Details

sample55.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
18.0ms	265×	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: 35.0b

Counts

2 → 1

localize24.0ms

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))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite82.0ms

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:

39.0ms	(/ (+ (* (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))
15.0ms	(sqrt (+ (* re re) (* im im)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	447	3802
1	1736	3598
2	5001	3555

prune381.0ms

Filtered

251 candidates to 84 candidates (33.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	237	14	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	238	14	252

Merged error: 7.5b

Counts

252 → 14

localize23.0ms

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))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

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))
7.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
154.0ms	(* (log base) (log base))
152.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify150.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	258	738
1	946	659
2	4588	619
3	5001	602

prune366.0ms

Filtered

132 candidates to 71 candidates (53.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	130	16	146

Merged error: 7.5b

Counts

146 → 16

localize28.0ms

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))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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))
15.0ms	(sqrt (+ (* re re) (* im im)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
156.0ms	(* (log base) (log base))
156.0ms	(* (log base) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify145.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	258	738
1	946	659
2	4588	619
3	5001	602

prune386.0ms

Filtered

132 candidates to 71 candidates (53.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	131	17	148

Merged error: 7.5b

Counts

148 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (* (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))
0.5b	(* (log base) (log base))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

197×	`*-un-lft-identity`
72×	`associate-l`
71×	`distribute-lft-out`
63×	`pow1`
56×	`swap-sqr`
53×	`associate-r`
51×	`add-sqr-sqrt`
48×	`log-pow`
41×	`times-frac`
39×	`add-cube-cbrt` `associate-/r*`
38×	`frac-times`
22×	`flip3-+` `flip-+`
19×	`associate-*r/`
17×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`log-prod`
10×	`associate-/l*`
8×	`sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
5×	`unswap-sqr`
4×	`clear-num` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `un-div-inv` `*-commutative`
2×	`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` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 218

Calls

4 calls:

51.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
18.0ms	(sqrt (+ (* re re) (* im im)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
291.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
167.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	662	3693
1	3009	3527
2	5001	3449

prune366.0ms

Filtered

230 candidates to 96 candidates (41.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	226	4	230
Fresh	3	12	15
Picked	1	0	1
Done	0	1	1
Total	230	17	247

Merged error: 7.5b

Counts

247 → 17

regimes463.0ms

Accuracy

55.2% (11.0b remaining)

Error of 18.2b against oracle of 7.2b and baseline of 31.7b

bsearch328.0ms

Steps

Iters	Range		Point
10	1.1822453681052812e+79	1.8546993644098514e+95	7.916959787142804e+93
7	-1.2410605495858746e-179	-2.048623835292368e-181	-1.0096510313516879e-179
9	-5.117019008798285e-115	-2.5804612905466032e-120	-2.6070767088458903e-120
10	-6.849196822845392e+117	-1.0235707267949737e+108	-1.4185974229156341e+116

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	78
1	63	78
2	66	78
3	66	78

end0.0ms

sample1.5s

Algorithm

intervals

Results

597.0ms	8000×	body	80	valid
559.0ms	7955×	body	80	nan