370459786577098e+126	-2.1045401481442277e+128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	64
1	49	64

end0.0ms

sample1.1s

Algorithm

intervals

Results

805.0ms	8000×	body	80	valid
89.0ms	956×	body	80	nan

Details

analyze463.0ms

sample40.0ms

simplify91.0ms

prune11.0ms

localize10.0ms

rewrite18.0ms

series31.0ms

simplify50.0ms

prune108.0ms

localize11.0ms

rewrite23.0ms

series73.0ms

simplify59.0ms

prune151.0ms

localize15.0ms

rewrite33.0ms

series149.0ms

simplify78.0ms

prune200.0ms

localize16.0ms

rewrite30.0ms

series100.0ms

simplify47.0ms

prune84.0ms

regimes413.0ms

bsearch152.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling