Details

Time bar (total: 6.5s)

sample356.0ms

Algorithm
intervals
Results
36.0ms61×body1280valid
22.0ms239×body80valid
18.0ms46×body640valid
7.0ms26×body320valid
2.0ms9×body160valid

simplify37.0ms

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: 33.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(cos (+ (* (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×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.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)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune342.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)
2.2b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

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)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
90.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune309.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.2b
(pow (/ -1 x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
13×unpow-prod-down
9×times-frac
8×add-exp-log
6×pow1 exp-prod
5×add-cbrt-cube add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×pow-exp rem-exp-log
1×neg-sub0 distribute-lft-neg-in exp-neg pow-to-exp neg-mul-1 pow-pow distribute-rgt-neg-in exp-diff div-exp pow-prod-down neg-log prod-exp *-commutative cbrt-unprod div-inv unswap-sqr sqr-pow
Counts
3 → 63
Calls
3 calls:
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
4.0ms
(pow (/ -1 x.re) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)

series98.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
58.0ms
(pow (/ -1 x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify39.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0335337
11279310
25002309

prune251.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (pow (/ -1 x.re) y.re)))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.2b
(pow (/ -1 x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt unpow-prod-down
24×add-cube-cbrt *-un-lft-identity
23×exp-prod
18×times-frac log-pow
9×add-exp-log
8×pow1
6×add-cbrt-cube add-log-exp
3×pow-unpow log-prod associate-*r* associate-*l*
2×pow-exp div-inv rem-exp-log sqr-pow
1×neg-sub0 distribute-lft-neg-in exp-neg pow-to-exp neg-mul-1 pow-pow distribute-rgt-neg-in exp-diff div-exp rem-log-exp pow-prod-down neg-log prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 92
Calls
4 calls:
6.0ms
(log (exp (pow (/ -1 x.re) y.re)))
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
5.0ms
(pow (/ -1 x.re) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)

series158.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(log (exp (pow (/ -1 x.re) y.re)))
23.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
60.0ms
(pow (/ -1 x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify42.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0386490
11364447
25001445

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

regimes345.0ms

Accuracy

52.9% (7.5b remaining)

Error of 11.2b against oracle of 3.7b and baseline of 19.6b

bsearch297.0ms

Steps
ItersRangePoint
9
-1.3660599968596594e-302
4.521562716650534e-309
-3.4831262277498e-310
7
-1.8054879539703964e-56
-1.6100361634839777e-58
-2.1426491008291027e-57
8
-3.8266789121121317e+155
-4.0918767517713647e+152
-1.3446615524165113e+154

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05452
16252
26252

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2064×body1280valid
679.0ms7974×body80valid
583.0ms1459×body640valid
180.0ms668×body320valid
56.0ms317×body160valid