Details

sample65.0ms

Algorithm

intervals

Results

24.0ms	246×	body	80	nan
23.0ms	256×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

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: 31.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
29.5b	(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:

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

series380.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
152.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5002	1203

prune444.0ms

Filtered

122 candidates to 84 candidates (68.9%)

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: 6.9b

Counts

123 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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))
7.0ms	(sqrt (+ (* re re) (* im im)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
154.0ms	(* (log base) (log base))
151.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify155.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (146.0ms)

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

prune396.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	127	15	142

Merged error: 6.9b

Counts

142 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`pow1`
23×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod`
11×	`times-frac`
10×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv`

Counts

4 → 121

Calls

4 calls:

17.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
289.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	569	1511
1	2601	1356
2	5002	1312

prune424.0ms

Filtered

133 candidates to 85 candidates (63.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	130	18	148

Merged error: 6.9b

Counts

148 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (log base) 2)
29.5b	(sqrt (+ (* re re) (* im im)))
29.5b	(sqrt (+ (* re re) (* im im)))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (log base) 2)
36.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	169	373
1	482	348
2	1597	348
3	5002	344

prune292.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	76	18	94

Merged error: 6.9b

Counts

94 → 18

regimes467.0ms

Accuracy

58.5% (10.1b remaining)

Error of 17.7b against oracle of 7.6b and baseline of 31.9b

bsearch214.0ms

Steps

Iters	Range		Point
11	1.5263731768188856e+46	3.003842095153293e+77	1.464180329742239e+68
9	-5.990984502720751e+78	-9.855852910738255e+72	-1.0982261757761181e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	49
1	62	49

end0.0ms

sample1.8s

Algorithm

intervals

Results

738.0ms	8000×	body	80	valid
689.0ms	7932×	body	80	nan

Details

sample65.0ms

simplify4.0ms

prune4.0ms

localize19.0ms

rewrite28.0ms

series380.0ms

simplify58.0ms

prune444.0ms

localize22.0ms

rewrite26.0ms

series433.0ms

simplify155.0ms

prune396.0ms

localize20.0ms

rewrite35.0ms

series519.0ms

simplify77.0ms

prune424.0ms

localize24.0ms

rewrite16.0ms

series262.0ms

simplify63.0ms

prune292.0ms

regimes467.0ms

bsearch214.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling