Details

Time bar (total: 6.8s)

sample428.0ms

Algorithm
intervals
Results
43.0ms76×body1280valid
33.0ms34×body640valid
22.0ms254×body80valid
5.0ms21×body320valid
2.0ms8×body160valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120
done500120

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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:
7.0ms
(* (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)))
25.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381
done5001381

prune299.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize15.0ms

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)
1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite49.0ms

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:
19.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
14.0ms
(* (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)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
89.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0280545
1825486
22118481
35001481
done5001481

prune265.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (- (* (atan2 x.im x.re) y.im))))
1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×associate-*l*
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-exp-log sqrt-prod add-cbrt-cube
6×pow1 associate-*r*
5×unswap-sqr
4×prod-exp
3×add-log-exp
2×exp-neg sqrt-div associate-*r/ *-commutative cbrt-unprod sqr-pow
1×neg-sub0 pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 exp-diff pow-prod-down pow-exp un-div-inv flip-+
Counts
3 → 65
Calls
3 calls:
52.0ms
(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (- (* (atan2 x.im x.re) y.im))))
6.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series175.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (- (* (atan2 x.im x.re) y.im))))
18.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify103.0ms

Counts
74 → 74
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0299606
11032556
23955542
35002542
done5002542

prune237.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (pow (/ 1 x.re) (* -1 y.re)) (exp (* (atan2 x.im x.re) y.im)))
1.4b
(* (atan2 x.im x.re) y.im)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
56×add-sqr-sqrt
54×add-cube-cbrt *-un-lft-identity
52×unpow-prod-down
17×associate-/l*
10×add-exp-log
8×div-exp
6×add-cbrt-cube
5×div-inv
4×pow1 pow-exp sqr-pow
3×associate-*r* associate-*l* associate-/r*
2×add-log-exp
1×cbrt-undiv pow-to-exp pow-neg rec-exp frac-2neg mul-1-neg 1-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
2 → 107
Calls
2 calls:
25.0ms
(/ (pow (/ 1 x.re) (* -1 y.re)) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)

series100.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(/ (pow (/ 1 x.re) (* -1 y.re)) (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify42.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
04281349
114431281
250011266
done50011266

prune296.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

regimes256.0ms

Accuracy

54.8% (6.9b remaining)

Error of 11.3b against oracle of 4.4b and baseline of 19.7b

bsearch424.0ms

Steps
ItersRangePoint
10
7.704108445868586e-11
33183.92535515244
0.049666903313089414
10
2.67271266005654e-166
2.2896112546321894e-155
8.333241630915609e-157
9
-1.2772633849980886e-303
5.690367183293641e-307
-2.4485621286449e-310
10
-2.75541712276274e-251
-1.6878141620607126e-261
-8.512054391915102e-257

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05944
17044
27344
37344
done7344

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2143×body1280valid
651.0ms7948×body80valid
549.0ms1451×body640valid
174.0ms669×body320valid
55.0ms319×body160valid