Details

Time bar (total: 6.5s)

sample357.0ms

Algorithm
intervals
Results
40.0ms67×body1280valid
25.0ms255×body80valid
18.0ms44×body640valid
5.0ms19×body320valid
2.0ms8×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.im)
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(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:
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune324.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 20.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (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)
1.3b
(* (atan2 x.im x.re) y.im)
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* (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)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (* (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)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify79.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune272.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b
(* (log (* -1 x.re)) y.re)
1.3b
(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
8×associate-*l*
7×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r*
5×add-log-exp
3×pow-prod-down
2×prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log flip--
Counts
3 → 50
Calls
3 calls:
3.0ms
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
7.0ms
(* (log (* -1 x.re)) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series188.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
67.0ms
(* (log (* -1 x.re)) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify99.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0225318
1816291
24159287
35001287

prune170.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.im)
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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

series227.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
135.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune322.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 2.3b

regimes269.0ms

Accuracy

66.5% (5.3b remaining)

Error of 8.9b against oracle of 3.6b and baseline of 19.5b

bsearch105.0ms

Steps
ItersRangePoint
9
-1.8644950954430464e-305
6.689632292389639e-306
-3.3994141027546e-310

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13515
23515

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s2064×body1280valid
713.0ms7997×body80valid
581.0ms1433×body640valid
194.0ms673×body320valid
70.0ms349×body160valid