Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	257×	pre	80	false

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	100	11
4	190	11
5	330	11
6	557	11
7	1632	11
done	5000	11

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
11.0b	(/ (- (* a a) (* b b)) (* a a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 60

Calls

3 calls:

3.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms	(/ (- (* a a) (* b b)) (* a a))

series102.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(- (* a a) (* b b))
18.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
53.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify708.0ms

Counts

69 → 69

Iterations

Useful iterations: done (706.0ms)

Iter	Nodes	Cost
0	99	979
1	236	843
2	840	744
done	5000	736

prune167.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (- a (* (/ b a) b)))
0.0b	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
0.0b	(/ 1 (/ a (- a (* (/ b a) b))))
0.1b	(* (/ b a) b)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
71×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
18×	`associate-/r*`
16×	`add-cbrt-cube`
13×	`associate-l`
11×	`associate-/r/`
9×	`div-exp`
8×	`pow1`
7×	`div-inv`
6×	`associate-/l*`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `sqrt-prod`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 166

Calls

4 calls:

4.0ms	(/ a (- a (* (/ b a) b)))
1.0ms	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
8.0ms	(/ 1 (/ a (- a (* (/ b a) b))))
9.0ms	(* (/ b a) b)

series136.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ a (- a (* (/ b a) b)))
15.0ms	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
55.0ms	(/ 1 (/ a (- a (* (/ b a) b))))
19.0ms	(* (/ b a) b)

simplify2.0s

Counts

178 → 178

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	252	2932
1	550	2678
2	1512	2350
done	5000	2296

prune372.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (expm1 (log1p (- 1 (* (/ b a) (/ b a)))))))
0.0b	(expm1 (log1p (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `expm1-udef`

Counts

3 → 95

Calls

3 calls:

1.0ms	(sqrt (fabs (expm1 (log1p (- 1 (* (/ b a) (/ b a)))))))
0.0ms	(expm1 (log1p (- 1 (* (/ b a) (/ b a)))))
14.0ms	(* (/ b a) (/ b a))

series182.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(sqrt (fabs (expm1 (log1p (- 1 (* (/ b a) (/ b a)))))))
138.0ms	(expm1 (log1p (- 1 (* (/ b a) (/ b a)))))
26.0ms	(* (/ b a) (/ b a))

simplify898.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	167	1355
1	435	1166
2	1462	1016
done	5001	1016

prune266.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	13	13
done	13	13

end0.0ms

sample613.0ms

Algorithm

intervals

Results

193.0ms	8000×	body	80	valid
98.0ms	8219×	pre	80	false
92.0ms	8000×	pre	80	true