Details

Time bar (total: 16.6s)

sample437.0ms

Algorithm
intervals
Results
67.0ms81×body1280valid
23.0ms257×body80valid
18.0ms46×body640valid
4.0ms14×body320valid
2.0ms1×body2560valid
1.0ms7×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.7b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×times-frac
12×unpow-prod-down
10×add-exp-log add-cbrt-cube
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×div-exp associate-/r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cbrt-undiv pow-to-exp frac-2neg sin-sum pow-exp clear-num fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
11.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
180.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
109 → 109
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01851599
13381557
28441449
324231444
done50001443

prune486.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.7b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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×sin-sum log-pow fma-udef
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (log (hypot x.re x.im)) y.re)
18.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
164.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts
83 → 83
Iterations

Useful iterations: 3 (335.0ms)

IterNodesCost
0120757
1232741
2569653
31000649
41430649
52733649
done5000649

prune344.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (atan2 x.im x.re) y.im)
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sin-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
9.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
161.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
164.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
161.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
62 → 62
Iterations

Useful iterations: 3 (136.0ms)

IterNodesCost
070827
1122818
2260726
3444720
4623720
51042720
62091720
done5001720

prune361.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize28.0ms

Local error

Found 4 expressions with local error:

34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series657.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
161.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
165.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
166.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
52 → 52
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
041880
166872
294776
3139768
4217768
5329768
6460768
7668768
81031768
92516768
done5000768

prune334.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

regimes278.0ms

Accuracy

0% (0.6b remaining)

Error of 3.8b against oracle of 3.2b and baseline of 3.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01855
12355
done2355

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2164×body1280valid
666.0ms7971×body80valid
539.0ms1369×body640valid
149.0ms519×body320valid
73.0ms49×body2560valid
41.0ms233×body160valid