Details

sample76.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
19.0ms	236×	body	80	nan

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	11	14
1	22	12
2	44	11
3	63	11
4	67	11
5	68	11
done	68	11

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize12.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ (* x y) (* x z))
1.8b	(+ (+ (* x y) (* x z)) (* y z))
18.0b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite127.0ms

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:

16.0ms	(+ (* x y) (* x z))
71.0ms	(+ (+ (* x y) (* x z)) (* y z))
39.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* x y) (* x z))
37.0ms	(+ (+ (* x y) (* x z)) (* y z))
143.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify3.6s

Counts

60 → 60

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	92	853
1	271	652
2	970	584
3	4050	573
done	5000	572

prune296.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.8b	(+ (* x y) (* z (+ x y)))
18.0b	(sqrt (+ (* x y) (* z (+ x y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

16.0ms	(+ (* x y) (* z (+ x y)))
8.0ms	(sqrt (+ (* x y) (* z (+ x y))))

series194.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* x y) (* z (+ x y)))
159.0ms	(sqrt (+ (* x y) (* z (+ x y))))

simplify2.8s

Counts

39 → 39

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	71	571
1	202	481
2	706	451
3	3408	445
done	5000	443

prune187.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x y (* z (+ x y)))
0.6b	(* (sqrt (sqrt (fma x y (* z (+ x y))))) (sqrt (sqrt (fma x y (* z (+ x y))))))
18.0b	(sqrt (fma x y (* z (+ x y))))
18.0b	(sqrt (fma x y (* z (+ x y))))

rewrite49.0ms

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 y (* z (+ x y)))
40.0ms	(* (sqrt (sqrt (fma x y (* z (+ x y))))) (sqrt (sqrt (fma x y (* z (+ x y))))))
3.0ms	(sqrt (fma x y (* z (+ x y))))
2.0ms	(sqrt (fma x y (* z (+ x y))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma x y (* z (+ x y)))
157.0ms	(* (sqrt (sqrt (fma x y (* z (+ x y))))) (sqrt (sqrt (fma x y (* z (+ x y))))))
134.0ms	(sqrt (fma x y (* z (+ x y))))
152.0ms	(sqrt (fma x y (* z (+ x y))))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	109	2711
1	202	1644
2	483	1506
3	1611	1452
done	5002	1401

prune368.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (* (fabs (cbrt (fma x y (* z (+ x y))))) (sqrt (cbrt (fma x y (* z (+ x y))))))) (sqrt (sqrt (fma x y (* z (+ x y))))))
18.0b	(sqrt (fma x y (* z (+ x y))))
18.5b	(cbrt (fma x y (* z (+ x y))))
18.5b	(cbrt (fma x y (* z (+ x y))))

rewrite51.0ms

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:

44.0ms	(* (sqrt (* (fabs (cbrt (fma x y (* z (+ x y))))) (sqrt (cbrt (fma x y (* z (+ x y))))))) (sqrt (sqrt (fma x y (* z (+ x y))))))
2.0ms	(sqrt (fma x y (* z (+ x y))))
1.0ms	(cbrt (fma x y (* z (+ x y))))
1.0ms	(cbrt (fma x y (* z (+ x y))))

series1.3s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* (sqrt (* (fabs (cbrt (fma x y (* z (+ x y))))) (sqrt (cbrt (fma x y (* z (+ x y))))))) (sqrt (sqrt (fma x y (* z (+ x y))))))
174.0ms	(sqrt (fma x y (* z (+ x y))))
380.0ms	(cbrt (fma x y (* z (+ x y))))
328.0ms	(cbrt (fma x y (* z (+ x y))))

simplify2.3s

Counts

86 → 86

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	162	2222
1	378	2068
2	1033	1914
3	3110	1858
done	5000	1853

prune601.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.0b

regimes181.0ms

Accuracy

0% (0.1b remaining)

Error of 19.8b against oracle of 19.7b and baseline of 19.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	15	12
done	15	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

744.0ms	8000×	body	80	valid
622.0ms	7981×	body	80	nan