Details

Time bar (total: 3.7m)

sample6.2s

Algorithm
intervals
Results
6.0s1445×body10240exit
67.0ms256×body80valid

simplify176.0ms

Calls
1 calls:
Slowest
175.0ms
(* (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))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize54.0ms

Local error

Found 4 expressions with local error:

39.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×sqrt-prod
4×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
3×associate-*l*
2×rem-sqrt-square flip3-+ pow1/2 flip-+
1×sin-sum *-commutative
Calls
4 calls:
Slowest
22.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series361.0ms

Calls
4 calls:
Slowest
218.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(* (atan2 x.im x.re) y.im)

simplify949.0ms

Calls
27 calls:
Slowest
253.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
180.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
153.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
84.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
76.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.0b

localize25.0ms

Local error

Found 4 expressions with local error:

38.9b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (log (- x.re)) y.im)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity associate-*l* add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×sqrt-div *-commutative
1×rem-sqrt-square flip3-+ pow1/2 sin-sum log-pow flip-+
Calls
4 calls:
Slowest
11.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(* (log (- x.re)) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series456.0ms

Calls
4 calls:
Slowest
234.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
129.0ms
(* (log (- x.re)) y.im)
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(* (atan2 x.im x.re) y.im)

simplify893.0ms

Calls
23 calls:
Slowest
195.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
139.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
130.0ms
(* -1 (* y.im (log (/ -1 x.re))))
85.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
68.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

38.9b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (log (- x.re)) y.im)
0.3b
(* (atan2 x.im x.re) y.re)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×*-commutative
1×sin-sum log-pow
Calls
4 calls:
Slowest
11.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms
(* (log (- x.re)) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)

series340.0ms

Calls
4 calls:
Slowest
180.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
106.0ms
(* (log (- x.re)) y.im)
30.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)

simplify630.0ms

Calls
19 calls:
Slowest
151.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
141.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
102.0ms
(* -1 (* y.im (log (/ -1 x.re))))
60.0ms
(* y.im (- (log -1) (log (/ 1 x.re))))
53.0ms
(+ (* y.im (log -1)) (+ (* (atan2 x.im x.re) y.re) (* y.im (log x.re))))

prune967.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

38.9b
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
0.5b
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
0.5b
(cbrt (log (- x.re)))
0.5b
(cbrt (log (- x.re)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-prod
13×pow1
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×pow1/3 add-exp-log
4×add-cbrt-cube log-pow insert-posit16 add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus sin-sum prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
93.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
7.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
1.0ms
(cbrt (log (- x.re)))
1.0ms
(cbrt (log (- x.re)))

series1.7s

Calls
4 calls:
Slowest
543.0ms
(cbrt (log (- x.re)))
486.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
470.0ms
(cbrt (log (- x.re)))
190.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify941.0ms

Calls
43 calls:
Slowest
131.0ms
(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
111.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
110.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
77.0ms
(* (sin (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im))) (cos (* (atan2 x.im x.re) y.re)))
74.0ms
(pow (- (log -1) (log (/ 1 x.re))) 1/3)

prune1.5s

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 5.1b

regimes1.2s

Accuracy

47.2% (5.8b remaining)

Error of 10.7b against oracle of 4.9b and baseline of 15.9b

bsearch2.3s

end0.0ms

sample3.3m

Algorithm
intervals
Results
3.3m47210×body10240exit
3.1s8000×body80valid