Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
16.0ms	226×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

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

rewrite33.0ms

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:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series368.0ms

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)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
143.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune465.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

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)))

rewrite25.0ms

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))
7.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify149.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592

prune435.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
30.8b	(sqrt (+ (* re re) (* im im)))
30.8b	(sqrt (+ (* re re) (* im im)))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

2.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
41.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	146	481
1	405	458
2	1153	456
3	5001	452

prune426.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.0b

localize37.0ms

Local error

Found 4 expressions with local error:

5.1b	(pow (sqrt (+ (* re re) (* im im))) 1/3)
30.8b	(sqrt (+ (* re re) (* im im)))
30.8b	(sqrt (+ (* re re) (* im im)))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
6×	`unpow-prod-down` `sqrt-div`
5×	`add-exp-log`
4×	`sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `pow-pow` `flip3-+` `flip-+`
1×	`pow-to-exp` `unpow1/3` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

5.0ms	(pow (sqrt (+ (* re re) (* im im))) 1/3)
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (sqrt (+ (* re re) (* im im))) 1/3)
34.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	197	459
1	647	422
2	2237	420
3	5001	420

prune400.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.0b

regimes385.0ms

Accuracy

56.9% (10.4b remaining)

Error of 18.2b against oracle of 7.8b and baseline of 32.0b

bsearch284.0ms

Steps

Iters	Range		Point
7	5.617467149036996e+119	4.0732344434354675e+121	6.558112066263903e+120
8	2.4188702810987967e-207	8.183730222618262e-204	4.6486626548515276e-207
7	-1.3157788970525727e-225	-1.0019362147008816e-227	-3.3317444190136695e-227
8	-7.736809382031255e+132	-2.4034400986011796e+129	-5.954061345307104e+129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	95
1	61	95

end0.0ms

sample1.5s

Algorithm

intervals

Results

572.0ms	7928×	body	80	nan
564.0ms	8000×	body	80	valid