Details

Time bar (total: 7.2s)

sample366.0ms

Algorithm
intervals
Results
47.0ms73×body1280valid
24.0ms260×body80valid
21.0ms50×body640valid
5.0ms17×body320valid
2.0ms1×body2560valid
1.0ms7×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×sin-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.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0196425
1506388
21139386
32509386
45001386

prune316.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.0b

localize33.0ms

Local error

Found 4 expressions with local error:

29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
143.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
142.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify162.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 4 (53.0ms)

IterNodesCost
0142553
1288487
2611487
31523487
44766486
55002486

prune336.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
16.6b
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 59
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series160.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
90.0ms
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify87.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 4 (82.0ms)

IterNodesCost
0240354
1670318
21580316
33230316
45001312

prune290.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 13.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (log x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
16.6b
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow
Counts
4 → 63
Calls
4 calls:
4.0ms
(* (log x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (log x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
91.0ms
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))

simplify50.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0217333
1706290
21728280
35002280

prune209.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 13.0b

regimes537.0ms

Accuracy

74.3% (5.2b remaining)

Error of 18.0b against oracle of 12.7b and baseline of 33.1b

bsearch246.0ms

Steps
ItersRangePoint
7
4.271736699251887e+34
1.6404928499711188e+36
4.35620541367004e+34
10
-3.1733683408219374e-304
1.957129954217898e-303
7.7747768769685e-312

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05553
15553

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s2143×body1280valid
700.0ms7995×body80valid
568.0ms1394×body640valid
155.0ms537×body320valid
61.0ms39×body2560valid
42.0ms228×body160valid