Details

Time bar (total: 2.4m)

sample4.6s

Algorithm
intervals
Results
4.3s1042×body10240exit
76.0ms256×body80valid

simplify3.9s

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize101.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.4b
(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)

rewrite79.0ms

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×sqrt-div insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
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.im)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series484.0ms

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)))
117.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
89.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.3s

Counts
75 → 75

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize46.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.2b
(* (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))

rewrite35.0ms

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×insert-posit16
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-- diff-log flip-+ flip--
Counts
4 → 70
Calls
4 calls:
Slowest
13.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
125.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
74.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms
(* (atan2 x.im x.re) y.im)

simplify952.0ms

Counts
82 → 82

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

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×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 52
Calls
3 calls:
Slowest
10.0ms
(* (log (- x.re)) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

series252.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
130.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
104.0ms
(* (log (- x.re)) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify2.1s

Counts
61 → 61

prune829.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes368.0ms

Accuracy

97% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 6.8b

bsearch1.3s

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m29790×body10240exit
3.2s8000×body80valid