Details

Time bar (total: 7.3s)

sample429.0ms

Algorithm
intervals
Results
42.0ms247×body80valid
41.0ms73×body1280valid
18.0ms49×body640valid
6.0ms22×body320valid
2.0ms12×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (atan2 x.im x.re) y.im)
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(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)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
145.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune321.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

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)
2.9b
(* (atan2 x.im x.re) y.im)
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite50.0ms

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:
19.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
84.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (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 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune300.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×add-exp-log
7×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×sqrt-prod
4×sqrt-div add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum associate-*r* *-commutative unswap-sqr
Counts
4 → 57
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
127.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify138.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (132.0ms)

IterNodesCost
0232495
1586443
21587439
34527432
45002431

prune382.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize37.0ms

Local error

Found 4 expressions with local error:

3.6b
(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cbrt-prod cos-sum pow1/3
Counts
4 → 47
Calls
4 calls:
17.0ms
(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
125.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify103.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
0184440
1396400
21041398
33217396
45001396

prune345.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

regimes306.0ms

Accuracy

62.9% (6.1b remaining)

Error of 9.6b against oracle of 3.6b and baseline of 19.9b

bsearch312.0ms

Steps
ItersRangePoint
8
-1.3287558847979414e-305
4.527111501653717e-308
-1.1974408710008e-310
9
-2.141684871670345e-153
-2.352808649179745e-159
-3.011667906396995e-159
10
-3.854589780371342e+164
-1.6181289332921645e+150
-6.451247643666555e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04934
15534
25534

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2046×body1280valid
655.0ms7961×body80valid
548.0ms1466×body640valid
168.0ms648×body320valid
55.0ms322×body160valid