Details

Time bar (total: 23.9s)

sample310.0ms

Algorithm
intervals
Results
66.0ms28×body320valid
55.0ms44×body1280valid
50.0ms263×body80valid
35.0ms45×body640valid
4.0ms10×body160valid

simplify630.0ms

Counts
1 → 1

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.re)
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite61.0ms

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:
7.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (atan2 x.im x.re) y.re)
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
207.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
68 → 68

prune542.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (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)
0.7b
(* (atan2 x.im x.re) y.im)
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
21.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
109.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify946.0ms

Counts
81 → 81

prune403.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.2b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
0.7b
(* (atan2 x.im x.re) y.im)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
58×add-sqr-sqrt
56×add-cube-cbrt *-un-lft-identity
52×unpow-prod-down
17×associate-/r*
11×add-exp-log
8×div-exp
7×add-cbrt-cube
6×exp-prod
5×pow1 div-inv add-log-exp
4×pow-exp sqr-pow
3×associate-*r* associate-*l* associate-/l*
2×neg-sub0 exp-neg exp-diff rem-exp-log associate-/l/
1×cbrt-undiv distribute-lft-neg-in pow-to-exp neg-mul-1 rec-exp distribute-rgt-neg-in frac-2neg 1-exp pow-prod-down neg-log prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 125
Calls
3 calls:
11.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
42.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
7.0ms
(* (atan2 x.im x.re) y.im)

series242.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
156.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
37.0ms
(* (atan2 x.im x.re) y.im)

simplify831.0ms

Counts
134 → 134

prune695.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (/ 1 x.re) y.re) (sqrt (exp (- (* (atan2 x.im x.re) y.im)))))
0.3b
(/ (sqrt (exp (- (* (atan2 x.im x.re) y.im)))) (/ (pow (/ 1 x.re) y.re) (sqrt (exp (- (* (atan2 x.im x.re) y.im))))))
0.7b
(* (atan2 x.im x.re) y.im)
0.7b
(* (atan2 x.im x.re) y.im)

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
1905×times-frac
903×add-sqr-sqrt
899×add-cube-cbrt *-un-lft-identity
738×sqrt-prod
637×unpow-prod-down
114×associate-/r*
58×div-inv
49×sqr-pow
40×add-exp-log
23×div-exp associate-/l*
18×sqrt-div
17×associate-/r/
15×add-cbrt-cube
9×neg-sub0 exp-neg exp-diff
8×pow1 pow-exp
6×associate-*r* associate-*l*
4×cbrt-undiv add-log-exp
2×pow-to-exp rec-exp frac-2neg 1-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
4 → 964
Calls
4 calls:
32.0ms
(/ (pow (/ 1 x.re) y.re) (sqrt (exp (- (* (atan2 x.im x.re) y.im)))))
115.0ms
(/ (sqrt (exp (- (* (atan2 x.im x.re) y.im)))) (/ (pow (/ 1 x.re) y.re) (sqrt (exp (- (* (atan2 x.im x.re) y.im))))))
14.0ms
(* (atan2 x.im x.re) y.im)
14.0ms
(* (atan2 x.im x.re) y.im)

series404.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (pow (/ 1 x.re) y.re) (sqrt (exp (- (* (atan2 x.im x.re) y.im)))))
162.0ms
(/ (sqrt (exp (- (* (atan2 x.im x.re) y.im)))) (/ (pow (/ 1 x.re) y.re) (sqrt (exp (- (* (atan2 x.im x.re) y.im))))))
19.0ms
(* (atan2 x.im x.re) y.im)
29.0ms
(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts
976 → 976

prune5.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

regimes406.0ms

Accuracy

52.9% (7.5b remaining)

Error of 11.2b against oracle of 3.7b and baseline of 19.6b

bsearch748.0ms

Steps
ItersRangePoint
8
1.1145942107568126e-66
8.595478378008582e-64
1.3583839762007739e-64
9
-9.012458963526052e-38
-3.5738082614524564e-46
-6.066276555501724e-38

simplify650.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.4s1961×body1280valid
1.7s8017×body80valid
1.3s1468×body640valid
375.0ms674×body320valid
101.0ms307×body160valid