Details

Time bar (total: 6.5s)

sample445.0ms

Algorithm
intervals
Results
53.0ms59×body1280valid
25.0ms58×body640valid
21.0ms254×body80valid
4.0ms16×body320valid
2.0ms10×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.2b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(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)))

simplify82.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411
done5002411

prune366.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.9b

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)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite50.0ms

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*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log prod-diff flip-+ hypot-def
Counts
4 → 79
Calls
4 calls:
22.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
12.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
100.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Counts
91 → 91
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0308585
1921522
22504484
35002467
done5002467

prune321.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.4b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt exp-prod
11×add-cube-cbrt *-un-lft-identity
8×pow-pow
7×pow1
6×add-exp-log unpow-prod-down add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*r* associate-*l*
2×rem-exp-log sqr-pow
1×neg-sub0 distribute-lft-neg-in exp-neg pow-to-exp neg-mul-1 hypot-udef distribute-rgt-neg-in exp-diff pow-prod-down neg-log pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 75
Calls
4 calls:
0.0ms
(hypot x.re x.im)
10.0ms
(pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im))))
5.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
9.0ms
(* (atan2 x.im x.re) y.im)

series280.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(hypot x.re x.im)
185.0ms
(pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im))))
26.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify36.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0283500
11006472
25002454
done5002454

prune352.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)

rewrite30.0ms

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*
6×exp-prod add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×rem-exp-log
1×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in exp-diff neg-log
Counts
4 → 79
Calls
4 calls:
5.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.im)

series85.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify59.0ms

Counts
91 → 91
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0123335
1483303
22294302
35002300
done5002300

prune389.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.4b

regimes155.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02722
13122
23122
done3122

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s2003×body1280valid
649.0ms8000×body80valid
564.0ms1489×body640valid
168.0ms628×body320valid
53.0ms301×body160valid