Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	273×	pre	80	false
3.0ms	256×	pre	80	true

simplify42.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
13.4b	(/ (- (* a a) (* b b)) (* a a))

rewrite42.0ms

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:

17.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
23.0ms	(/ (- (* a a) (* b b)) (* a a))

series115.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(- (* a a) (* b b))
20.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
56.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify159.0ms

Counts: 61 → 61

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite95.0ms

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))))
19.0ms	(/ (+ a b) a)
18.0ms	(/ (- a b) a)
51.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series144.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
24.0ms	(/ (+ a b) a)
32.0ms	(/ (- a b) a)
66.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify59.0ms

Counts: 155 → 155

prune360.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (+ a b)) (sqrt a))
0.0b	(/ (- a b) a)
0.0b	(* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))
0.1b	(* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

169×	`times-frac`
159×	`*-un-lft-identity`
154×	`add-sqr-sqrt`
150×	`sqrt-prod`
107×	`add-cube-cbrt`
92×	`associate-l`
61×	`add-exp-log` `add-cbrt-cube`
22×	`prod-exp` `cbrt-unprod`
20×	`associate-r`
19×	`cbrt-undiv` `div-exp` `distribute-lft-out`
12×	`associate-/l*`
11×	`pow1`
10×	`unswap-sqr`
9×	`associate-/r*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`frac-times` `associate-*r/`
5×	`div-inv`
4×	`pow-prod-down` `associate-*l/` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `sqrt-div` `clear-num` `*-commutative`
1×	`sqrt-undiv` `flip3--` `flip3-+` `div-sub` `flip--` `flip-+`

Counts

4 → 287

Calls

4 calls:

17.0ms	(/ (sqrt (+ a b)) (sqrt a))
17.0ms	(/ (- a b) a)
104.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))
72.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a))

series313.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (sqrt (+ a b)) (sqrt a))
32.0ms	(/ (- a b) a)
107.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))
103.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a))

simplify44.0ms

Counts: 299 → 299

prune765.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`times-frac`
23×	`add-cube-cbrt`
16×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `difference-of-squares`
7×	`pow1` `distribute-lft-out`
6×	`add-log-exp`
4×	`associate-/l*`
3×	`sub-neg` `flip3--` `associate-/r*` `sqrt-prod` `flip--`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip-+`

Counts

4 → 111

Calls

4 calls:

12.0ms	(- 1 (/ b a))
1.0ms	(sqrt (fabs (* (/ (+ a b) a) (- 1 (/ b a)))))
19.0ms	(/ (+ a b) a)
80.0ms	(* (/ (+ a b) a) (- 1 (/ b a)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- 1 (/ b a))
15.0ms	(sqrt (fabs (* (/ (+ a b) a) (- 1 (/ b a)))))
23.0ms	(/ (+ a b) a)
67.0ms	(* (/ (+ a b) a) (- 1 (/ b a)))

simplify46.0ms

Counts: 123 → 123

prune279.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample955.0ms

Algorithm

intervals

Results

293.0ms	8000×	body	80	valid
168.0ms	8000×	pre	80	true
107.0ms	7920×	pre	80	false