Details

Time bar (total: 8.3s)

sample419.0ms

Algorithm
intervals
Results
60.0ms64×body1280valid
50.0ms261×body80valid
24.0ms37×body640valid
9.0ms20×body320valid
3.0ms10×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
29.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite27.0ms

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)
11.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
140.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune328.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.6b

localize16.0ms

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)
1.8b
(* (atan2 x.im x.re) y.im)
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:
8.0ms
(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)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
87.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune301.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
1.8b
(* (atan2 x.im x.re) y.im)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
58×add-sqr-sqrt
56×add-cube-cbrt *-un-lft-identity
52×unpow-prod-down
17×associate-/r*
11×add-exp-log
8×div-exp
7×add-cbrt-cube
6×exp-prod
5×pow1 div-inv add-log-exp
4×pow-exp sqr-pow
3×associate-*r* associate-*l* associate-/l*
2×neg-sub0 exp-neg exp-diff rem-exp-log associate-/l/
1×cbrt-undiv distribute-lft-neg-in pow-to-exp neg-mul-1 rec-exp distribute-rgt-neg-in frac-2neg 1-exp pow-prod-down neg-log prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 125
Calls
3 calls:
14.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)

series116.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
23.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
16.0ms
(* (atan2 x.im x.re) y.im)

simplify51.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04471462
116651379
250011369

prune402.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (exp (- (* (atan2 x.im x.re) y.im))))
1.8b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×cbrt-prod pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×cbrt-div
1×neg-sub0 exp-neg exp-diff pow1/3
Counts
4 → 67
Calls
4 calls:
2.0ms
(cbrt (exp (- (* (atan2 x.im x.re) y.im))))
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)

series93.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(cbrt (exp (- (* (atan2 x.im x.re) y.im))))
16.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify53.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0119340
1434305
21846303
35001300

prune302.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

regimes252.0ms

Accuracy

65.1% (5.8b remaining)

Error of 9.1b against oracle of 3.3b and baseline of 19.9b

bsearch235.0ms

Steps
ItersRangePoint
8
1.488227557880836e-30
5.035419372348236e-26
4.1903614976012866e-30
7
-1.520137727543878e-284
-4.140871043413466e-286
-1.178078840228313e-285

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04727
15927
25927

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.8s2036×body1280valid
1.4s7997×body80valid
915.0ms1448×body640valid
289.0ms626×body320valid
105.0ms328×body160valid