Details

sample557.0ms

Algorithm

intervals

Results

225.0ms	84×	body	1280	valid
84.0ms	29×	body	320	valid
84.0ms	261×	body	80	valid
36.0ms	49×	body	640	valid
10.0ms	3×	body	2560	valid
2.0ms	6×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (48.0ms)

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.5b

localize54.0ms

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)))

rewrite85.0ms

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:

39.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
15.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (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)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
21.0ms	(* (atan2 x.im x.re) y.re)
24.0ms	(* (atan2 x.im x.re) y.im)
252.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

109 → 109

Iterations

Useful iterations: done (2.4s)

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

prune769.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize49.0ms

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)))

rewrite43.0ms

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:

9.0ms	(* (log (hypot x.re x.im)) y.re)
11.0ms	(* (atan2 x.im x.re) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (log (hypot x.re x.im)) y.re)
30.0ms	(* (atan2 x.im x.re) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)
232.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts

83 → 83

Iterations

Useful iterations: 3 (520.0ms)

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

prune614.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize33.0ms

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)))

rewrite7.0ms

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)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (atan2 x.im x.re))
83.0ms	(cbrt (atan2 x.im x.re))
81.0ms	(cbrt (atan2 x.im x.re))
240.0ms	(sin (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 (105.0ms)

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

prune434.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize49.0ms

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)))

rewrite7.0ms

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)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(cbrt (atan2 x.im x.re))
64.0ms	(cbrt (atan2 x.im x.re))
70.0ms	(cbrt (atan2 x.im x.re))
265.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

61 → 61

Iterations

Useful iterations: 3 (110.0ms)

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

prune495.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

regimes396.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	52
1	29	52
done	29	52

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.4s	2078×	body	1280	valid
2.5s	1389×	body	640	valid
1.8s	7985×	body	80	valid
406.0ms	568×	body	320	valid
88.0ms	36×	body	2560	valid
87.0ms	230×	body	160	valid