Details

Time bar (total: 6.3s)

sample368.0ms

Algorithm
intervals
Results
40.0ms68×body1280valid
23.0ms251×body80valid
16.0ms41×body640valid
6.0ms24×body320valid
2.0ms12×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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:
4.0ms
(* (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
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
154.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune328.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
4.0ms
(exp (- (* (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)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify60.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune299.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 1 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
1×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp unswap-sqr
Counts
1 → 18
Calls
1 calls:
4.0ms
(* (atan2 x.im x.re) y.im)

series18.0ms

Counts
1 → 3
Calls
1 calls:
17.0ms
(* (atan2 x.im x.re) y.im)

simplify60.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06174
122064
251764
379764
4189364
5500164

prune87.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 2 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
4.3b
(log (exp (* (atan2 x.im x.re) y.im)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube
3×log-prod associate-*r* associate-*l* log-pow add-log-exp
1×exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 32
Calls
2 calls:
4.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(log (exp (* (atan2 x.im x.re) y.im)))

series33.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(log (exp (* (atan2 x.im x.re) y.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 5 (76.0ms)

IterNodesCost
079142
1238122
2541122
3973122
42817122
55002118

prune108.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

regimes328.0ms

Accuracy

57.9% (6.6b remaining)

Error of 10.3b against oracle of 3.6b and baseline of 19.4b

bsearch672.0ms

Steps
ItersRangePoint
9
1.399452955633998e-08
6.164824567421913
2.4512483530906244
9
2.447827825119605e-135
4.7008950856665656e-126
2.992637786114339e-130
8
-2.293787866138921e-305
-3.058996228144634e-308
-3.10085515308595e-308
9
-5.085486404844717e-253
-5.058854985061063e-259
-6.904544359255171e-255
6
-5.70617462706012e-172
-1.1219980269637772e-172
-1.5964916719967018e-172
6
-1.6922119400335083e-137
-1.0798862212648827e-138
-7.006562832746294e-138
8
-6.749616526709704e-39
-2.988981061142875e-43
-1.0320343030662579e-39

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06780
17980
27980

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s1983×body1280valid
675.0ms7943×body80valid
590.0ms1514×body640valid
174.0ms631×body320valid
57.0ms302×body160valid