Details

Time bar (total: 32.3s)

sample337.0ms

Algorithm
intervals
Results
104.0ms255×body80valid
69.0ms54×body1280valid
42.0ms49×body640valid
9.0ms14×body320valid
9.0ms3×body2560valid
5.0ms10×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
0.8b
(* (atan2 x.im x.re) y.im)
1.1b
(* (atan2 x.im x.re) y.re)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:
18.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
25.0ms
(* (atan2 x.im x.re) y.im)
21.0ms
(* (atan2 x.im x.re) y.re)
270.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
109 → 109
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01851599
13381557
28441449
324261444
done50011443

prune738.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
0.8b
(* (atan2 x.im x.re) y.im)
1.1b
(* (atan2 x.im x.re) y.re)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

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.im)
7.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (log (hypot x.re x.im)) y.re)
32.0ms
(* (atan2 x.im x.re) y.im)
31.0ms
(* (atan2 x.im x.re) y.re)
238.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts
83 → 83
Iterations

Useful iterations: 3 (550.0ms)

IterNodesCost
0120757
1232741
2572653
31000649
41430649
52734649
done5001649

prune476.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize76.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite43.0ms

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:
15.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
16.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series818.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.re)
269.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
256.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
262.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts
62 → 62
Iterations

Useful iterations: 3 (218.0ms)

IterNodesCost
069827
1120818
2253726
3432720
4611720
51026720
62136720
done5001720

prune647.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize81.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite22.0ms

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:
7.0ms
(* (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)))
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series822.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
247.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
262.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
292.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify5.3s

Counts
62 → 62
Iterations

Useful iterations: 4 (495.0ms)

IterNodesCost
085925
1143916
2289810
3499756
4681720
51283720
63155720
done5000720

prune604.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

regimes308.0ms

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02562
13262
done3262

end0.0ms

sample9.3s

Algorithm
intervals
Results
4.0s2272×body1280valid
2.0s7965×body80valid
1.8s1408×body640valid
342.0ms586×body320valid
136.0ms40×body2560valid
130.0ms250×body160valid