Details

Time bar (total: 11.4s)

sample378.0ms

Algorithm
intervals
Results
43.0ms71×body1280valid
24.0ms266×body80valid
16.0ms42×body640valid
5.0ms19×body320valid
2.0ms12×body160valid

simplify369.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01937
13137
25336
38436
420136
586536
done500036

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(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
Iterations

Useful iterations: 3 (166.0ms)

IterNodesCost
094836
1193778
2456690
3965677
41948677
done5000677

prune333.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.9b

localize16.0ms

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)
1.1b
(* (atan2 x.im x.re) y.im)
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

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:
8.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
90.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify925.0ms

Counts
81 → 81
Iterations

Useful iterations: 3 (275.0ms)

IterNodesCost
01321042
1286985
2764871
31812860
done5000860

prune316.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ -1 x.re) y.re)
0.0b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.im)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
67×add-sqr-sqrt
65×add-cube-cbrt unpow-prod-down *-un-lft-identity
17×associate-/r*
13×add-exp-log
8×add-cbrt-cube
7×pow1
6×exp-prod div-exp div-inv add-log-exp
5×sqr-pow
4×pow-exp
3×pow-unpow associate-*r* associate-*l* associate-/l*
2×neg-sub0 exp-neg pow-to-exp exp-diff rem-exp-log associate-/l/
1×cbrt-undiv distribute-lft-neg-in neg-mul-1 pow-pow distribute-rgt-neg-in frac-2neg pow-prod-down neg-log prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
4 → 151
Calls
4 calls:
4.0ms
(pow (/ -1 x.re) y.re)
12.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)

series187.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(pow (/ -1 x.re) y.re)
88.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
20.0ms
(* (atan2 x.im x.re) y.im)

simplify798.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (186.0ms)

IterNodesCost
02842933
15422822
221212730
done50002730

prune542.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.im)
1.1b
(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×exp-prod
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×associate-*r* associate-*l*
4×rem-exp-log
2×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in exp-diff pow-prod-down neg-log prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 70
Calls
4 calls:
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)

series84.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
17.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(* (atan2 x.im x.re) y.im)

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: 3 (195.0ms)

IterNodesCost
064640
1122614
2430556
31868550
done5000550

prune310.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

regimes326.0ms

Accuracy

69.8% (8.1b remaining)

Error of 12.0b against oracle of 3.9b and baseline of 30.8b

bsearch327.0ms

Steps
ItersRangePoint
8
-9.087081146583301e-305
3.1975683632284187e-308
-9.3171400507965e-312
8
-2.0495441492633144e+58
-1.157062344343007e+54
-1.5993696563270364e+57
10
-6.332555553102272e+164
-9.029005633733514e+147
-1.669808635902091e+152

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
048135
164129
270129
done70129

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2022×body1280valid
670.0ms7969×body80valid
573.0ms1479×body640valid
171.0ms628×body320valid
56.0ms309×body160valid