Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	217×	pre	80	false

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	97	11
4	179	11
5	293	11
6	455	11
7	1416	11
done	5000	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

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))))
13.9b	(/ (- (* a a) (* b b)) (* a a))

rewrite16.0ms

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×	`sqrt-prod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 52

Calls

3 calls:

2.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
12.0ms	(/ (- (* a a) (* b b)) (* a a))

series98.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
48.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify607.0ms

Counts

61 → 61

Iterations

Useful iterations: done (605.0ms)

Iter	Nodes	Cost
0	90	893
1	224	771
2	791	676
done	5000	668

prune131.0ms

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

rewrite26.0ms

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-r`
11×	`associate-/r/`
9×	`div-exp`
8×	`pow1`
7×	`div-inv`
6×	`associate-/l*`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`add-log-exp`
3×	`associate-l` `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` `associate-r/` `pow-prod-down` `-commutative` `inv-pow`

Counts

4 → 158

Calls

4 calls:

4.0ms	(/ a (- a (* b (/ b a))))
1.0ms	(sqrt (fabs (/ 1 (/ a (- a (* b (/ b a)))))))
7.0ms	(/ 1 (/ a (- a (* b (/ b a)))))
8.0ms	(* b (/ b a))

series129.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ a (- a (* b (/ b a))))
14.0ms	(sqrt (fabs (/ 1 (/ a (- a (* b (/ b a)))))))
52.0ms	(/ 1 (/ a (- a (* b (/ b a)))))
18.0ms	(* b (/ b a))

simplify2.5s

Counts

170 → 170

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	245	2864
1	548	2553
2	1303	2289
3	4911	2245
done	5000	2245

prune321.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 143

Calls

4 calls:

1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
7.0ms	(/ (- a b) a)
8.0ms	(/ (+ a b) a)
29.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series128.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
31.0ms	(/ (- a b) a)
21.0ms	(/ (+ a b) a)
60.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify978.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (437.0ms)

Iter	Nodes	Cost
0	184	1937
1	489	1843
2	1789	1679
done	5000	1679

prune326.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes23.0ms

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

sample603.0ms

Algorithm

intervals

Results

192.0ms	8000×	body	80	valid
97.0ms	8109×	pre	80	false
93.0ms	8000×	pre	80	true