Details

Time bar (total: 6.6s)

sample342.0ms

Algorithm
intervals
Results
27.0ms45×body1280valid
24.0ms260×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

prune24.0ms

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)))

rewrite22.0ms

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)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(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)))

series236.0ms

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)))
148.0ms
(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
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0205456
1546415
21264411
32748411
45001411

prune370.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(* (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)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
141.0ms
(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

prune381.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (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)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×pow1
11×associate-*l*
10×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod unswap-sqr
2×log-pow
1×cos-sum
Counts
4 → 72
Calls
4 calls:
7.0ms
(* (log (* 1 (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)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
144.0ms
(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0232439
1717383
22069376
35001374

prune347.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.0b

localize28.0ms

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)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(expm1 (cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re))))
16.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0189444
1523388
21168388
32018388
45001388

prune302.0ms

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
03342
13542
23542

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2007×body1280valid
690.0ms7993×body80valid
556.0ms1405×body640valid
168.0ms614×body320valid
62.0ms315×body160valid