Details

Time bar (total: 2.4m)

sample2.9s

Algorithm
intervals
Results
1.4s71×body1280valid
502.0ms257×body80valid
149.0ms20×body320valid
140.0ms48×body640valid
14.0ms9×body160valid
9.0ms2×body2560valid

simplify14.2s

Counts
1 → 1
Iterations
IterNodes
done5000
5809
4197
382
253
131
019

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize998.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite213.0ms

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:
14.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series3.0s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.im)
87.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
135.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.7s
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify8.9s

Counts
68 → 68
Iterations
IterNodes
done5000
42066
3895
2426
1202
098

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.9b

localize604.0ms

Local error

Found 4 expressions with local error:

28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite414.0ms

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:
24.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
87.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
96.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
147.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series2.6s

Counts
4 → 12
Calls
4 calls:
144.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
927.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
822.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
715.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify18.5s

Counts
51 → 51
Iterations
IterNodes
done5000
53757
41190
3542
2268
1144
071

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.9b

localize186.0ms

Local error

Found 4 expressions with local error:

4.3b
(log (exp (* (atan2 x.im x.re) y.im)))
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-prod
5×add-log-exp
4×add-exp-log sqrt-div add-cbrt-cube
3×log-prod log-pow
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×exp-prod exp-to-pow sin-sum rem-log-exp
Counts
4 → 52
Calls
4 calls:
7.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.1s

Counts
4 → 12
Calls
4 calls:
332.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
84.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
110.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
547.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify16.5s

Counts
64 → 64
Iterations
IterNodes
done5003
54259
41365
3622
2311
1166
090

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 15.9b

localize488.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
20.5b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite501.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 59
Calls
4 calls:
59.0ms
(* (atan2 x.im x.re) y.re)
368.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series840.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (atan2 x.im x.re) y.re)
96.0ms
(* (atan2 x.im x.re) y.im)
440.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
261.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify11.9s

Counts
71 → 71
Iterations
IterNodes
done5000
43010
31242
2552
1256
0124

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 8.3b

regimes1.4s

Accuracy

75% (5.3b remaining)

Error of 18.2b against oracle of 12.9b and baseline of 34.1b

bsearch937.0ms

Steps
ItersRangePoint
10
-1.6859549200065964e-301
1.84024826104789e-298
3.03306001074454e-310
6
-9.370678333643723e-70
-1.3034971086952715e-70
-9.243103292273186e-70

simplify22.0ms

Iterations
IterNodes
done48
148
036

end0.0ms

sample53.0s

Algorithm
intervals
Results
25.1s2194×body1280valid
14.2s7938×body80valid
7.1s1396×body640valid
3.5s538×body320valid
1.6s45×body2560valid
311.0ms225×body160valid