Details

analyze443.0ms

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	34×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

prune4.0ms

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: 33.4b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`pow1_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`times-frac_binary64`
8×	`associate-r_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 110

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
11.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
30.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
14.0ms	(*.f64 (log.f64 base) (log.f64 base))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4986	2010
1	4986	2010

prune205.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 7.9b

Counts

123 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.4b	(.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (/.f64 1 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0))))
0.5b	(pow.f64 (log.f64 base) 2)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
19×	`associate-r_binary64` `add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
14×	`pow1_binary64`
11×	`add-cbrt-cube_binary64` `times-frac_binary64`
9×	`associate-l_binary64`
6×	`log-prod_binary64`
5×	`log-pow_binary64` `prod-exp_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 104

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
16.0ms	(.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (/.f64 1 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0))))
3.0ms	(pow.f64 (log.f64 base) 2)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
33.0ms	(.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (/.f64 1 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0))))
14.0ms	(pow.f64 (log.f64 base) 2)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4937	2093
1	4937	2093

prune168.0ms

Filtered

78 candidates to 116 candidates (-48.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	115	16	131

Merged error: 7.8b

Counts

131 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (-.f64 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4))) (-.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))
0.5b	(pow.f64 (log.f64 base) 2)
0.9b	(pow.f64 (log.f64 base) 4)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
51×	`associate-l_binary64`
46×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
39×	`unpow-prod-down_binary64`
31×	`difference-of-squares_binary64`
29×	`add-cube-cbrt_binary64`
21×	`sqr-pow_binary64`
14×	`pow1_binary64`
11×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64`
6×	`pow-unpow_binary64`
5×	`log-pow_binary64`
4×	`add-log-exp_binary64`
3×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `associate-*r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-times_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 132

Calls

4 calls:

31.0ms	(.f64 (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (-.f64 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4))) (-.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))
3.0ms	(pow.f64 (log.f64 base) 2)
3.0ms	(pow.f64 (log.f64 base) 4)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (-.f64 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4))) (-.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))
14.0ms	(pow.f64 (log.f64 base) 2)
18.0ms	(pow.f64 (log.f64 base) 4)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4993	3055
1	4993	3055

prune258.0ms

Filtered

109 candidates to 144 candidates (-32.1%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	2	12	14
Picked	0	1	1
Done	0	1	1
Total	142	18	160

Merged error: 7.8b

Counts

160 → 18

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (cbrt.f64 (pow.f64 (log.f64 base) 6)) (*.f64 0.0 0.0)))
0.5b	(cbrt.f64 (pow.f64 (log.f64 base) 6))
1.2b	(pow.f64 (log.f64 base) 6)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64` `unpow-prod-down_binary64` `cbrt-prod_binary64`
7×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-/r_binary64` `associate-/l_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `log-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`

Counts

4 → 80

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (cbrt.f64 (pow.f64 (log.f64 base) 6)) (*.f64 0.0 0.0)))
2.0ms	(cbrt.f64 (pow.f64 (log.f64 base) 6))
3.0ms	(pow.f64 (log.f64 base) 6)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (cbrt.f64 (pow.f64 (log.f64 base) 6)) (*.f64 0.0 0.0)))
14.0ms	(cbrt.f64 (pow.f64 (log.f64 base) 6))
23.0ms	(pow.f64 (log.f64 base) 6)
10.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4999	1648
1	4999	1648

prune103.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	15	15
Picked	1	0	1
Done	0	2	2
Total	91	19	110

Merged error: 7.8b

Counts

110 → 19

regimes584.0ms

Accuracy

54.1% (11.2b remaining)

Error of 18.5b against oracle of 7.3b and baseline of 31.7b

bsearch180.0ms

Steps

Iters	Range		Point
10	1.7732951930628207e+43	3.2619386735714566e+53	1.702622659109618e+52
8	-1.2917131679977722e-74	-8.286737828436817e-79	-1.267660774867362e-74
9	-3.0820256303824825e-44	-6.169081402694406e-50	-6.248145331558188e-50
9	-2.16952560437672e+123	-4.0088116396452295e+117	-1.506084148724459e+120

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	106
1	87	106

end0.0ms

sample1.1s

Algorithm

intervals

Results

787.0ms	8000×	body	80	valid
96.0ms	1068×	body	80	nan

Details

analyze443.0ms

sample40.0ms

simplify5.0ms

prune4.0ms

localize20.0ms

rewrite34.0ms

series77.0ms

simplify76.0ms

prune205.0ms

localize25.0ms

rewrite33.0ms

series79.0ms

simplify47.0ms

prune168.0ms

localize27.0ms

rewrite47.0ms

series71.0ms

simplify72.0ms

prune258.0ms

localize22.0ms

rewrite24.0ms

series77.0ms

simplify52.0ms

prune103.0ms

regimes584.0ms

bsearch180.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling