Details

sample67.0ms

Algorithm

intervals

Results

25.0ms	267×	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: 28.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (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))
26.6b	(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)))

series383.0ms

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)))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

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

prune443.0ms

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: 7.5b

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))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

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)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (/ (+ (* (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))))
149.0ms	(* (log base) (log base))
150.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify123.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	839	8780
1	3156	8145
2	5001	8032

prune745.0ms

Filtered

290 candidates to 136 candidates (46.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	289	15	304

Merged error: 7.5b

Counts

304 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
22×	`pow1`
19×	`associate-l`
18×	`log-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
12×	`add-exp-log` `associate--l+`
11×	`add-cbrt-cube`
10×	`times-frac`
8×	`associate-r`
7×	`log-pow`
6×	`swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `sub-neg` `flip3--` `flip3-+` `sqrt-div` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `flip--` `flip-+`
1×	`cbrt-undiv` `pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `associate-*l/` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv` `difference-of-squares` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

20.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
3.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
149.0ms	(* (log base) (log base))
163.0ms	(pow (log base) 4)
183.0ms	(sqrt (+ (* re re) (* im im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	662	2168
1	3246	1970
2	5002	1964

prune534.0ms

Filtered

136 candidates to 84 candidates (61.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	134	17	151

Merged error: 7.5b

Counts

151 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (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))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 174

Calls

4 calls:

28.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (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))
8.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
154.0ms	(* (log base) (log base))
148.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	676	3306
1	3783	2940
2	5001	2757

prune520.0ms

Filtered

186 candidates to 105 candidates (56.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	185	18	203

Merged error: 7.5b

Counts

203 → 18

regimes396.0ms

Accuracy

57.6% (10.3b remaining)

Error of 17.3b against oracle of 7.0b and baseline of 31.3b

bsearch166.0ms

Steps

Iters	Range		Point
6	1.0028925967356206e+28	9.190413205136228e+28	8.216361596326438e+28
10	-2.2638280961448626e+135	-7.657926935493531e+121	-6.798070878250835e+132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	58
1	58	58

end0.0ms

sample1.7s

Algorithm

intervals

Results

699.0ms	8000×	body	80	valid
660.0ms	7918×	body	80	nan