Details

sample54.0ms

Algorithm

intervals

Results

31.0ms

490×

body

valid

simplify4.2s

Counts

1 → 1

Iterations

Useful iterations: 6 (2.6s)

Iter	Nodes	Cost
0	11	19
1	24	18
2	57	17
3	157	17
4	421	14
5	1225	11
6	3119	10
done	5000	10

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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:

1.0ms	(fma x.im (* -3 (* x.im x.re)) (pow x.re 3))
31.0ms	(* -3 (* x.im x.re))

series146.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(fma x.im (* -3 (* x.im x.re)) (pow x.re 3))
34.0ms	(* -3 (* x.im x.re))

simplify2.9s

Counts

36 → 36

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	55	338
1	124	327
2	401	282
3	1456	282
done	5000	282

prune119.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

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:

1.0ms	(fma x.im (* (* -3 x.im) x.re) (pow x.re 3))
36.0ms	(* (* -3 x.im) x.re)

series140.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(fma x.im (* (* -3 x.im) x.re) (pow x.re 3))
27.0ms	(* (* -3 x.im) x.re)

simplify3.1s

Counts

36 → 36

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	59	341
1	134	326
2	497	283
3	1865	283
done	5000	283

prune124.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3))) (cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3))))
16.5b	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))
16.5b	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))
16.5b	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

26.0ms	(* (cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3))) (cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3))))
2.0ms	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))
2.0ms	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))
2.0ms	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))

series919.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3))) (cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3))))
215.0ms	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))
258.0ms	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))
184.0ms	(cbrt (fma x.im (* (* -3 x.im) x.re) (pow x.re 3)))

simplify3.4s

Counts

93 → 93

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	95	1990
1	191	1849
2	455	1692
3	1135	1447
4	3653	1406
done	5000	1334

prune425.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (pow x.im 2) x.re) -3) (pow x.re 3))
0.2b	(* (* (pow x.im 2) x.re) -3)
7.7b	(* (pow x.im 2) x.re)

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt`
10×	`prod-exp` `add-cbrt-cube`
9×	`associate-l`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`pow1` `add-log-exp`
4×	`unpow-prod-down` `cbrt-unprod` `unswap-sqr`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-to-exp` `pow-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `flip-+`

Counts

3 → 64

Calls

3 calls:

50.0ms	(+ (* (* (pow x.im 2) x.re) -3) (pow x.re 3))
41.0ms	(* (* (pow x.im 2) x.re) -3)
30.0ms	(* (pow x.im 2) x.re)

series167.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(+ (* (* (pow x.im 2) x.re) -3) (pow x.re 3))
32.0ms	(* (* (pow x.im 2) x.re) -3)
27.0ms	(* (pow x.im 2) x.re)

simplify2.1s

Counts

73 → 73

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	102	753
1	255	661
2	999	591
done	5000	590

prune225.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes88.0ms

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

sample1.9s

Algorithm

intervals

Results

1.4s

14161×

body

valid