Details

Time bar (total: 9.8s)

sample222.0ms

Algorithm
intervals
Results
67.0ms255×body80valid
43.0ms57×body1280valid
27.0ms49×body640valid
11.0ms31×body320valid
4.0ms11×body160valid

simplify30.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize59.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
28.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite54.0ms

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:
8.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
171.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify69.0ms

Counts
68 → 68

prune356.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (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)
1.5b
(* (atan2 x.im x.re) y.im)
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
14.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms
(* (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)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
101.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify72.0ms

Counts
78 → 78

prune294.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.8b

localize43.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series162.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify135.0ms

Counts
72 → 72

prune488.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
0.0b
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity add-log-exp
8×add-exp-log add-cbrt-cube
7×associate-*l*
6×associate-*r*
3×exp-prod
2×sub-neg diff-log exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff log-pow flip--
Counts
4 → 64
Calls
4 calls:
20.0ms
(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
13.0ms
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
8.0ms
(* (log x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series268.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
110.0ms
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
71.0ms
(* (log x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)

simplify82.0ms

Counts
76 → 76

prune200.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.8b

regimes271.0ms

Accuracy

61.4% (6.2b remaining)

Error of 9.7b against oracle of 3.5b and baseline of 19.5b

bsearch191.0ms

Steps
ItersRangePoint
6
1.3461159678365104e-246
5.574194012540767e-246
1.948311381039227e-246
8
-7.258689502823683e-75
-3.998174291922989e-78
-6.606413508708837e-75

simplify1.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.0s1485×body640valid
1.7s2001×body1280valid
1.2s8024×body80valid
350.0ms676×body320valid
73.0ms299×body160valid