Details

Time bar (total: 18.6s)

sample290.0ms

Algorithm
intervals
Results
96.0ms247×body80valid
55.0ms59×body1280valid
31.0ms47×body640valid
12.0ms25×body320valid
3.0ms8×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize81.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite94.0ms

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:
15.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
195.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.3s

Counts
68 → 68
Iterations

Useful iterations: 3 (362.0ms)

IterNodesCost
095836
1193778
2437690
3816677
41651677
54087677
done5001677

prune485.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize46.0ms

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)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite100.0ms

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:
42.0ms
(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)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
127.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
25.0ms
(* (atan2 x.im x.re) y.im)
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.8s

Counts
81 → 81
Iterations

Useful iterations: 4 (2.0s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune491.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.3b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×cbrt-prod
14×add-cube-cbrt *-un-lft-identity
10×pow1
9×sqrt-prod
8×add-exp-log associate-*l* add-cbrt-cube
6×unpow-prod-down cube-prod associate-*r*
4×sqrt-div add-log-exp
2×cube-div cbrt-div flip3-+ pow1/3 pow-prod-down prod-exp log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 82
Calls
4 calls:
14.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series268.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
27.0ms
(* (atan2 x.im x.re) y.im)
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify2.1s

Counts
94 → 94
Iterations

Useful iterations: 3 (907.0ms)

IterNodesCost
01461404
13311042
2782958
32348944
done5001944

prune985.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
0.0b
(exp (* (atan2 x.im x.re) y.im))
1.2b
(* (atan2 x.im x.re) y.im)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
7×add-exp-log add-cbrt-cube associate-/l*
5×pow1 add-log-exp
4×sqr-pow
3×div-exp associate-*r* associate-*l* associate-/r*
1×cbrt-undiv pow-to-exp exp-prod exp-to-pow frac-2neg pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv rem-exp-log unswap-sqr
Counts
3 → 73
Calls
3 calls:
22.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(exp (* (atan2 x.im x.re) y.im))
7.0ms
(* (atan2 x.im x.re) y.im)

series213.0ms

Counts
3 → 9
Calls
3 calls:
139.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
53.0ms
(exp (* (atan2 x.im x.re) y.im))
21.0ms
(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts
82 → 82
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01401140
12581099
26741035
322511026
done50001024

prune371.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes618.0ms

bsearch2.0ms