Details

Time bar (total: 2.5m)

sample4.0s

Algorithm
intervals
Results
3.8s984×body10240exit
98.0ms256×body80valid

simplify3.8s

Counts
1 → 1

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

24.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.3b
(* y.re (log (hypot x.re x.im)))
0.2b
(* (atan2 x.im x.re) y.re)
0.2b
(* (atan2 x.im x.re) y.im)

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
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
108.0ms
(* y.re (log (hypot x.re x.im)))
30.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)

simplify1.4s

Counts
93 → 93

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize90.0ms

Local error

Found 4 expressions with local error:

32.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*l* add-exp-log sqrt-prod
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
43.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
132.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.0s

Counts
85 → 85

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

32.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.2b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite42.0ms

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
16.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
10.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
132.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(* (atan2 x.im x.re) y.im)

simplify1.1s

Counts
93 → 93

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
0.2b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- fma-neg diff-log prod-diff log-pow flip--
Counts
3 → 60
Calls
3 calls:
Slowest
13.0ms
(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms
(* (log (hypot x.re x.im)) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)

series355.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
209.0ms
(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
120.0ms
(* (log (hypot x.re x.im)) y.re)
27.0ms
(* (atan2 x.im x.re) y.im)

simplify965.0ms

Counts
69 → 69

prune1.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.2m

Algorithm
intervals
Results
2.1m30733×body10240exit
2.8s8000×body80valid