Details

Time bar (total: 15.3s)

sample370.0ms

Algorithm
intervals
Results
107.0ms248×body80valid
92.0ms66×body1280valid
49.0ms51×body640valid
7.0ms17×body160valid
7.0ms11×body320valid

simplify44.0ms

Counts
1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.9b

localize82.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (atan2 x.im x.re) y.im)
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
293.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify68.0ms

Counts
68 → 68

prune514.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.6b
(* (atan2 x.im x.re) y.im)
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
15.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
33.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
129.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
36.0ms
(* (atan2 x.im x.re) y.im)
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify79.0ms

Counts
78 → 78

prune396.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im)))
0.0b
(- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im))
0.1b
(* y.re (log (/ -1 x.re)))
2.6b
(* (atan2 x.im x.re) y.im)

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
130×log-prod
117×distribute-rgt-in distribute-lft-in
104×associate--l+
90×times-frac
83×add-sqr-sqrt
79×add-cube-cbrt *-un-lft-identity
54×exp-sum
10×div-inv
9×pow1 add-log-exp
8×add-exp-log add-cbrt-cube
7×associate-*r*
6×associate-*l*
3×exp-prod
2×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff log-pow flip--
Counts
4 → 194
Calls
4 calls:
104.0ms
(exp (- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im)))
78.0ms
(- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im))
27.0ms
(* y.re (log (/ -1 x.re)))
14.0ms
(* (atan2 x.im x.re) y.im)

series278.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(exp (- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im)))
116.0ms
(- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im))
69.0ms
(* y.re (log (/ -1 x.re)))
20.0ms
(* (atan2 x.im x.re) y.im)

simplify96.0ms

Counts
206 → 206

prune904.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im))
0.1b
(log (exp (exp (- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im)))))
0.1b
(* y.re (log (/ -1 x.re)))
2.6b
(* (atan2 x.im x.re) y.im)

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
133×log-prod
117×distribute-rgt-in distribute-lft-in
104×associate--l+
90×times-frac
84×add-sqr-sqrt
80×add-cube-cbrt *-un-lft-identity
59×log-pow
57×exp-prod
54×exp-sum
10×pow1 div-inv
8×add-exp-log add-cbrt-cube
7×associate-*r*
6×associate-*l* add-log-exp
2×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- diff-log rem-log-exp flip--
Counts
4 → 196
Calls
4 calls:
39.0ms
(- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im))
167.0ms
(log (exp (exp (- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im)))))
17.0ms
(* y.re (log (/ -1 x.re)))
13.0ms
(* (atan2 x.im x.re) y.im)

series313.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im))
93.0ms
(log (exp (exp (- (* -1 (* y.re (log (/ -1 x.re)))) (* (atan2 x.im x.re) y.im)))))
61.0ms
(* y.re (log (/ -1 x.re)))
34.0ms
(* (atan2 x.im x.re) y.im)

simplify74.0ms

Counts
208 → 208

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

regimes387.0ms

Accuracy

66.4% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 20.1b

bsearch191.0ms

Steps
ItersRangePoint
8
-5.975627622668562e-307
2.7102750047534304e-307
-3.6252543666988e-312

simplify114.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.7s2073×body1280valid
2.0s7987×body80valid
1.7s1488×body640valid
326.0ms624×body320valid
155.0ms335×body160valid