Details

Time bar (total: 3.8m)

sample7.1s

Algorithm
intervals
Results
6.7s1584×body10240exit
125.0ms256×body80valid

simplify381.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
380.0ms
(* (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))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize108.0ms

Local error

Found 4 expressions with local error:

33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite63.0ms

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
36.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
11.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
135.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
37 → 75
Calls
37 calls:
Slowest
422.0ms
(* (* (* (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))
362.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
295.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
268.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
255.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.3b

localize84.0ms

Local error

Found 4 expressions with local error:

33.4b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
29.0b
(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)

rewrite63.0ms

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
31.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (atan2 x.im x.re) y.re)

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
137.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(* (atan2 x.im x.re) y.re)

simplify2.2s

Counts
39 → 78
Calls
39 calls:
Slowest
450.0ms
(* (* (* (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))
359.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
339.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
290.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
149.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.0b

localize48.0ms

Local error

Found 4 expressions with local error:

33.4b
(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)
0.3b
(* (atan2 x.im x.re) y.im)

rewrite81.0ms

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
41.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms
(* (log (- x.re)) y.re)
12.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (atan2 x.im x.re) y.im)

series397.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
130.0ms
(* (log (- x.re)) y.re)
36.0ms
(* (atan2 x.im x.re) y.im)
31.0ms
(* (atan2 x.im x.re) y.re)

simplify1.7s

Counts
40 → 79
Calls
40 calls:
Slowest
369.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
319.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
279.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
153.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
122.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.9b

localize69.0ms

Local error

Found 4 expressions with local error:

33.4b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
33.4b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
33.4b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
0.6b
(cbrt (sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod sin-sum
1×pow1/3
Counts
4 → 39
Calls
4 calls:
Slowest
26.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms
(cbrt (sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re))))

series846.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
277.0ms
(cbrt (sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re))))
200.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
193.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
177.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
18 → 51
Calls
18 calls:
Slowest
362.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
327.0ms
(pow (sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re))))) 1/3)
221.0ms
(exp (* 1/3 (+ (log (atan2 x.im x.re)) (log y.re))))
158.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
153.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.0s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 5.9b

regimes1.5s

Accuracy

49.6% (5.4b remaining)

Error of 10.4b against oracle of 5.0b and baseline of 15.7b

bsearch19.0ms

end0.0ms

sample3.4m

Algorithm
intervals
Results
3.3m46441×body10240exit
3.5s8000×body80valid