Details

Time bar (total: 3.9m)

sample6.8s

Algorithm
intervals
Results
6.5s1466×body10240exit
68.0ms256×body80valid

simplify146.0ms

Calls
1 calls:
Slowest
146.0ms
(* (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))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize58.0ms

Local error

Found 4 expressions with local error:

39.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×sqrt-prod
5×pow1 associate-*l*
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
3×pow1/2
2×rem-sqrt-square flip3-+ log-pow flip-+
1×sin-sum *-commutative
Calls
4 calls:
Slowest
12.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
2.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series305.0ms

Calls
4 calls:
Slowest
173.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
87.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
25.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Calls
27 calls:
Slowest
209.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
202.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
108.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
106.0ms
(* -1 (* y.im (log (/ -1 x.re))))
103.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.5b

localize17.0ms

Local error

Found 4 expressions with local error:

39.0b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt associate-*l*
7×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×pow1/2 sqrt-div log-pow *-commutative
1×rem-sqrt-square flip3-+ sin-sum flip-+
Calls
4 calls:
Slowest
25.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

series271.0ms

Calls
4 calls:
Slowest
136.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
104.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(* (atan2 x.im x.re) y.im)

simplify820.0ms

Calls
23 calls:
Slowest
180.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
114.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
101.0ms
(* -1 (* y.re (log (/ 1 x.re))))
93.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
82.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.9b

localize22.0ms

Local error

Found 4 expressions with local error:

39.0b
(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
(* (log (- x.re)) y.re)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×*-commutative
2×log-pow
1×sin-sum
Calls
4 calls:
Slowest
21.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (log (- x.re)) y.im)
3.0ms
(* (log (- x.re)) y.re)

series316.0ms

Calls
4 calls:
Slowest
140.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
86.0ms
(* (log (- x.re)) y.im)
69.0ms
(* (log (- x.re)) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)

simplify669.0ms

Calls
19 calls:
Slowest
120.0ms
(* -1 (* y.re (log (/ -1 x.re))))
109.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
102.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
100.0ms
(* -1 (* y.im (log (/ -1 x.re))))
67.0ms
(* y.im (- (log -1) (log (/ 1 x.re))))

prune943.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 4 expressions with local error:

39.0b
(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)))

rewrite70.0ms

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
60.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
6.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
1.0ms
(cbrt (log (- x.re)))
1.0ms
(cbrt (log (- x.re)))

series1.3s

Calls
4 calls:
Slowest
421.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
359.0ms
(cbrt (log (- x.re)))
330.0ms
(cbrt (log (- x.re)))
154.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify918.0ms

Calls
43 calls:
Slowest
122.0ms
(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
98.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
96.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
68.0ms
(* (sin (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im))) (cos (* (atan2 x.im x.re) y.re)))
57.0ms
(pow (- (log (/ -1 x.re))) 1/3)

prune1.4s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 3.9b

regimes1.2s

Accuracy

29.4% (7.9b remaining)

Error of 12.9b against oracle of 5.0b and baseline of 16.2b

bsearch14.4s

end0.0ms

sample3.4m

Algorithm
intervals
Results
3.3m47699×body10240exit
3.1s8000×body80valid