Details

analyze426.0ms

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

sample39.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
3.0ms	34×	body	80	nan

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5536	12

prune8.0ms

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: 33.7b

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))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite15.0ms

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)))

series32.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5798	1032

prune73.0ms

Filtered

45 candidates to 69 candidates (-53.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	58	11	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	12	71

Merged error: 7.3b

Counts

71 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
40×	`cbrt-prod_binary64`
29×	`sqrt-prod_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`sqrt-div_binary64`
14×	`pow1_binary64`
12×	`cbrt-div_binary64`
11×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`pow1/3_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

15.0ms	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
4.0ms	(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)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4986	1753
1	4986	1753

prune79.0ms

Filtered

81 candidates to 121 candidates (-49.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	122	11	133

Merged error: 7.3b

Counts

133 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (log.f64 (.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) (log.f64 base))
0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
34.4b	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
17×	`pow1_binary64`
16×	`log-pow_binary64`
7×	`add-exp-log_binary64`
6×	`pow1/3_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64` `sqrt-div_binary64`
5×	`pow-prod-down_binary64` `associate-/l*_binary64`
4×	`cbrt-div_binary64` `associate-/r*_binary64` `add-log-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
2×	`associate-*r/_binary64` `div-sub_binary64` `log-div_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow1/3_binary64`

Counts

4 → 92

Calls

4 calls:

14.0ms	(/.f64 (log.f64 (.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) (log.f64 base))
5.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)

series73.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (log.f64 (.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) (log.f64 base))
18.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)

simplify53.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4998	1431
1	4998	1431

prune71.0ms

Filtered

74 candidates to 104 candidates (-40.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 7.3b

Counts

115 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1 (log.f64 base))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
16×	`pow1_binary64` `associate-r_binary64` `add-exp-log_binary64`
10×	`log-pow_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64`
4×	`associate-/r*_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

3 → 92

Calls

3 calls:

4.0ms	(/.f64 1 (log.f64 base))
10.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series46.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.f64 1 (log.f64 base))
26.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5573	1000

prune34.0ms

Filtered

58 candidates to 101 candidates (-74.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	99	13	112

Merged error: 7.2b

Counts

112 → 13

regimes479.0ms

Accuracy

56.6% (10.7b remaining)

Error of 17.9b against oracle of 7.2b and baseline of 31.9b

bsearch218.0ms

Steps

Iters	Range		Point
10	7.694466699650491e+145	1.0223007436382462e+156	7.776536635168688e+145
9	8.848477728819113e-166	4.402127163387715e-158	3.9152423703811223e-165
4	1.8840521537471827e-270	3.4226481879566407e-270	3.3742910823838554e-270
7	-1.0880160709422895e-304	-8.877316170807312e-307	-3.2580037546917335e-305
5	-1.1530211998001502e-184	-3.337019404838314e-185	-8.006226079427904e-185
11	-2.0226477789440453e+140	-2.458998588545436e+119	-1.0190895301535234e+121

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	118
1	53	118

end0.0ms

sample1.1s

Algorithm

intervals

Results

769.0ms	8000×	body	80	valid
93.0ms	1056×	body	80	nan

Details

analyze426.0ms

sample39.0ms

simplify93.0ms

prune8.0ms

localize10.0ms

rewrite15.0ms

series32.0ms

simplify54.0ms

prune73.0ms

localize14.0ms

rewrite33.0ms

series45.0ms

simplify57.0ms

prune79.0ms

localize22.0ms

rewrite31.0ms

series73.0ms

simplify53.0ms

prune71.0ms

localize11.0ms

rewrite21.0ms

series46.0ms

simplify59.0ms

prune34.0ms

regimes479.0ms

bsearch218.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling