Details

sample509.0ms

Algorithm

intervals

Results

122.0ms	255×	body	80	valid
98.0ms	65×	body	1280	valid
85.0ms	47×	body	640	valid
16.0ms	15×	body	320	valid
4.0ms	6×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	96	25
4	215	25
5	843	25
done	5000	25

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.9b

localize28.0ms

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)))
1.4b	(* (atan2 x.im x.re) y.im)
2.0b	(* (atan2 x.im x.re) y.re)
33.6b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite55.0ms

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:

23.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
12.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(* (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)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (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)
25.0ms	(* (atan2 x.im x.re) y.re)
291.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

109 → 109

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	185	1599
1	338	1557
2	844	1449
3	2426	1444
done	5001	1443

prune931.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (hypot x.re x.im)) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
2.0b	(* (atan2 x.im x.re) y.re)
33.6b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite55.0ms

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)
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)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (log (hypot x.re x.im)) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
28.0ms	(* (atan2 x.im x.re) y.re)
257.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.9s

Counts

83 → 83

Iterations

Useful iterations: 3 (533.0ms)

Iter	Nodes	Cost
0	120	757
1	232	741
2	572	653
3	1000	649
4	1430	649
5	2734	649
done	5001	649

prune582.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (hypot x.re x.im)) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
2.0b	(* (atan2 x.im x.re) y.re)
33.6b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

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)
14.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(* (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)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (log (hypot x.re x.im)) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
33.0ms	(* (atan2 x.im x.re) y.re)
243.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.2s

Counts

83 → 83

Iterations

Useful iterations: 3 (567.0ms)

Iter	Nodes	Cost
0	120	757
1	232	741
2	572	653
3	1000	649
4	1430	649
5	2734	649
done	5001	649

prune721.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
1.4b	(* (atan2 x.im x.re) y.im)
1.5b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt 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))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `*-commutative`
2×	`unswap-sqr`
1×	`sin-sum` `fma-udef`

Counts

4 → 77

Calls

4 calls:

95.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
7.0ms	(* (atan2 x.im x.re) y.im)
48.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt 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))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
36.0ms	(* (atan2 x.im x.re) y.im)
118.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
323.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify5.7s

Counts

89 → 89

Iterations

Useful iterations: 4 (4.0s)

Iter	Nodes	Cost
0	135	1192
1	285	1170
2	875	883
3	2012	776
4	3288	756
done	5001	756

prune672.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.8b

regimes503.0ms

Accuracy

0% (0.1b remaining)

Error of 3.3b against oracle of 3.2b and baseline of 3.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	30
1	23	30
done	23	30

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.3s	2214×	body	1280	valid
1.8s	8010×	body	80	valid
1.4s	1390×	body	640	valid
411.0ms	539×	body	320	valid
184.0ms	41×	body	2560	valid
74.0ms	203×	body	160	valid