Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
8.0ms	247×	body	80	nan

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	11	14
1	22	12
2	42	11
3	59	11
4	63	11
5	64	11
done	64	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ (* x y) (* x z))
0.6b	(+ (+ (* x y) (* x z)) (* y z))
16.4b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
4×	`pow1` `sum-log`
3×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

3 → 51

Calls

3 calls:

3.0ms	(+ (* x y) (* x z))
13.0ms	(+ (+ (* x y) (* x z)) (* y z))
17.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x y) (* x z))
23.0ms	(+ (+ (* x y) (* x z)) (* y z))
134.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify1.5s

Counts

60 → 60

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	92	853
1	281	652
2	943	584
3	3683	573
done	5000	570

prune434.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x z (* y (+ z x)))
0.5b	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
16.4b	(sqrt (fma x z (* y (+ z x))))
16.4b	(sqrt (fma x z (* y (+ z x))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma x z (* y (+ z x)))
12.0ms	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
1.0ms	(sqrt (fma x z (* y (+ z x))))
1.0ms	(sqrt (fma x z (* y (+ z x))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(fma x z (* y (+ z x)))
124.0ms	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
116.0ms	(sqrt (fma x z (* y (+ z x))))
126.0ms	(sqrt (fma x z (* y (+ z x))))

simplify4.2s

Counts

129 → 129

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	109	2711
1	200	1661
2	706	1506
3	3832	1452
done	5001	1443

prune299.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.2b

localize14.0ms

Local error

Found 4 expressions with local error:

14.1b	(cbrt (* x (+ y z)))
14.1b	(cbrt (* x (+ y z)))
14.1b	(cbrt (* x (+ y z)))
16.4b	(sqrt (+ (* (* (cbrt (* x (+ y z))) (cbrt (* x (+ y z)))) (cbrt (* x (+ y z)))) (* y z)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `cbrt-div` `associate-*r/`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (* x (+ y z)))
3.0ms	(cbrt (* x (+ y z)))
3.0ms	(cbrt (* x (+ y z)))
34.0ms	(sqrt (+ (* (* (cbrt (* x (+ y z))) (cbrt (* x (+ y z)))) (cbrt (* x (+ y z)))) (* y z)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (* x (+ y z)))
118.0ms	(cbrt (* x (+ y z)))
118.0ms	(cbrt (* x (+ y z)))
118.0ms	(sqrt (+ (* (* (cbrt (* x (+ y z))) (cbrt (* x (+ y z)))) (cbrt (* x (+ y z)))) (* y z)))

simplify793.0ms

Counts

68 → 68

Iterations

Useful iterations: done (791.0ms)

Iter	Nodes	Cost
0	105	1172
1	272	1074
2	699	667
3	2137	652
done	5000	649

prune289.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (* (fabs (cbrt (fma x z (* y (+ z x))))) (sqrt (cbrt (fma x z (* y (+ z x))))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
16.4b	(sqrt (fma x z (* y (+ z x))))
17.0b	(cbrt (fma x z (* y (+ z x))))
17.0b	(cbrt (fma x z (* y (+ z x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`sqrt-prod`
12×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`sqrt-pow1` `pow-prod-down`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `unswap-sqr`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

17.0ms	(* (sqrt (* (fabs (cbrt (fma x z (* y (+ z x))))) (sqrt (cbrt (fma x z (* y (+ z x))))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
1.0ms	(sqrt (fma x z (* y (+ z x))))
0.0ms	(cbrt (fma x z (* y (+ z x))))
1.0ms	(cbrt (fma x z (* y (+ z x))))

series883.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(* (sqrt (* (fabs (cbrt (fma x z (* y (+ z x))))) (sqrt (cbrt (fma x z (* y (+ z x))))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
120.0ms	(sqrt (fma x z (* y (+ z x))))
230.0ms	(cbrt (fma x z (* y (+ z x))))
244.0ms	(cbrt (fma x z (* y (+ z x))))

simplify2.0s

Counts

86 → 86

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	165	2222
1	386	2073
2	1151	1914
3	4235	1862
done	5000	1860

prune378.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 17.2b

regimes239.0ms

Accuracy

0% (0.1b remaining)

Error of 19.4b against oracle of 19.3b and baseline of 19.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	17	14
done	17	14

end0.0ms

sample878.0ms

Algorithm

intervals

Results

273.0ms	8000×	body	80	valid
261.0ms	7989×	body	80	nan