Details

Time bar (total: 8.2s)

sample412.0ms

Algorithm
intervals
Results
57.0ms68×body1280valid
39.0ms58×body640valid
38.0ms256×body80valid
10.0ms23×body320valid
2.0ms8×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
31.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite28.0ms

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:
4.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
139.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune329.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.7b

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)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
86.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune300.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.3b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
1.7b
(* (atan2 x.im x.re) y.im)

rewrite24.0ms

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*
9×add-exp-log
7×add-cbrt-cube
6×exp-prod
5×pow1 div-exp div-inv add-log-exp
4×sqr-pow
3×associate-*r* associate-*l* associate-/l*
2×neg-sub0 exp-neg exp-diff pow-exp rem-exp-log associate-/l/
1×cbrt-undiv distribute-lft-neg-in pow-to-exp neg-mul-1 distribute-rgt-neg-in frac-2neg pow-prod-down neg-log prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 123
Calls
3 calls:
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
14.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
3.0ms
(* (atan2 x.im x.re) y.im)

series126.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
87.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
16.0ms
(* (atan2 x.im x.re) y.im)

simplify53.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04671459
117531413
250011411

prune464.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
1.7b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.im)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
66×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
52×unpow-prod-down
17×associate-/r*
14×add-exp-log
12×add-cbrt-cube
10×pow1
9×associate-*r* associate-*l*
5×div-exp div-inv
4×add-log-exp sqr-pow
3×pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l* unswap-sqr
2×pow-exp associate-/l/
1×cbrt-undiv neg-sub0 exp-neg pow-to-exp frac-2neg exp-diff clear-num
Counts
4 → 142
Calls
4 calls:
11.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
3.0ms
(* (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)

series138.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
17.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.im)

simplify49.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04341519
115511458
250011455

prune648.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

regimes342.0ms

Accuracy

80.1% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 30.4b

bsearch121.0ms

Steps
ItersRangePoint
9
-5.459969929633657e-306
2.8649750194033813e-305
1.73062623171225e-310

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03216
14216
24216

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.6s1986×body1280valid
1.1s7939×body80valid
839.0ms1432×body640valid
281.0ms679×body320valid
88.0ms314×body160valid