Details

analyze418.0ms

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

sample37.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	35×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.4b

Counts

2 → 1

localize18.0ms

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 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms

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:

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)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series73.0ms

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 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
23.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
13.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4986	2010
1	4986	2010

prune203.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	17	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	17	123

Merged error: 7.3b

Counts

123 → 17

localize24.0ms

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))
0.5b	(pow.f64 (log.f64 base) 2)
0.5b	(*.f64 (log.f64 base) (log.f64 base))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1_binary64`
22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
11×	`log-pow_binary64`
10×	`associate-l_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64` `add-cbrt-cube_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-prod-up_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow-exp_binary64` `pow2_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
3.0ms	(pow.f64 (log.f64 base) 2)
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
12.0ms	(pow.f64 (log.f64 base) 2)
14.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4819	923
1	4819	923

prune148.0ms

Filtered

65 candidates to 110 candidates (-69.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	110	17	127

Merged error: 7.3b

Counts

127 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))) (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (*.f64 0.0 0.0)))))
0.5b	(pow.f64 (log.f64 base) 2)
0.5b	(pow.f64 (log.f64 base) 2)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
32×	`sqrt-prod_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
16×	`add-cbrt-cube_binary64`
15×	`unswap-sqr_binary64`
11×	`pow1_binary64`
8×	`unpow-prod-down_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`pow-unpow_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 140

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))) (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (sqrt.f64 (+.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) 2)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))) (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (*.f64 0.0 0.0)))))
12.0ms	(pow.f64 (log.f64 base) 2)
12.0ms	(pow.f64 (log.f64 base) 2)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4957	4112
1	4957	4112

prune229.0ms

Filtered

92 candidates to 152 candidates (-65.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	150	19	169

Merged error: 7.2b

Counts

169 → 19

localize24.0ms

Local error

Found 4 expressions with local error:

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 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4)))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
0.8b	(pow.f64 (log.f64 base) 4)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
45×	`times-frac_binary64`
44×	`unpow-prod-down_binary64`
36×	`difference-of-squares_binary64`
33×	`add-cube-cbrt_binary64`
25×	`sqr-pow_binary64`
24×	`pow1_binary64`
15×	`associate-/r*_binary64`
12×	`distribute-lft-out--_binary64`
11×	`log-pow_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`swap-sqr_binary64` `log-prod_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`pow-unpow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `pow-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

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 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4)))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
3.0ms	(pow.f64 (log.f64 base) 4)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.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 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4)))
12.0ms	(*.f64 (log.f64 base) (log.f64 base))
16.0ms	(pow.f64 (log.f64 base) 4)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4981	3959
1	4981	3959

prune162.0ms

Filtered

94 candidates to 160 candidates (-70.2%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	2	14	16
Picked	1	0	1
Done	0	2	2
Total	157	22	179

Merged error: 7.2b

Counts

179 → 22

regimes543.0ms

Accuracy

57% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 31.9b

bsearch151.0ms

Steps

Iters	Range		Point
9	2.742846384821079e+28	2.573805552041366e+35	2.5362193761446767e+35
9	9.317771181504113e-281	5.196805194780243e-272	8.950330598317258e-276
6	-5.093211122374936e-261	-3.65607763076758e-262	-4.337372021152796e-262
8	-2.1915322657080793e+63	-2.1090434721521167e+59	-1.8073559612423165e+63

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	137
1	99	137

end0.0ms

sample1.0s

Algorithm

intervals

Results

736.0ms	8000×	body	80	valid
84.0ms	975×	body	80	nan

Details

analyze418.0ms

sample37.0ms

simplify5.0ms

prune4.0ms

localize18.0ms

rewrite33.0ms

series73.0ms

simplify75.0ms

prune203.0ms

localize24.0ms

rewrite21.0ms

series56.0ms

simplify56.0ms

prune148.0ms

localize22.0ms

rewrite50.0ms

series66.0ms

simplify61.0ms

prune229.0ms

localize24.0ms

rewrite38.0ms

series78.0ms

simplify87.0ms

prune162.0ms

regimes543.0ms

bsearch151.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling