Details

Time bar (total: 7.1s)

sample357.0ms

Algorithm
intervals
Results
41.0ms65×body1280valid
24.0ms250×body80valid
18.0ms44×body640valid
8.0ms28×body320valid
2.0ms8×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune15.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (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)))
34.3b
(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:
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(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)))

series250.0ms

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)))
159.0ms
(cos (+ (* (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
0191422
1501385
21134381
32496381
45001381

prune319.0ms

Filtered
68 candidates to 54 candidates (79.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.0b

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)
2.1b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
92.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(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

prune296.0ms

Filtered
81 candidates to 60 candidates (74.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (atan2 x.im x.re) y.im)
2.1b
(* (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)))

rewrite16.0ms

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

series106.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify67.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0145348
1428322
21017320
32145320
45002320

prune364.0ms

Filtered
78 candidates to 56 candidates (71.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(exp (- (* (atan2 x.im x.re) y.im)))
0.3b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
2.1b
(* (atan2 x.im x.re) y.im)

rewrite21.0ms

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:
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
10.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
4.0ms
(* (atan2 x.im x.re) y.im)

series122.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
81.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
17.0ms
(* (atan2 x.im x.re) y.im)

simplify50.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04471462
116651379
250011369

prune365.0ms

Filtered
134 candidates to 87 candidates (64.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

regimes306.0ms

Accuracy

60.3% (6.4b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 19.8b

bsearch520.0ms

Steps
ItersRangePoint
9
1.3269947651243872e-32
3.102459557861999e-25
2.067311824338759e-25
6
7.526030467558641e-222
6.785927064947826e-221
9.308969534566799e-222
9
-3.6673493662649983e-305
1.2855573319070472e-303
-2.6666463243396e-313
9
-3.7155244174179247e-274
-1.563765694791047e-279
-1.624735018582303e-274
7
-2.556279654011066e-145
-3.8142219411690784e-147
-3.0758773469992465e-146

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06480
17280
27280

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2141×body1280valid
730.0ms7969×body80valid
603.0ms1435×body640valid
209.0ms710×body320valid
62.0ms328×body160valid