Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	266×	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

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

localize23.0ms

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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

413×	`*-un-lft-identity`
189×	`distribute-lft-out`
182×	`associate-l`
117×	`times-frac`
111×	`pow1`
98×	`log-pow`
88×	`swap-sqr`
44×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
13×	`associate-/r*`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-r` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`flip3-+` `flip-+`
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 → 239

Calls

4 calls:

45.0ms	(/ (+ (* (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))
16.0ms	(sqrt (+ (* re re) (* im im)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
89.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
150.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	458	3802
1	1772	3596
2	5001	3555

prune451.0ms

Filtered

251 candidates to 84 candidates (33.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	238	13	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	239	13	252

Merged error: 6.6b

Counts

252 → 13

localize26.0ms

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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
36×	`pow1`
28×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`log-prod` `associate-l`
16×	`log-pow`
14×	`swap-sqr`
12×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`sqrt-prod`
5×	`distribute-lft-out`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-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 → 120

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))
16.0ms	(sqrt (+ (* re re) (* im im)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(* (log base) (log base))
151.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify159.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	264	738
1	967	659
2	4682	619
3	5001	612

prune456.0ms

Filtered

132 candidates to 71 candidates (53.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	129	16	145

Merged error: 6.5b

Counts

145 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
25×	`pow1`
22×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
14×	`associate-l`
12×	`log-prod`
11×	`log-pow`
9×	`add-exp-log`
8×	`swap-sqr` `associate-r` `sqrt-prod` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`distribute-lft-out`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
16.0ms	(sqrt (+ (* re re) (* im im)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
148.0ms	(* (log base) (log base))
165.0ms	(pow (log base) 4)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	321	661
1	1271	588
2	5002	559

prune488.0ms

Filtered

114 candidates to 66 candidates (57.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	113	17	130

Merged error: 6.5b

Counts

130 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
20.0ms	(sqrt (+ (* re re) (* im im)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
180.0ms	(cbrt base)
175.0ms	(cbrt base)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	228	514
1	631	471
2	1683	447
3	5002	442

prune338.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	3	12	15
Picked	0	1	1
Done	0	1	1
Total	81	18	99

Merged error: 6.5b

Counts

99 → 18

regimes496.0ms

Accuracy

55.2% (11.1b remaining)

Error of 18.7b against oracle of 7.5b and baseline of 32.4b

bsearch261.0ms

Steps

Iters	Range		Point
6	2157434815204663.0	13141120828988944.0	8121789251388552.0
8	7.613724523315994e-199	4.58538657554641e-194	6.1019822211320945e-198
7	-8.758535608358512e-222	-1.1508617725285748e-223	-3.970425082207529e-222
8	-2.930375697785199e+121	-7.490667611783549e+116	-8.428333082377683e+116

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	99
1	72	99
2	75	99
3	75	99

end0.0ms

sample1.5s

Algorithm

intervals

Results

555.0ms	8000×	body	80	valid
551.0ms	8146×	body	80	nan