Details

sample37.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify281.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

281.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.1b

localize16.0ms

Local error

Found 2 expressions with local error:

8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`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

2 → 86

Calls

2 calls:

Slowest

23.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series40.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

27.0ms	(* (/ b a) (/ b a))
13.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.5s

Counts

86 → 92

Calls

86 calls:

Slowest

403.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
235.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
175.0ms	(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))
155.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
144.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))

prune889.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.0b

localize41.0ms

Local error

Found 4 expressions with local error:

8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
40×	`times-frac`
35×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
9×	`sqrt-prod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 118

Calls

4 calls:

Slowest

13.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

26.0ms	(* (/ b a) (/ b a))
24.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
20.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
19.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.4s

Counts

102 → 130

Calls

102 calls:

Slowest

335.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
205.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
153.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
146.0ms	(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))
124.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

prune1.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 8.0b

localize39.0ms

Local error

Found 3 expressions with local error:

8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.4b	(expm1 (log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
0.4b	(* (/ b a) (/ b a))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
32×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `expm1-udef`

Counts

3 → 98

Calls

3 calls:

Slowest

30.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms	(expm1 (log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

series86.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

43.0ms	(expm1 (log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
30.0ms	(* (/ b a) (/ b a))
13.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.7s

Counts

90 → 107

Calls

90 calls:

Slowest

456.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
206.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
168.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
138.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
136.0ms	(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 8.0b

regimes60.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

898.0ms	8000×	body	80	valid
334.0ms	8000×	pre	80	true