Details

Time bar (total: 8.0s)

sample350.0ms

Algorithm
intervals
Results
43.0ms72×body1280valid
21.0ms259×body80valid
14.0ms38×body640valid
4.0ms15×body320valid
2.0ms9×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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

series234.0ms

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)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

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: 18.5b

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)
0.7b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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
4×expm1-log1p-u log1p-expm1-u
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-+ fma-neg diff-log prod-diff flip-- flip-+ hypot-def
Counts
4 → 77
Calls
4 calls:
4.0ms
(- (* (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)
4.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
88.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune311.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
0.0b
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (* 1 (hypot x.re x.im))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity add-log-exp
8×add-exp-log associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum pow-prod-down
2×sub-neg diff-log prod-diff prod-exp log-pow *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff fma-neg flip--
Counts
4 → 76
Calls
4 calls:
6.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)

series341.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
126.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
97.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)

simplify102.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0269584
1861528
23384509
35001508

prune303.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (* 1 (hypot x.re x.im))) y.re)
0.2b
(* (log (* 1 (hypot x.re x.im))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
0.7b
(* (atan2 x.im x.re) y.im)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×pow1
16×associate-*l*
12×add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* add-cbrt-cube
6×pow-prod-down
4×expm1-log1p-u prod-exp log-pow *-commutative cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
Counts
4 → 84
Calls
4 calls:
6.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
8.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(* (atan2 x.im x.re) y.im)

series224.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
96.0ms
(* (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.im)

simplify1.6s

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0154438
1493380
21522366
34883362
45001362

prune389.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 3.0b

regimes149.0ms

Accuracy

0% (0.5b remaining)

Error of 4.3b against oracle of 3.8b and baseline of 4.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0208
1248
2248

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2068×body1280valid
640.0ms7915×body80valid
555.0ms1439×body640valid
166.0ms633×body320valid
58.0ms321×body160valid