Details

sample61.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
20.0ms	247×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune5.0ms

Filtered

1 candidates to 0 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: 33.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
101.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1362
1	1751	1236
2	5002	1203

prune620.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	106	16	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 9.7b

Counts

123 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
150.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify152.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4724	599
3	5001	592

prune428.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	126	17	143

Merged error: 9.7b

Counts

143 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
177.0ms	(cbrt base)
177.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	366	1306
1	1283	1187
2	5001	1169

prune459.0ms

Filtered

80 candidates to 67 candidates (83.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	5	10	15
Picked	1	0	1
Done	0	1	1
Total	81	16	97

Merged error: 9.6b

Counts

97 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (+ (* 2 (log (cbrt base))) (log (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `cbrt-prod` `associate-r` `add-cbrt-cube`
4×	`associate-l` `add-log-exp`
3×	`sqrt-prod`
2×	`distribute-rgt-out` `flip3-+` `pow1/3` `sqrt-div` `associate-*r/` `log-pow` `flip-+`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `distribute-lft1-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

8.0ms	(* (log base) (+ (* 2 (log (cbrt base))) (log (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series808.0ms

Counts

4 → 12

Calls

4 calls:

421.0ms	(* (log base) (+ (* 2 (log (cbrt base))) (log (cbrt base))))
175.0ms	(cbrt base)
174.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	300	451
1	1210	376
2	5001	285

prune353.0ms

Filtered

75 candidates to 60 candidates (80.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	73	18	91

Merged error: 9.6b

Counts

91 → 18

regimes465.0ms

Accuracy

57.7% (10.3b remaining)

Error of 18.2b against oracle of 7.9b and baseline of 32.3b

bsearch186.0ms

Steps

Iters	Range		Point
9	1.260001555397826e+122	9.318392138428343e+130	1.0257444546793604e+130
10	-2.806313247885832e+86	-6.904507716888469e+73	-1.1055706967184089e+82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	50
1	50	50

end0.0ms

sample1.7s

Algorithm

intervals

Results

692.0ms	8000×	body	80	valid
649.0ms	7871×	body	80	nan

Details

sample61.0ms

simplify4.0ms

prune5.0ms

localize24.0ms

rewrite28.0ms

series383.0ms

simplify64.0ms

prune620.0ms

localize22.0ms

rewrite23.0ms

series434.0ms

simplify152.0ms

prune428.0ms

localize26.0ms

rewrite20.0ms

series583.0ms

simplify46.0ms

prune459.0ms

localize28.0ms

rewrite16.0ms

series808.0ms

simplify40.0ms

prune353.0ms

regimes465.0ms

bsearch186.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling