Details

sample257.0ms

Algorithm

intervals

Results

97.0ms	60×	body	1280	valid
37.0ms	255×	body	80	valid
32.0ms	50×	body	640	valid
10.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

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	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite67.0ms

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` `cos-sum` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 97

Calls

4 calls:

22.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
14.0ms	(* (atan2 x.im x.re) y.im)
15.0ms	(* (atan2 x.im x.re) y.re)
9.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
33.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(* (atan2 x.im x.re) y.re)
320.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

109 → 109

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	183	1590
1	333	1549
2	838	1441
3	2407	1436
done	5001	1435

prune623.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`cos-sum`

Counts

4 → 60

Calls

4 calls:

1.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
11.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
33.0ms	(* (atan2 x.im x.re) y.im)
26.0ms	(* (atan2 x.im x.re) y.re)
223.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.9s

Counts

72 → 72

Iterations

Useful iterations: 3 (297.0ms)

Iter	Nodes	Cost
0	101	729
1	177	720
2	414	634
3	809	630
4	1501	630
5	4377	630
done	5000	630

prune497.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize43.0ms

Local error

Found 4 expressions with local error:

4.2b	(cbrt (atan2 x.im x.re))
4.2b	(cbrt (atan2 x.im x.re))
4.2b	(cbrt (atan2 x.im x.re))
33.6b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series462.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt (atan2 x.im x.re))
70.0ms	(cbrt (atan2 x.im x.re))
78.0ms	(cbrt (atan2 x.im x.re))
263.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	54	529
1	82	516
2	134	456
3	235	445
4	567	445
5	2110	445
done	5000	445

prune480.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize39.0ms

Local error

Found 4 expressions with local error:

4.2b	(cbrt (atan2 x.im x.re))
4.2b	(cbrt (atan2 x.im x.re))
4.2b	(cbrt (atan2 x.im x.re))
33.6b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series400.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt (atan2 x.im x.re))
65.0ms	(cbrt (atan2 x.im x.re))
55.0ms	(cbrt (atan2 x.im x.re))
229.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	54	529
1	82	516
2	134	456
3	235	445
4	567	445
5	2110	445
done	5000	445

prune476.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

regimes433.0ms

Accuracy

0% (0.5b remaining)

Error of 3.2b against oracle of 2.7b and baseline of 3.2b

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	52
1	33	52
2	46	52
3	52	52
4	54	52
done	54	52

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.2s	2058×	body	1280	valid
2.2s	8031×	body	80	valid
2.0s	1437×	body	640	valid
431.0ms	607×	body	320	valid
99.0ms	264×	body	160	valid