Details

Time bar (total: 3.9m)

sample6.6s

Algorithm
intervals
Results
6.3s1439×body10240exit
104.0ms256×body80valid

simplify373.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
372.0ms
(* (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))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize63.0ms

Local error

Found 4 expressions with local error:

35.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.re)

rewrite58.0ms

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
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (atan2 x.im x.re) y.re)

series356.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(* (atan2 x.im x.re) y.re)

simplify1.7s

Counts
36 → 72
Calls
36 calls:
Slowest
360.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
299.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
298.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
211.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
209.0ms
(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: 10.9b

localize73.0ms

Local error

Found 4 expressions with local error:

35.3b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.re)
0.2b
(* (atan2 x.im x.re) y.im)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
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 flip-+
Counts
4 → 63
Calls
4 calls:
Slowest
14.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(* (atan2 x.im x.re) y.re)

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)

simplify1.6s

Counts
38 → 75
Calls
38 calls:
Slowest
334.0ms
(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.re y.re) y.re))
287.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
227.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
132.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.9b

localize51.0ms

Local error

Found 4 expressions with local error:

35.3b
(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)
0.2b
(* (atan2 x.im x.re) y.im)

rewrite34.0ms

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
14.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(* (log (- x.re)) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(* (atan2 x.im x.re) y.re)

series394.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
211.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
124.0ms
(* (log (- x.re)) y.re)
32.0ms
(* (atan2 x.im x.re) y.re)
27.0ms
(* (atan2 x.im x.re) y.im)

simplify1.7s

Counts
40 → 79
Calls
40 calls:
Slowest
330.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
297.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
264.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
168.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
143.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

localize56.0ms

Local error

Found 4 expressions with local error:

35.3b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
35.3b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
35.3b
(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))))

rewrite68.0ms

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
27.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(cbrt (sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re))))

series818.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(cbrt (sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re))))
209.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
192.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
173.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
18 → 51
Calls
18 calls:
Slowest
333.0ms
(pow (sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re))))) 1/3)
321.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
223.0ms
(exp (* 1/3 (+ (log (atan2 x.im x.re)) (log y.re))))
152.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
151.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune935.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.8b

regimes1.1s

Accuracy

63.3% (5.6b remaining)

Error of 10.4b against oracle of 4.8b and baseline of 20.0b

bsearch12.0ms

end0.0ms

sample3.5m

Algorithm
intervals
Results
3.4m46926×body10240exit
3.8s8000×body80valid