Details

Time bar (total: 21.3s)

sample612.0ms

Algorithm
intervals
Results
132.0ms70×body1280valid
106.0ms246×body80valid
58.0ms52×body640valid
16.0ms25×body320valid
9.0ms3×body2560valid
3.0ms7×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01937
13526
26325
39925
424925
5113025
done500125

prune46.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize64.0ms

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)))
1.8b
(* (atan2 x.im x.re) y.re)
2.6b
(* (atan2 x.im x.re) y.im)
32.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
21×times-frac
12×unpow-prod-down
10×add-cbrt-cube add-exp-log
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×associate-/r* div-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×pow-to-exp cbrt-undiv clear-num frac-2neg sin-sum pow-exp fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
17.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
11.0ms
(* (atan2 x.im x.re) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
30.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
249.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify795.0ms

Counts
109 → 109
Iterations

Useful iterations: done (791.0ms)

IterNodesCost
01871599
13591557
212521451
done50011444

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.8b
(* (atan2 x.im x.re) y.re)
2.6b
(* y.im (atan2 x.im x.re))
32.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
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:
6.0ms
(* (log (hypot x.re x.im)) y.re)
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* y.im (atan2 x.im x.re))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (log (hypot x.re x.im)) y.re)
34.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* y.im (atan2 x.im x.re))
260.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify670.0ms

Counts
83 → 83
Iterations

Useful iterations: done (667.0ms)

IterNodesCost
0121757
1248741
2894657
done5000649

prune826.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt y.im) (atan2 x.im x.re))
1.8b
(* (atan2 x.im x.re) y.re)
2.0b
(* (* (cbrt y.im) (cbrt y.im)) (* (cbrt y.im) (atan2 x.im x.re)))
32.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
15×add-sqr-sqrt
13×add-cbrt-cube
10×associate-*l* pow-prod-down prod-exp cbrt-unprod
9×*-un-lft-identity add-cube-cbrt
7×associate-*r*
4×cbrt-prod expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr
1×sin-sum fma-udef
Counts
4 → 78
Calls
4 calls:
8.0ms
(* (cbrt y.im) (atan2 x.im x.re))
10.0ms
(* (atan2 x.im x.re) y.re)
38.0ms
(* (* (cbrt y.im) (cbrt y.im)) (* (cbrt y.im) (atan2 x.im x.re)))
2.0ms
(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:
89.0ms
(* (cbrt y.im) (atan2 x.im x.re))
24.0ms
(* (atan2 x.im x.re) y.re)
36.0ms
(* (* (cbrt y.im) (cbrt y.im)) (* (cbrt y.im) (atan2 x.im x.re)))
198.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify955.0ms

Counts
90 → 90
Iterations

Useful iterations: done (951.0ms)

IterNodesCost
01311025
13021006
21497779
done5000699

prune791.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize63.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
6.9b
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
6.9b
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
32.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×sin-sum fma-udef
Counts
4 → 43
Calls
4 calls:
6.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
7.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
5.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series744.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
168.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
163.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
228.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
55 → 55
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
066625
1111614
2194545
3483534
41723534
done5000534

prune530.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

regimes644.0ms

Accuracy

0% (0.1b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02352
12952
done2952

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.6s2194×body1280valid
2.4s7935×body80valid
1.5s1386×body640valid
398.0ms537×body320valid
122.0ms49×body2560valid
86.0ms243×body160valid