Details

Time bar (total: 8.8s)

sample427.0ms

Algorithm
intervals
Results
55.0ms57×body1280valid
24.0ms259×body80valid
16.0ms40×body640valid
4.0ms14×body320valid
2.0ms1×body2560valid
1.0ms7×body160valid

simplify39.0ms

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: 34.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.re)
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b
(sin (+ (* (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×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-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.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
170.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify72.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0194425
1496388
21117386
32398386
45002386
done5002386

prune321.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.2b

localize31.0ms

Local error

Found 4 expressions with local error:

30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
153.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify161.0ms

Counts
51 → 51
Iterations

Useful iterations: 4 (52.0ms)

IterNodesCost
0142553
1288487
2611487
31523487
44766486
55002486
done5002486

prune345.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.2b

localize37.0ms

Local error

Found 4 expressions with local error:

33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
Counts
4 → 32
Calls
4 calls:
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series625.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
153.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
163.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify44.0ms

Counts
44 → 44
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
065604
186520
2122520
3273520
4554520
55001520
done5001520

prune334.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.2b

localize40.0ms

Local error

Found 4 expressions with local error:

33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
Counts
4 → 32
Calls
4 calls:
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
151.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
155.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify43.0ms

Counts
44 → 44
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
065604
186520
2122520
3273520
4554520
55001520
done5001520

prune335.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.2b

regimes470.0ms

Accuracy

77% (3.2b remaining)

Error of 22.3b against oracle of 19.1b and baseline of 32.9b

bsearch350.0ms

Steps
ItersRangePoint
7
-2.9539567512785007e-307
4.605039840866011e-308
4.7378467986632e-310
10
-7.483371281609126e-227
-3.96723709819903e-241
-3.310592978427305e-228
7
-5.712262307180586e-207
-6.037566401448638e-209
-7.165681593660874e-209

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05875
15875
done5875

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2166×body1280valid
687.0ms7961×body80valid
591.0ms1453×body640valid
171.0ms598×body320valid
67.0ms43×body2560valid
37.0ms204×body160valid