Details

sample282.0ms

Algorithm

intervals

Results

76.0ms	84×	body	1280	valid
73.0ms	49×	body	640	valid
35.0ms	261×	body	80	valid
13.0ms	29×	body	320	valid
5.0ms	3×	body	2560	valid
2.0ms	6×	body	160	valid

simplify2.2s

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.5b

localize51.0ms

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)))
1.7b	(* (atan2 x.im x.re) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
34.4b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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:

11.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(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:

193.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
20.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(* (atan2 x.im x.re) y.im)
257.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

109 → 109

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	185	1599
1	338	1557
2	844	1449
3	2423	1444
done	5000	1443

prune701.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.re)
1.7b	(* (atan2 x.im x.re) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
34.4b	(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)
14.0ms	(* (atan2 x.im x.re) y.re)
12.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (log (hypot x.re x.im)) y.re)
34.0ms	(* (atan2 x.im x.re) y.re)
34.0ms	(* (atan2 x.im x.re) y.im)
270.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.1s

Counts

83 → 83

Iterations

Useful iterations: 3 (551.0ms)

Iter	Nodes	Cost
0	120	757
1	232	741
2	569	653
3	1000	649
4	1430	649
5	2733	649
done	5000	649

prune507.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize54.0ms

Local error

Found 4 expressions with local error:

4.4b	(cbrt (atan2 x.im x.re))
4.4b	(cbrt (atan2 x.im x.re))
4.4b	(cbrt (atan2 x.im x.re))
34.4b	(sin (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×	`sin-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	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (atan2 x.im x.re))
79.0ms	(cbrt (atan2 x.im x.re))
60.0ms	(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)))

simplify2.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	57	538
1	88	524
2	143	464
3	237	453
4	559	453
5	2156	453
done	5000	453

prune476.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize40.0ms

Local error

Found 4 expressions with local error:

4.4b	(cbrt (atan2 x.im x.re))
4.4b	(cbrt (atan2 x.im x.re))
4.4b	(cbrt (atan2 x.im x.re))
34.4b	(sin (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×	`sin-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	(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:

57.0ms	(cbrt (atan2 x.im x.re))
57.0ms	(cbrt (atan2 x.im x.re))
66.0ms	(cbrt (atan2 x.im x.re))
286.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	57	538
1	88	524
2	143	464
3	237	453
4	559	453
5	2156	453
done	5000	453

prune512.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

regimes423.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	52
1	30	52
done	30	52

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.2s	2078×	body	1280	valid
1.9s	7985×	body	80	valid
1.5s	1389×	body	640	valid
313.0ms	568×	body	320	valid
141.0ms	36×	body	2560	valid
87.0ms	230×	body	160	valid