Details

Time bar (total: 24.6s)

sample265.0ms

Algorithm
intervals
Results
113.0ms88×body1280valid
35.0ms58×body640valid
33.0ms256×body80valid
7.0ms20×body320valid
3.0ms13×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01937
13137
25336
38536
422036
5102336
done500036

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize49.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b
(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)))

rewrite75.0ms

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:
14.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.im)
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
225.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts
68 → 68
Iterations

Useful iterations: 3 (671.0ms)

IterNodesCost
095836
1197778
2554692
32818677
done5000677

prune495.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize27.0ms

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)
1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite80.0ms

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:
32.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
24.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
137.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify807.0ms

Counts
81 → 81
Iterations

Useful iterations: done (804.0ms)

IterNodesCost
01321042
1290985
2920871
done5000867

prune520.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
6×add-exp-log sqrt-div add-cbrt-cube
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.7s

Counts
75 → 75
Iterations

Useful iterations: 3 (619.0ms)

IterNodesCost
067794
1151710
2472644
32585624
done5001624

prune578.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

localize18.0ms

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)))
1.6b
(* (atan2 x.im x.re) y.im)

rewrite67.0ms

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*
9×add-exp-log
7×add-cbrt-cube
6×exp-prod
5×pow1 div-exp div-inv add-log-exp
4×sqr-pow
3×associate-*r* associate-*l* associate-/l*
2×neg-sub0 exp-neg exp-diff pow-exp rem-exp-log associate-/l/
1×cbrt-undiv distribute-lft-neg-in pow-to-exp neg-mul-1 distribute-rgt-neg-in frac-2neg pow-prod-down neg-log prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 123
Calls
3 calls:
40.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
8.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
14.0ms
(* (atan2 x.im x.re) y.im)

series231.0ms

Counts
3 → 9
Calls
3 calls:
154.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
54.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
23.0ms
(* (atan2 x.im x.re) y.im)

simplify1.8s

Counts
132 → 132
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02622582
14792495
222942418
done50002413

prune751.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

regimes475.0ms

Accuracy

59.7% (7.6b remaining)

Error of 12.5b against oracle of 4.8b and baseline of 23.7b

bsearch1.9s

Steps
ItersRangePoint
7
1.320929265984738e-171
1.0976071592437177e-169
1.3467276961577541e-171
10
1.7198883733347406e-210
1.2162394280746478e-200
1.2057998402706758e-200
6
-1.3595042956760654e-308
9.591531608959521e-308
-1.2955598695306e-310
9
-5.840558046559514e-269
-5.4735328192046755e-275
-3.1188013699207257e-271
8
-2.0864093490319646e-233
-2.5501859063416286e-236
-1.4965505062601128e-235
10
-2.1138442810782786e-129
-1.4700793538695453e-143
-1.7597595967955698e-130
8
-9.72486159108584e-09
-7.12100996291553e-13
-1.3334139786794843e-11

simplify39.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
067316
190291
295291
done95291

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.1s2048×body1280valid
1.9s1511×body640valid
1.9s7982×body80valid
579.0ms305×body160valid
364.0ms612×body320valid