Details

sample68.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
16.0ms	246×	body	80	nan

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	69
3	64
2	44
1	22
0	11

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize31.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ (* x y) (* x z))
0.6b	(+ (+ (* x y) (* x z)) (* y z))
17.7b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`fma-def` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `sum-log`
3×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `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:

6.0ms	(+ (* x y) (* x z))
44.0ms	(+ (+ (* x y) (* x z)) (* y z))
53.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* x y) (* x z))
27.0ms	(+ (+ (* x y) (* x z)) (* y z))
171.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify962.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
2	1221
1	271
0	91

prune413.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ y z))
0.6b	(+ (* x (+ y z)) (* y z))
17.7b	(sqrt (+ (* x (+ y z)) (* y z)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

30.0ms	(* x (+ y z))
19.0ms	(+ (* x (+ y z)) (* y z))
23.0ms	(sqrt (+ (* x (+ y z)) (* y z)))

series294.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* x (+ y z))
37.0ms	(+ (* x (+ y z)) (* y z))
216.0ms	(sqrt (+ (* x (+ y z)) (* y z)))

simplify882.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1313
1	307
0	108

prune494.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x (+ y z) (* z y))
17.7b	(sqrt (* (sqrt (fma x (+ y z) (* z y))) (sqrt (fma x (+ y z) (* z y)))))
17.7b	(sqrt (fma x (+ y z) (* z y)))
17.7b	(sqrt (fma x (+ y z) (* z y)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-pow1`
22×	`pow1`
11×	`pow1/2`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
1×	`pow2` `pow-plus` `fma-udef`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma x (+ y z) (* z y))
7.0ms	(sqrt (* (sqrt (fma x (+ y z) (* z y))) (sqrt (fma x (+ y z) (* z y)))))
2.0ms	(sqrt (fma x (+ y z) (* z y)))
1.0ms	(sqrt (fma x (+ y z) (* z y)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma x (+ y z) (* z y))
167.0ms	(sqrt (* (sqrt (fma x (+ y z) (* z y))) (sqrt (fma x (+ y z) (* z y)))))
207.0ms	(sqrt (fma x (+ y z) (* z y)))
166.0ms	(sqrt (fma x (+ y z) (* z y)))

simplify1.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
3	2031
2	374
1	156
0	80

prune490.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.5b

localize30.0ms

Local error

Found 4 expressions with local error:

17.7b	(sqrt (fma x (+ y z) (* z y)))
17.7b	(sqrt (* (sqrt (fma x (+ y z) (* z y))) (* (fabs (cbrt (fma x (+ y z) (* y z)))) (sqrt (cbrt (fma x (+ y z) (* y z)))))))
18.2b	(cbrt (fma x (+ y z) (* y z)))
18.2b	(cbrt (fma x (+ y z) (* y z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow1/2` `pow1/3`
1×	`rem-sqrt-square`

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt (fma x (+ y z) (* z y)))
21.0ms	(sqrt (* (sqrt (fma x (+ y z) (* z y))) (* (fabs (cbrt (fma x (+ y z) (* y z)))) (sqrt (cbrt (fma x (+ y z) (* y z)))))))
1.0ms	(cbrt (fma x (+ y z) (* y z)))
8.0ms	(cbrt (fma x (+ y z) (* y z)))

series1.3s

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (fma x (+ y z) (* z y)))
441.0ms	(sqrt (* (sqrt (fma x (+ y z) (* z y))) (* (fabs (cbrt (fma x (+ y z) (* y z)))) (sqrt (cbrt (fma x (+ y z) (* y z)))))))
403.0ms	(cbrt (fma x (+ y z) (* y z)))
339.0ms	(cbrt (fma x (+ y z) (* y z)))

simplify2.3s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	4471
2	1021
1	332
0	142

prune669.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.5b

regimes234.0ms

Accuracy

0% (0.1b remaining)

Error of 20.2b against oracle of 20.2b and baseline of 20.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	7937×	body	80	nan
685.0ms	8000×	body	80	valid