Details

Time bar (total: 4.0m)

sample5.9s

Algorithm
intervals
Results
5.7s1388×body10240exit
128.0ms256×body80valid

simplify388.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
388.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize63.0ms

Local error

Found 4 expressions with local error:

37.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*l* add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
Slowest
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
118.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
37 → 75
Calls
37 calls:
Slowest
439.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
333.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
289.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
275.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
265.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.7b

localize75.0ms

Local error

Found 4 expressions with local error:

37.2b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
31.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.3b
(* (atan2 x.im x.re) y.re)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r*
4×insert-posit16 add-log-exp
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square flip3-+ sin-sum flip-+
Counts
4 → 66
Calls
4 calls:
Slowest
28.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(* (atan2 x.im x.re) y.re)

series375.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
143.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(* (atan2 x.im x.re) y.re)

simplify2.1s

Counts
39 → 78
Calls
39 calls:
Slowest
418.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
345.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
304.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
236.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
141.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize80.0ms

Local error

Found 4 expressions with local error:

37.2b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
37.2b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
37.2b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
31.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 43
Calls
4 calls:
Slowest
37.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
28.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
22.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series593.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
186.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
176.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.5s

Counts
22 → 55
Calls
22 calls:
Slowest
286.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
241.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
150.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
146.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
119.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.8b

localize66.0ms

Local error

Found 4 expressions with local error:

37.2b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (log (- x.re)) y.re)
0.3b
(* (atan2 x.im x.re) y.re)
0.2b
(* (atan2 x.im x.re) y.im)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
9×associate-*r*
4×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow
Counts
4 → 67
Calls
4 calls:
Slowest
27.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms
(* (atan2 x.im x.re) y.im)
13.0ms
(* (log (- x.re)) y.re)
11.0ms
(* (atan2 x.im x.re) y.re)

series356.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
121.0ms
(* (log (- x.re)) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)

simplify1.6s

Counts
40 → 79
Calls
40 calls:
Slowest
326.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
293.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
280.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
132.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
128.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

regimes747.0ms

Accuracy

32.2% (7.6b remaining)

Error of 12.4b against oracle of 4.9b and baseline of 16.0b

bsearch10.5s

end0.0ms

sample3.5m

Algorithm
intervals
Results
3.4m47987×body10240exit
3.6s8000×body80valid