Details

Time bar (total: 2.4m)

sample4.8s

Algorithm
intervals
Results
4.5s1009×body10240exit
133.0ms256×body80valid

simplify429.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
428.0ms
(* (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

localize53.0ms

Local error

Found 4 expressions with local error:

27.1b
(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)))

rewrite23.0ms

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
7.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(* (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)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
105.0ms
(* y.re (log (hypot x.re x.im)))
34.0ms
(* (atan2 x.im x.re) y.im)
30.0ms
(* (atan2 x.im x.re) y.re)

simplify1.9s

Counts
48 → 93
Calls
48 calls:
Slowest
361.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
314.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
275.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
261.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
148.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

27.1b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0b
(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)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt log-prod
11×*-un-lft-identity add-cube-cbrt
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* exp-sum
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum exp-prod exp-to-pow rem-log-exp fma-udef
Counts
4 → 76
Calls
4 calls:
Slowest
10.0ms
(log (exp (* 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)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
118.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
30.0ms
(* (atan2 x.im x.re) y.im)
22.0ms
(* (atan2 x.im x.re) y.re)

simplify3.1s

Counts
42 → 88
Calls
42 calls:
Slowest
725.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
369.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
314.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
265.0ms
(log (exp (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.re)))
210.0ms
(log (exp (* y.re (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))))))

prune1.5s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30668×body10240exit
3.7s8000×body80valid