Details

Time bar (total: 2.4m)

sample4.0s

Algorithm
intervals
Results
3.8s937×body10240exit
79.0ms256×body80valid

simplify331.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
330.0ms
(* (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))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

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)

rewrite25.0ms

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

series370.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
95.0ms
(* y.re (log (hypot x.re x.im)))
30.0ms
(* (atan2 x.im x.re) y.im)
27.0ms
(* (atan2 x.im x.re) y.re)

simplify2.0s

Counts
48 → 93
Calls
48 calls:
Slowest
352.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
343.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
325.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
292.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
155.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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)

rewrite40.0ms

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
14.0ms
(* y.re (log (hypot x.re x.im)))
12.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
97.0ms
(* y.re (log (hypot x.re x.im)))
97.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
29.0ms
(* (atan2 x.im x.re) y.im)

simplify2.8s

Counts
50 → 95
Calls
50 calls:
Slowest
323.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
298.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
286.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
204.0ms
(log (exp (* y.re (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))))))
193.0ms
(log (exp (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.re)))

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

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)

rewrite75.0ms

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
32.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series448.0ms

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)))
132.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts
37 → 85
Calls
37 calls:
Slowest
370.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
353.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
345.0ms
(* (* (* (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))
276.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
213.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes252.0ms

Accuracy

0% (0.0b remaining)

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

bsearch6.0ms

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30412×body10240exit
4.4s8000×body80valid