Details

Time bar (total: 2.4m)

sample3.8s

Algorithm
intervals
Results
3.7s953×body10240exit
71.0ms256×body80valid

simplify298.0ms

Calls
1 calls:
Slowest
297.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize77.0ms

Local error

Found 4 expressions with local error:

30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.re)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 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
Calls
4 calls:
Slowest
28.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series372.0ms

Calls
4 calls:
Slowest
201.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms
(* (atan2 x.im x.re) y.re)

simplify1.8s

Calls
36 calls:
Slowest
338.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
294.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
277.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
249.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
216.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize36.0ms

Local error

Found 4 expressions with local error:

30.6b
(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.im)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite66.0ms

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* add-log-exp
4×insert-posit16
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 sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Calls
4 calls:
Slowest
23.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
19.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(* (atan2 x.im x.re) y.im)

series406.0ms

Calls
4 calls:
Slowest
180.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
139.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms
(* (atan2 x.im x.re) y.im)

simplify2.2s

Calls
39 calls:
Slowest
442.0ms
(* (* (* (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))
336.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
296.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
247.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
236.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (log (- x.re)) y.re)
0.3b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
3×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Calls
3 calls:
Slowest
18.0ms
(* (log (- x.re)) y.re)
15.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms
(* (atan2 x.im x.re) y.im)

series290.0ms

Calls
3 calls:
Slowest
154.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
105.0ms
(* (log (- x.re)) y.re)
32.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Calls
28 calls:
Slowest
343.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
314.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
195.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
163.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
162.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))

prune756.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes249.0ms

Accuracy

93.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 7.3b

bsearch1.4s

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30138×body10240exit
3.6s8000×body80valid