Details

sample423.0ms

Algorithm

intervals

Results

119.0ms	83×	body	1280	valid
63.0ms	6×	body	160	valid
57.0ms	258×	body	80	valid
43.0ms	43×	body	640	valid
15.0ms	23×	body	320	valid
7.0ms	2×	body	2560	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	99	25
4	232	25
5	1034	25
done	5000	25

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.4b

localize33.0ms

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)))
1.5b	(* (atan2 x.im x.re) y.im)
1.8b	(* (atan2 x.im x.re) y.re)
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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:

12.0ms	(/ (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)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
21.0ms	(* (atan2 x.im x.re) y.im)
24.0ms	(* (atan2 x.im x.re) y.re)
286.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify963.0ms

Counts

109 → 109

Iterations

Useful iterations: done (958.0ms)

Iter	Nodes	Cost
0	185	1599
1	353	1557
2	1229	1451
done	5001	1444

prune815.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (hypot x.re x.im)) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
1.8b	(* (atan2 x.im x.re) y.re)
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

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:

17.0ms	(* (log (hypot x.re x.im)) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (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)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (log (hypot x.re x.im)) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(* (atan2 x.im x.re) y.re)
294.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify734.0ms

Counts

83 → 83

Iterations

Useful iterations: done (731.0ms)

Iter	Nodes	Cost
0	120	757
1	241	741
2	836	655
done	5000	649

prune563.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.5b

localize64.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.re)
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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:

8.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(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)))
16.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.re)
250.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
232.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
207.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts

62 → 62

Iterations

Useful iterations: 3 (448.0ms)

Iter	Nodes	Cost
0	69	827
1	124	818
2	356	726
3	2316	720
done	5001	720

prune617.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize85.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (atan2 x.im x.re))
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.5b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.6b	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `sin-sum` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(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)))
5.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series811.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(cbrt (atan2 x.im x.re))
276.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
226.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
235.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify2.4s

Counts

55 → 55

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	74	920
1	118	910
2	226	708
3	624	663
4	2657	663
done	5001	663

prune508.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.5b

regimes566.0ms

Accuracy

0% (0.6b remaining)

Error of 4.2b against oracle of 3.6b and baseline of 4.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	66
1	32	66
done	32	66

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.2s	2154×	body	1280	valid
2.8s	7946×	body	80	valid
1.3s	1429×	body	640	valid
309.0ms	545×	body	320	valid
131.0ms	224×	body	160	valid
109.0ms	47×	body	2560	valid