Details

Time bar (total: 6.5s)

sample361.0ms

Algorithm
intervals
Results
37.0ms62×body1280valid
24.0ms264×body80valid
22.0ms56×body640valid
6.0ms22×body320valid
2.0ms12×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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.im)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune313.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 17.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)
0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

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)))
7.0ms
(* (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)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify59.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune284.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.0b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
0.5b
(* (atan2 x.im x.re) y.im)

rewrite21.0ms

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)))
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)

series130.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
90.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
16.0ms
(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04671459
117531413
250011411

prune447.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (- (- (* (atan2 x.im x.re) y.im)) (log (pow (/ -1 x.re) y.re))))
0.5b
(* (atan2 x.im x.re) y.im)
2.6b
(log (pow (/ -1 x.re) y.re))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×log-prod
16×*-un-lft-identity
14×add-cube-cbrt
13×unpow-prod-down
9×add-exp-log times-frac
6×add-log-exp
5×pow1 exp-prod add-cbrt-cube
4×rem-log-exp
3×associate-*r* associate-*l* rem-exp-log
2×diff-log exp-sum pow-exp
1×pow-to-exp sub-neg exp-diff div-exp pow-prod-down neg-log prod-exp log-pow *-commutative cbrt-unprod div-inv distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
3 → 65
Calls
3 calls:
12.0ms
(exp (- (- (* (atan2 x.im x.re) y.im)) (log (pow (/ -1 x.re) y.re))))
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(log (pow (/ -1 x.re) y.re))

series188.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(exp (- (- (* (atan2 x.im x.re) y.im)) (log (pow (/ -1 x.re) y.re))))
18.0ms
(* (atan2 x.im x.re) y.im)
80.0ms
(log (pow (/ -1 x.re) y.re))

simplify86.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0345441
1986397
23377391
35001390

prune218.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

regimes294.0ms

Accuracy

85.9% (2.3b remaining)

Error of 5.6b against oracle of 3.3b and baseline of 19.6b

bsearch198.0ms

Steps
ItersRangePoint
9
9.165364975569095e-17
2.7654013913247297e-11
2.687600014275229e-11
10
-8.020324993682032e-16
-2.4313708196933896e-27
-7.937272784933259e-16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04017
14617
24617

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s1989×body1280valid
688.0ms8076×body80valid
551.0ms1408×body640valid
170.0ms614×body320valid
53.0ms294×body160valid