Details

Time bar (total: 2.5m)

sample3.9s

Algorithm
intervals
Results
3.7s959×body10240exit
71.0ms256×body80valid

simplify390.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
389.0ms
(* (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))))

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize64.0ms

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)

rewrite28.0ms

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
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
7.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.re)

series285.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
93.0ms
(* y.re (log (hypot x.re x.im)))
33.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.re)

simplify1.6s

Counts
48 → 93
Calls
48 calls:
Slowest
253.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
247.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
244.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
236.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
168.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize64.0ms

Local error

Found 4 expressions with local error:

32.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(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)

rewrite69.0ms

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
32.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(* (atan2 x.im x.re) y.im)

series342.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms
(* (atan2 x.im x.re) y.im)

simplify2.0s

Counts
36 → 82
Calls
36 calls:
Slowest
369.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
369.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
336.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
288.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
262.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

32.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sub-neg flip3-+ flip3-- fma-neg diff-log prod-diff flip-+ hypot-def flip--
Counts
4 → 81
Calls
4 calls:
Slowest
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (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.im)

series885.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
627.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
178.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(* (atan2 x.im x.re) y.im)

simplify2.3s

Counts
42 → 93
Calls
42 calls:
Slowest
342.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
333.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
324.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
320.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
247.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (log (hypot x.re x.im)) y.re)
0.0b
(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.0b
(hypot x.re x.im)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×pow1
8×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
7×associate-*l*
6×associate-*r* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef sub-neg flip3-- fma-neg diff-log prod-diff log-pow flip--
Counts
4 → 71
Calls
4 calls:
Slowest
23.0ms
(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
14.0ms
(* (log (hypot x.re x.im)) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
0.0ms
(hypot x.re x.im)

series435.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
193.0ms
(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
146.0ms
(* (log (hypot x.re x.im)) y.re)
65.0ms
(hypot x.re x.im)
31.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
34 → 83
Calls
34 calls:
Slowest
344.0ms
(* (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))) (* (* y.re y.re) y.re))
312.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
233.0ms
(/ (exp (* (log (hypot x.re x.im)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
186.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
100.0ms
(- (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))

prune1.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.2m

Algorithm
intervals
Results
2.1m31061×body10240exit
3.2s8000×body80valid