Details

sample596.0ms

Algorithm

intervals

Results

161.0ms	84×	body	1280	valid
46.0ms	261×	body	80	valid
36.0ms	49×	body	640	valid
17.0ms	29×	body	320	valid
7.0ms	3×	body	2560	valid
2.0ms	6×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (69.0ms)

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

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)))

rewrite47.0ms

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.re)
7.0ms	(* (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)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (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)
25.0ms	(* (atan2 x.im x.re) y.im)
262.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

109 → 109

Iterations

Useful iterations: done (2.7s)

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

prune794.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize37.0ms

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)))

rewrite32.0ms

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:

8.0ms	(* (log (hypot x.re x.im)) y.re)
9.0ms	(* (atan2 x.im x.re) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (log (hypot x.re x.im)) y.re)
33.0ms	(* (atan2 x.im x.re) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
248.0ms	(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 (565.0ms)

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

prune619.0ms

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)))

rewrite13.0ms

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:

2.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (atan2 x.im x.re))
84.0ms	(cbrt (atan2 x.im x.re))
63.0ms	(cbrt (atan2 x.im x.re))
292.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

61 → 61

Iterations

Useful iterations: 3 (80.0ms)

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

prune470.0ms

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)))

rewrite13.0ms

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:

2.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(cbrt (atan2 x.im x.re))
55.0ms	(cbrt (atan2 x.im x.re))
61.0ms	(cbrt (atan2 x.im x.re))
249.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts

61 → 61

Iterations

Useful iterations: 3 (126.0ms)

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

prune436.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

regimes450.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.9s	2078×	body	1280	valid
2.4s	7985×	body	80	valid
1.3s	1389×	body	640	valid
430.0ms	568×	body	320	valid
99.0ms	36×	body	2560	valid
80.0ms	230×	body	160	valid