Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	261×	body	80	nan
8.0ms	256×	body	80	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	11	14
1	22	12
2	42	11
3	58	11
4	62	11
5	63	11
done	63	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ (* x y) (* x z))
1.4b	(+ (+ (* x y) (* x z)) (* y z))
17.5b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite32.0ms

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))
15.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* x y) (* x z))
23.0ms	(+ (+ (* x y) (* x z)) (* y z))
120.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify2.1s

Counts

60 → 60

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	92	853
1	270	652
2	908	584
3	3442	573
done	5001	570

prune213.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x z (* y (+ z x)))
0.5b	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
17.5b	(sqrt (fma x z (* y (+ z x))))
17.5b	(sqrt (fma x z (* y (+ z x))))

rewrite21.0ms

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)))
13.0ms	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
2.0ms	(sqrt (fma x z (* y (+ z x))))
1.0ms	(sqrt (fma x z (* y (+ z x))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma x z (* y (+ z x)))
122.0ms	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
125.0ms	(sqrt (fma x z (* y (+ z x))))
121.0ms	(sqrt (fma x z (* y (+ z x))))

simplify1.4s

Counts

129 → 129

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	109	2711
1	197	1644
2	506	1506
3	1933	1452
done	5001	1443

prune311.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (* (fabs (cbrt (fma x z (* y (+ z x))))) (sqrt (cbrt (fma x z (* y (+ z x))))))))
17.5b	(sqrt (fma x z (* y (+ z x))))
18.1b	(cbrt (fma x z (* y (+ z x))))
18.1b	(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-l`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`sqrt-pow1` `pow-prod-down`
4×	`expm1-log1p-u` `associate-r` `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 (sqrt (fma x z (* y (+ z x))))) (sqrt (* (fabs (cbrt (fma x z (* y (+ z x))))) (sqrt (cbrt (fma x z (* y (+ z x))))))))
1.0ms	(sqrt (fma x z (* y (+ z x))))
1.0ms	(cbrt (fma x z (* y (+ z x))))
1.0ms	(cbrt (fma x z (* y (+ z x))))

series886.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (* (fabs (cbrt (fma x z (* y (+ z x))))) (sqrt (cbrt (fma x z (* y (+ z x))))))))
124.0ms	(sqrt (fma x z (* y (+ z x))))
235.0ms	(cbrt (fma x z (* y (+ z x))))
236.0ms	(cbrt (fma x z (* y (+ z x))))

simplify1.5s

Counts

86 → 86

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	162	2216
1	376	2090
2	1014	1943
3	3217	1882
done	5000	1879

prune439.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x z (* y (+ z x)))
0.7b	(pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3)
17.5b	(sqrt (fma x z (* y (+ z x))))
17.5b	(sqrt (fma x z (* y (+ z x))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1`
7×	`pow-pow`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sqrt-pow2` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

0.0ms	(fma x z (* y (+ z x)))
5.0ms	(pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3)
1.0ms	(sqrt (fma x z (* y (+ z x))))
1.0ms	(sqrt (fma x z (* y (+ z x))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(fma x z (* y (+ z x)))
373.0ms	(pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3)
119.0ms	(sqrt (fma x z (* y (+ z x))))
120.0ms	(sqrt (fma x z (* y (+ z x))))

simplify2.4s

Counts

102 → 102

Iterations

Useful iterations: 3 (830.0ms)

Iter	Nodes	Cost
0	181	1775
1	464	1462
2	1148	1397
3	4545	1368
done	5000	1368

prune362.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 18.4b

regimes399.0ms

Accuracy

0% (0.1b remaining)

Error of 19.8b against oracle of 19.8b and baseline of 19.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample823.0ms

Algorithm

intervals

Results

251.0ms	8000×	body	80	valid
247.0ms	7980×	body	80	nan