Details

Time bar (total: 11.1s)

sample345.0ms

Algorithm
intervals
Results
111.0ms57×body640valid
86.0ms71×body1280valid
31.0ms246×body80valid
13.0ms22×body320valid
4.0ms2×body2560valid
2.0ms7×body160valid

simplify38.0ms

Counts
1 → 1

prune46.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.im)
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

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:
19.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
177.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Counts
68 → 68

prune367.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.im)
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1
7×add-exp-log
6×add-cbrt-cube
4×add-log-exp
3×unpow-prod-down pow-unpow associate-*r* associate-*l* sqrt-prod
2×sqrt-div
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 sin-sum pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ unpow1/2 unswap-sqr sqr-pow
Counts
4 → 59
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
170.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Counts
71 → 71

prune381.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

localize61.0ms

Local error

Found 4 expressions with local error:

28.9b
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×unpow-prod-down pow-unpow sin-sum
1×pow-to-exp pow-pow pow-exp unpow1/2 sqr-pow
Counts
4 → 42
Calls
4 calls:
10.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
20.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(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)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
169.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
169.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
164.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify41.0ms

Counts
54 → 54

prune408.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 17.5b

localize47.0ms

Local error

Found 4 expressions with local error:

10.4b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
6×pow1 unpow-prod-down
5×add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow cube-prod sqrt-prod
2×sqrt-div sqr-pow
1×cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 sin-sum pow1/3 unpow3 pow-exp rem-cbrt-cube flip-+ unpow1/2
Counts
4 → 62
Calls
4 calls:
13.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/2)
169.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify84.0ms

Counts
74 → 74

prune382.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 17.5b

regimes440.0ms

Accuracy

77.4% (3.2b remaining)

Error of 22.5b against oracle of 19.3b and baseline of 33.5b

bsearch155.0ms

Steps
ItersRangePoint
8
-6.254856394973222e-307
1.2846325586916615e-306
-5.271177671170173e-309

simplify1.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.7s2111×body1280valid
1.3s7987×body80valid
1.2s1404×body640valid
312.0ms538×body320valid
83.0ms49×body2560valid
53.0ms223×body160valid