Details

Time bar (total: 2.4m)

sample3.7s

Algorithm
intervals
Results
3.5s925×body10240exit
64.0ms256×body80valid

simplify335.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
334.0ms
(* (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))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

26.6b
(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)))
0.2b
(* (atan2 x.im x.re) y.re)

rewrite24.0ms

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
associate-*l*
log-prod
expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
cos-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
Slowest
6.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
82.0ms
(* y.re (log (hypot x.re x.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify3.6s

Counts
100 → 93
Calls
100 calls:
Slowest
393.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
371.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
340.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
315.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
250.0ms
(* (* (* y.re (log (hypot x.re x.im))) (* y.re (log (hypot x.re x.im)))) (* y.re (log (hypot x.re x.im))))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.6b
(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)

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
pow1 *-un-lft-identity add-cube-cbrt
add-cbrt-cube add-exp-log sqrt-prod
expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
associate-*r* associate-*l*
rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 70
Calls
4 calls:
Slowest
32.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
11.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(* (atan2 x.im x.re) y.im)

simplify3.8s

Counts
87 → 82
Calls
87 calls:
Slowest
337.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
324.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
317.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
293.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
281.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes311.0ms

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
2.0m30363×body10240exit
3.7s8000×body80valid