Details

Time bar (total: 2.4m)

sample4.3s

Algorithm
intervals
Results
4.1s1094×body10240exit
102.0ms256×body80valid

simplify689.0ms

Calls
1 calls:
Slowest
688.0ms
(* (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))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

30.1b
(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
(* (atan2 x.im x.re) y.re)
0.2b
(* y.re (log (hypot x.re x.im)))

rewrite34.0ms

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
Calls
4 calls:
Slowest
14.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series300.0ms

Calls
4 calls:
Slowest
159.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
92.0ms
(* y.re (log (hypot x.re x.im)))
25.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)

simplify1.8s

Calls
48 calls:
Slowest
307.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
277.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
254.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
250.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
128.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

30.1b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.6b
(log (exp (* y.re (log (hypot x.re x.im)))))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (atan2 x.im x.re) y.re)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
17×log-pow
15×log-prod
14×*-un-lft-identity add-cube-cbrt
13×exp-prod
10×pow1 associate-*r*
9×associate-*l* add-exp-log
8×add-cbrt-cube
6×exp-sum
5×add-log-exp
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×exp-to-pow rem-log-exp pow-prod-down prod-exp cbrt-unprod
1×cos-sum fma-udef
Calls
4 calls:
Slowest
11.0ms
(log (exp (* 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)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series304.0ms

Calls
4 calls:
Slowest
165.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
99.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
22.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)

simplify2.9s

Calls
54 calls:
Slowest
354.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
348.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
316.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
285.0ms
(log (exp (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.re)))
222.0ms
(log (exp (* y.re (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))))))

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

30.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
52×hypot-def
32×*-un-lft-identity
24×swap-sqr
21×*-commutative unswap-sqr
16×sqrt-prod
11×associate-*l*
10×distribute-lft-out
8×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×+-commutative associate-*r*
2×rem-sqrt-square cos-sum sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
119.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)

series332.0ms

Calls
4 calls:
Slowest
196.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(* (atan2 x.im x.re) y.im)

simplify2.1s

Calls
77 calls:
Slowest
371.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
325.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
319.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
297.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
274.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune2.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch6.0ms

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m29603×body10240exit
3.2s8000×body80valid