Details

Time bar (total: 24.7s)

sample570.0ms

Algorithm
intervals
Results
142.0ms257×body80valid
114.0ms70×body1280valid
91.0ms52×body640valid
15.0ms19×body320valid
3.0ms5×body160valid

simplify640.0ms

Counts
1 → 1

prune71.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.8b

localize42.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite83.0ms

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:
20.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
190.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
68 → 68

prune496.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.7b

localize62.0ms

Local error

Found 4 expressions with local error:

29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite89.0ms

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:
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(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)))
36.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series750.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
228.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
216.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
242.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts
51 → 51

prune563.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.7b

localize64.0ms

Local error

Found 4 expressions with local error:

4.2b
(log (exp (* (atan2 x.im x.re) y.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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:
3.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
74.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
220.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
64 → 64

prune626.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.7b

localize63.0ms

Local error

Found 4 expressions with local error:

29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.6b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×add-sqr-sqrt
12×sqrt-prod
11×add-cube-cbrt *-un-lft-identity
6×pow1 unpow-prod-down sqrt-div cube-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×cube-div rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 67
Calls
4 calls:
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(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)))
13.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series386.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
214.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
68.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.1s

Counts
79 → 79

prune580.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 21.7b

regimes380.0ms

Accuracy

75.3% (3.5b remaining)

Error of 23.2b against oracle of 19.6b and baseline of 33.9b

bsearch1.1s

Steps
ItersRangePoint
9
-9.214276440891805e-306
2.072267979179663e-306
-5.879793377467557e-309
8
-9.693252091975913e-68
-3.076054266716539e-71
-1.1973568690300334e-68
10
-4.388311460693464e+76
-6.499932935675829e+62
-4.484553050797036e+64

simplify1.8s

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.4s2165×body1280valid
2.3s7964×body80valid
1.8s1404×body640valid
406.0ms578×body320valid
152.0ms43×body2560valid
89.0ms246×body160valid