Details

sample26.0ms

Algorithm

intervals

Results

16.0ms

457×

body

valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 6 (411.0ms)

Iter	Nodes	Cost
0	11	19
1	23	18
2	56	17
3	138	17
4	369	14
5	900	11
6	2554	10
done	5000	10

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x.im (* -3 (* x.re x.im)) (pow x.re 3))
0.3b	(* -3 (* x.re x.im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma x.im (* -3 (* x.re x.im)) (pow x.re 3))
6.0ms	(* -3 (* x.re x.im))

series96.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(fma x.im (* -3 (* x.re x.im)) (pow x.re 3))
17.0ms	(* -3 (* x.re x.im))

simplify793.0ms

Counts

36 → 36

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	57	338
1	129	327
2	424	288
3	1695	288
done	5000	288

prune81.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x.im (* (* -3 x.re) x.im) (pow x.re 3))
0.2b	(* (* -3 x.re) x.im)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma x.im (* (* -3 x.re) x.im) (pow x.re 3))
7.0ms	(* (* -3 x.re) x.im)

series95.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(fma x.im (* (* -3 x.re) x.im) (pow x.re 3))
17.0ms	(* (* -3 x.re) x.im)

simplify1.4s

Counts

36 → 36

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	60	341
1	135	328
2	543	283
3	2817	283
done	5001	283

prune82.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma x.im (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* x.re x.im))) (pow x.re 3))
0.2b	(* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* x.re x.im)))
0.3b	(* (cbrt -3) (* x.re x.im))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
17×	`add-cbrt-cube`
7×	`associate-l`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`cbrt-prod` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`fma-udef`

Counts

3 → 63

Calls

3 calls:

0.0ms	(fma x.im (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* x.re x.im))) (pow x.re 3))
26.0ms	(* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* x.re x.im)))
10.0ms	(* (cbrt -3) (* x.re x.im))

series252.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(fma x.im (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* x.re x.im))) (pow x.re 3))
69.0ms	(* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* x.re x.im)))
42.0ms	(* (cbrt -3) (* x.re x.im))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (753.0ms)

Iter	Nodes	Cost
0	90	975
1	232	941
2	875	645
3	4818	517
done	5000	517

prune149.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* x.im (* x.re x.im)) -3) (pow x.re 3))
0.2b	(* x.im (* x.re x.im))
0.2b	(* (* x.im (* x.re x.im)) -3)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 57

Calls

3 calls:

22.0ms	(+ (* (* x.im (* x.re x.im)) -3) (pow x.re 3))
6.0ms	(* x.im (* x.re x.im))
18.0ms	(* (* x.im (* x.re x.im)) -3)

series107.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(+ (* (* x.im (* x.re x.im)) -3) (pow x.re 3))
17.0ms	(* x.im (* x.re x.im))
20.0ms	(* (* x.im (* x.re x.im)) -3)

simplify587.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	90	708
1	248	641
2	982	556
done	5000	556

prune126.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	10	10
done	10	10

end0.0ms

sample744.0ms

Algorithm

intervals

Results

517.0ms

14459×

body

valid