Details

Time bar (total: 6.5s)

sample334.0ms

Algorithm
intervals
Results
26.0ms45×body1280valid
23.0ms260×body80valid
13.0ms34×body640valid
7.0ms25×body320valid
1.0ms6×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b
(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×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205456
1546415
21264411
32748411
45001411

prune363.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.8b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.im)
1.3b
(* (atan2 x.im x.re) y.re)
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square cos-sum sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify109.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0257400
1746356
21815355
34329355
45001355

prune371.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.0b
(* (atan2 x.im x.re) y.im)
1.3b
(* (atan2 x.im x.re) y.re)
32.7b
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow
Counts
4 → 71
Calls
4 calls:
3.0ms
(* (log (hypot x.re x.im)) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (log (hypot x.re x.im)) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
142.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0232410
1770359
22153357
35001357

prune340.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(expm1 (cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
1.0b
(* (atan2 x.im x.re) y.im)
1.3b
(* (atan2 x.im x.re) y.re)
32.7b
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(expm1 (cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
18.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
141.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify64.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0189444
1523388
21168388
32018388
45001388

prune306.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.0b

regimes170.0ms

Accuracy

0% (1.1b remaining)

Error of 3.9b against oracle of 2.9b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03441
13841
23841

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2007×body1280valid
659.0ms7993×body80valid
537.0ms1405×body640valid
166.0ms614×body320valid
58.0ms315×body160valid