Details

sample56.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify289.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

289.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize25.0ms

Local error

Found 3 expressions with local error:

7.4b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b	(* (/ b a) (/ b a))
0.0b	(- 1 (* (/ b a) (/ b a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity`
32×	`add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod` `insert-posit16`
2×	`difference-of-squares`
1×	`pow2` `frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

3 → 97

Calls

3 calls:

Slowest

16.0ms	(* (/ b a) (/ b a))
4.0ms	(- 1 (* (/ b a) (/ b a)))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series109.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

56.0ms	(- 1 (* (/ b a) (/ b a)))
29.0ms	(* (/ b a) (/ b a))
23.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.2s

Counts

94 → 106

Calls

94 calls:

Slowest

443.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
254.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
240.0ms	(/ (exp 1) (exp (* (/ b a) (/ b a))))
189.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
186.0ms	(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))

prune993.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 7.3b

localize40.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
7.4b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b	(* (/ b a) (/ b a))
0.3b	(* (/ b a) (/ b a))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`times-frac`
62×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`sqrt-prod`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 164

Calls

4 calls:

Slowest

29.0ms	(* (/ b a) (/ b a))
24.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

49.0ms	(* (/ b a) (/ b a))
44.0ms	(* (/ b a) (/ b a))
23.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify7.4s

Counts

172 → 176

Calls

172 calls:

Slowest

512.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
461.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
218.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
214.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
193.0ms	(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))

prune2.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 7.3b

regimes75.0ms

Accuracy

0% (0.0b remaining)

Error of 7.5b against oracle of 7.5b and baseline of 7.5b

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

868.0ms	8000×	body	80	valid
351.0ms	8000×	pre	80	true