Details

Time bar (total: 2.3m)

sample4.3s

Algorithm
intervals
Results
4.1s1042×body10240exit
69.0ms256×body80valid

simplify337.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
336.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

23.9b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* y.re (log (hypot x.re x.im)))
0.3b
(* (atan2 x.im x.re) y.re)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
Slowest
24.0ms
(* y.re (log (hypot x.re x.im)))
10.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
114.0ms
(* y.re (log (hypot x.re x.im)))
34.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.re)

simplify2.0s

Counts
48 → 93
Calls
48 calls:
Slowest
369.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
349.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
325.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
315.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
123.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.im)

rewrite55.0ms

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×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 70
Calls
4 calls:
Slowest
36.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
432.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
183.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts
36 → 82
Calls
36 calls:
Slowest
329.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
322.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
301.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
295.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
288.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes259.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch5.0ms

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m29755×body10240exit
3.2s8000×body80valid