Details

sample206.0ms

Algorithm

intervals

Results

168.0ms	256×	body	80	valid
19.0ms	243×	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: 29.3b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (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))
27.0b	(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)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
144.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

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

prune446.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 6.8b

Counts

123 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
163×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
141×	`sqrt-prod`
31×	`pow1`
24×	`associate-/l*`
18×	`sqrt-div`
16×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`flip3-+` `flip-+`
8×	`associate-r` `associate-l` `div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

19.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
154.0ms	(* (log base) (log base))
154.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify124.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	839	8779
1	3156	8145
2	5001	8032

prune775.0ms

Filtered

290 candidates to 136 candidates (46.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	288	16	304

Merged error: 6.8b

Counts

304 → 16

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)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
147.0ms	(* (log base) (log base))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	386	1611
1	1345	1484
2	5001	1464

prune509.0ms

Filtered

142 candidates to 86 candidates (60.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	14	14
Picked	1	0	1
Done	0	1	1
Total	139	19	158

Merged error: 6.5b

Counts

158 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
156.0ms	(pow (log base) 2)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	443	1231
1	1594	1134
2	5002	1115

prune341.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	4	13	17
Picked	1	0	1
Done	0	1	1
Total	105	19	124

Merged error: 6.5b

Counts

124 → 19

regimes667.0ms

Accuracy

58.6% (10.3b remaining)

Error of 17.5b against oracle of 7.2b and baseline of 32.1b

bsearch311.0ms

Steps

Iters	Range		Point
8	2.5833103967853428e+125	1.3165516338391777e+130	2.9456484498390374e+125
10	5.336032226808832e-285	5.348812809366337e-275	6.51190185981464e-281
10	-2.8236653238890864e-258	-1.0352275344072811e-275	-4.4909879919105734e-275
6	-5.770661945367634e+105	-6.641091918017903e+104	-2.346181989253652e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	88
1	65	88

end0.0ms

sample1.7s

Algorithm

intervals

Results

672.0ms	8000×	body	80	valid
643.0ms	8051×	body	80	nan

Details

sample206.0ms

simplify4.0ms

prune4.0ms

localize20.0ms

rewrite28.0ms

series376.0ms

simplify60.0ms

prune446.0ms

localize22.0ms

rewrite52.0ms

series447.0ms

simplify124.0ms

prune775.0ms

localize23.0ms

rewrite29.0ms

series391.0ms

simplify55.0ms

prune509.0ms

localize22.0ms

rewrite29.0ms

series429.0ms

simplify51.0ms

prune341.0ms

regimes667.0ms

bsearch311.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling