Details

analyze445.0ms

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
2.0ms	25×	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: 31.9b

Counts

2 → 1

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 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

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

series80.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.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)))
24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
19.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4986	2010
1	4986	2010

prune209.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	104	18	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	18	123

Merged error: 8.2b

Counts

123 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(.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))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms

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:

8.0ms	(.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))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
18.0ms	(pow.f64 (log.f64 base) 2)
18.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4819	923
1	4819	923

prune155.0ms

Filtered

65 candidates to 110 candidates (-69.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	111	17	128

Merged error: 8.2b

Counts

128 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (log.f64 base) (log.f64 (cbrt.f64 base)))
0.5b	(cbrt.f64 base)
0.5b	(cbrt.f64 base)
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64` `cbrt-prod_binary64`
9×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`pow1/3_binary64` `log-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

6.0ms	(*.f64 (log.f64 base) (log.f64 (cbrt.f64 base)))
1.0ms	(cbrt.f64 base)
1.0ms	(cbrt.f64 base)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series135.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(*.f64 (log.f64 base) (log.f64 (cbrt.f64 base)))
33.0ms	(cbrt.f64 base)
30.0ms	(cbrt.f64 base)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4932	595
1	4932	595

prune139.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	80	19	99

Merged error: 8.2b

Counts

99 → 19

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
0.5b	(cbrt.f64 base)
0.5b	(cbrt.f64 base)
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`swap-sqr_binary64`
8×	`pow1/3_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
1.0ms	(cbrt.f64 base)
1.0ms	(cbrt.f64 base)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
31.0ms	(cbrt.f64 base)
29.0ms	(cbrt.f64 base)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5006	599

prune87.0ms

Filtered

66 candidates to 94 candidates (-42.4%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	16	17
Picked	0	1	1
Done	0	1	1
Total	92	21	113

Merged error: 8.2b

Counts

113 → 21

regimes634.0ms

Accuracy

55% (10.9b remaining)

Error of 17.7b against oracle of 6.8b and baseline of 31.1b

bsearch157.0ms

Steps

Iters	Range		Point
7	15004680.116774563	812719246.368939	800712819.842004
8	-2.0528925999939642e-265	-2.1201396879548627e-268	-1.5821814501140232e-267
8	-7.266638217871674e-189	-4.1060637446278703e-193	-7.823143127285978e-193
10	-3.0758993662576154e+128	-6.421666187812336e+117	-3.3734405662222592e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	110
1	65	110

end0.0ms

sample1.1s

Algorithm

intervals

Results

775.0ms	8000×	body	80	valid
98.0ms	1063×	body	80	nan

Details

analyze445.0ms

sample37.0ms

simplify5.0ms

prune4.0ms

localize22.0ms

rewrite30.0ms

series80.0ms

simplify73.0ms

prune209.0ms

localize25.0ms

rewrite22.0ms

series68.0ms

simplify65.0ms

prune155.0ms

localize27.0ms

rewrite15.0ms

series135.0ms

simplify53.0ms

prune139.0ms

localize32.0ms

rewrite16.0ms

series111.0ms

simplify49.0ms

prune87.0ms

regimes634.0ms

bsearch157.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling