Details

Time bar (total: 2.4m)

sample4.0s

Algorithm
intervals
Results
3.7s937×body10240exit
158.0ms256×body80valid

simplify340.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
339.0ms
(* (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))))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

23.0b
(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.im)
0.2b
(* (atan2 x.im x.re) y.re)

rewrite53.0ms

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
22.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(* y.re (log (hypot x.re x.im)))
10.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
100.0ms
(* y.re (log (hypot x.re x.im)))
29.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)

simplify1.7s

Counts
48 → 93
Calls
48 calls:
Slowest
291.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
281.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
273.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
232.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
135.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

23.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.9b
(log (exp (* y.re (log (hypot x.re x.im)))))
0.3b
(* y.re (log (hypot x.re x.im)))
0.2b
(* (atan2 x.im x.re) y.im)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
21×log-prod
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×pow1
8×add-cbrt-cube add-exp-log
7×associate-*r*
6×distribute-rgt-in distribute-lft-in associate-*l* exp-sum
5×add-log-exp
4×expm1-log1p-u log-pow insert-posit16 log1p-expm1-u
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 → 83
Calls
4 calls:
Slowest
6.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
115.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
92.0ms
(* y.re (log (hypot x.re x.im)))
31.0ms
(* (atan2 x.im x.re) y.im)

simplify3.1s

Counts
50 → 95
Calls
50 calls:
Slowest
651.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
348.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
320.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
205.0ms
(log (exp (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.re)))
183.0ms
(log (exp (* (log (sqrt (hypot x.re x.im))) y.re)))

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0b
(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.re)

rewrite63.0ms

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
30.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
133.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
70.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.1s

Counts
37 → 85
Calls
37 calls:
Slowest
347.0ms
(* (* (* (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))
323.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
299.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
271.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
241.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes267.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch3.0ms

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.1m30412×body10240exit
3.8s8000×body80valid