Details

Time bar (total: 4.0m)

sample5.7s

Algorithm
intervals
Results
5.0s1339×body10240exit
617.0ms256×body80valid

simplify781.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
780.0ms
(* (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: 33.4b

localize104.0ms

Local error

Found 4 expressions with local error:

36.1b
(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
(* (atan2 x.im x.re) y.im)

rewrite74.0ms

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×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
Slowest
34.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(* (atan2 x.im x.re) y.im)

series355.0ms

Counts
4 → 12
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)))
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts
36 → 72
Calls
36 calls:
Slowest
337.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
332.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
301.0ms
(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))))
212.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize80.0ms

Local error

Found 4 expressions with local error:

36.1b
(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
(* (atan2 x.im x.re) y.im)
0.3b
(* (log (- x.re)) y.im)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×pow1
9×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×associate-*l*
6×associate-*r*
4×insert-posit16 add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum log-pow flip-+
Counts
4 → 64
Calls
4 calls:
Slowest
28.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (log (- x.re)) y.im)
5.0ms
(* (atan2 x.im x.re) y.im)

series375.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
96.0ms
(* (log (- x.re)) y.im)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify2.0s

Counts
38 → 76
Calls
38 calls:
Slowest
337.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
292.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
290.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.im y.im) y.im))
277.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
131.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize85.0ms

Local error

Found 4 expressions with local error:

36.2b
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
31.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.6b
(cbrt (log (- x.re)))
0.6b
(cbrt (log (- x.re)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×pow1/3 sqrt-div log-pow
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 51
Calls
4 calls:
Slowest
90.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms
(cbrt (log (- x.re)))
1.0ms
(cbrt (log (- x.re)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
507.0ms
(cbrt (log (- x.re)))
505.0ms
(cbrt (log (- x.re)))
192.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
28 → 63
Calls
28 calls:
Slowest
336.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
282.0ms
(pow (- (log -1) (log (/ 1 x.re))) 1/3)
252.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
250.0ms
(pow (- (log -1) (log (/ 1 x.re))) 1/3)
202.0ms
(pow (- (log (/ -1 x.re))) 1/3)

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize73.0ms

Local error

Found 4 expressions with local error:

36.2b
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
31.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.6b
(cbrt (log (- x.re)))
0.6b
(cbrt (log (- x.re)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×pow1/3 sqrt-div log-pow
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 51
Calls
4 calls:
Slowest
167.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms
(cbrt (log (- x.re)))
1.0ms
(cbrt (log (- x.re)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
465.0ms
(cbrt (log (- x.re)))
445.0ms
(cbrt (log (- x.re)))
159.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
28 → 63
Calls
28 calls:
Slowest
325.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
263.0ms
(pow (- (log -1) (log (/ 1 x.re))) 1/3)
262.0ms
(pow (- (log (/ -1 x.re))) 1/3)
250.0ms
(pow (- (log -1) (log (/ 1 x.re))) 1/3)
219.0ms
(* (sin (* (* (cbrt (log (- x.re))) (cbrt (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im))) (cos (* (atan2 x.im x.re) y.re)))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

regimes783.0ms

Accuracy

44.1% (6.3b remaining)

Error of 11.3b against oracle of 5.0b and baseline of 16.2b

bsearch5.7s

end0.0ms

sample3.5m

Algorithm
intervals
Results
3.4m47643×body10240exit
3.6s8000×body80valid