Details

Time bar (total: 1.8m)

sample292.0ms

Algorithm
intervals
Results
57.0ms59×body1280valid
48.0ms8×body160valid
40.0ms247×body80valid
31.0ms47×body640valid
12.0ms25×body320valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
01937
13637
219636
3334936
done500036

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.7b

localize61.0ms

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)))

rewrite65.0ms

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)))
37.0ms
(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:
32.0ms
(* (atan2 x.im x.re) y.im)
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
245.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.9s

Counts
68 → 68
Iterations

Useful iterations: done (4.9s)

IterNodesCost
095836
1349778
done5001697

prune554.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize31.0ms

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)))

rewrite67.0ms

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:
30.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
13.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(* (atan2 x.im x.re) y.im)
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
126.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify18.3s

Counts
81 → 81
Iterations

Useful iterations: done (18.3s)

IterNodesCost
01321042
1601984
done5000878

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (cbrt (* (+ (* x.im x.im) (* x.re x.re)) (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)))
40.3b
(cbrt (* (+ (* x.im x.im) (* x.re x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×pow1
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log cbrt-div sqrt-div associate-*l* add-cbrt-cube
7×flip3-+ flip-+
6×associate-*r*
4×frac-times add-log-exp
3×sqrt-prod
2×pow1/3 associate-*r/ pow-prod-down associate-*l/ prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 70
Calls
4 calls:
53.0ms
(* (log (cbrt (* (+ (* x.im x.im) (* x.re x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
27.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(cbrt (* (+ (* x.im x.im) (* x.re x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* (log (cbrt (* (+ (* x.im x.im) (* x.re x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
76.0ms
(cbrt (* (+ (* x.im x.im) (* x.re x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify1.1m

Counts
82 → 82
Iterations

Useful iterations: done (1.1m)

IterNodesCost
01531520
16061457
done50001015

prune672.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (- (* (log (- x.im)) y.re) (* (atan2 x.im x.re) y.im)))
0.1b
(* (log (- x.im)) y.re)
1.2b
(* (atan2 x.im x.re) y.im)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
7×add-exp-log associate-*l* add-cbrt-cube
6×associate-*r* add-log-exp
3×exp-prod
2×exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg exp-diff diff-log log-pow
Counts
3 → 52
Calls
3 calls:
40.0ms
(exp (- (* (log (- x.im)) y.re) (* (atan2 x.im x.re) y.im)))
15.0ms
(* (log (- x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series231.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(exp (- (* (log (- x.im)) y.re) (* (atan2 x.im x.re) y.im)))
102.0ms
(* (log (- x.im)) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)

simplify3.9s

Counts
61 → 61
Iterations

Useful iterations: done (3.9s)

IterNodesCost
0104582
1452552
done5000485

prune189.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.4b

regimes570.0ms

Accuracy

69.9% (6.3b remaining)

Error of 9.9b against oracle of 3.6b and baseline of 24.5b

bsearch519.0ms

Steps
ItersRangePoint
12
-3.2120421718303128e-288
1.4555397631981125e-288
-3.5665767812761e-310
9
-1.5941905313614663e-254
-3.6230643635894966e-261
-1.5758027345738268e-254
8
-4.727723571273103e-199
-4.669540934034347e-203
-5.429027010745199e-203

simplify27.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03571
15063
done5063

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.3s1963×body1280valid
1.8s7927×body80valid
1.6s1424×body640valid
380.0ms654×body320valid
156.0ms322×body160valid