Details

Time bar (total: 6.7s)

sample368.0ms

Algorithm
intervals
Results
45.0ms72×body1280valid
22.0ms259×body80valid
15.0ms38×body640valid
4.0ms15×body320valid
2.0ms9×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune17.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify72.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0189422
1491385
21112381
32393381
45001381

prune328.0ms

Filtered
68 candidates to 54 candidates (79.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
94.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify78.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune283.0ms

Filtered
78 candidates to 56 candidates (71.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b
(* (log (* -1 x.re)) y.re)
0.7b
(* (atan2 x.im x.re) y.im)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
8×associate-*l*
7×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r*
5×add-log-exp
3×pow-prod-down
2×prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log flip--
Counts
3 → 50
Calls
3 calls:
3.0ms
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
7.0ms
(* (log (* -1 x.re)) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series191.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
69.0ms
(* (log (* -1 x.re)) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)

simplify101.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0225318
1816291
24159287
35001287

prune176.0ms

Filtered
59 candidates to 38 candidates (64.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 4 expressions with local error:

30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cos-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
141.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
135.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
136.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify159.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 4 (50.0ms)

IterNodesCost
0137538
1283472
2606472
31518472
44761471
55001471

prune331.0ms

Filtered
51 candidates to 48 candidates (94.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.1b

regimes247.0ms

Accuracy

68.1% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 20.0b

bsearch121.0ms

Steps
ItersRangePoint
10
-1.2633929192945347e-304
1.928209425921678e-301
1.4488852536328e-310

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13515
23515

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2068×body1280valid
683.0ms7915×body80valid
565.0ms1439×body640valid
172.0ms633×body320valid
58.0ms321×body160valid