Details

Time bar (total: 6.8s)

sample342.0ms

Algorithm
intervals
Results
36.0ms63×body1280valid
22.0ms244×body80valid
15.0ms40×body640valid
5.0ms18×body320valid
1.0ms6×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune26.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.7b

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (atan2 x.im x.re) y.im)
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series244.0ms

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)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune321.0ms

Filtered
68 candidates to 54 candidates (79.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.2b

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)
2.7b
(* (atan2 x.im x.re) y.im)
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

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)
5.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series234.0ms

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)))
89.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune300.0ms

Filtered
81 candidates to 60 candidates (74.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (atan2 x.im x.re) y.im)
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
6×add-exp-log sqrt-div add-cbrt-cube
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series123.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify66.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0145374
1428355
21017352
32145352
45002352

prune358.0ms

Filtered
75 candidates to 58 candidates (77.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (atan2 x.im x.re) y.im)
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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

series221.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
133.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune341.0ms

Filtered
68 candidates to 54 candidates (79.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

regimes289.0ms

Accuracy

64.4% (5.9b remaining)

Error of 9.5b against oracle of 3.6b and baseline of 20.1b

bsearch441.0ms

Steps
ItersRangePoint
7
9.808137995393928e-35
2.1475173904910715e-33
1.6471946110688965e-33
4
3.2364357890507887e-174
5.78828243737659e-174
5.683326641400739e-174
6
1.1428673676875916e-276
1.2023243154103857e-275
1.3585741357606672e-276
3
-3.475927158537529e-217
-2.899986792342497e-217
-3.3679383398759607e-217
7
-4.756344061121481e-110
-9.137140055959564e-112
-1.2278691858145578e-111
8
-4.288389801987159e+44
-4.743066161160227e+41
-1.450382572894597e+43

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066110
181110
284110
384110

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2047×body1280valid
671.0ms7978×body80valid
577.0ms1500×body640valid
171.0ms630×body320valid
59.0ms336×body160valid