Details

sample55.0ms

Algorithm

intervals

Results

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

simplify334.0ms

Calls

1 calls:

Slowest

334.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize20.0ms

Local error

Found 2 expressions with local error:

7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
81×	`frac-times`
72×	`*-un-lft-identity`
71×	`add-cube-cbrt`
61×	`associate-/l*`
60×	`associate-/r*`
40×	`times-frac`
21×	`clear-num`
20×	`frac-2neg`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
9×	`associate-l/` `associate-r/`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`expm1-log1p-u` `un-div-inv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Calls

2 calls:

Slowest

22.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series51.0ms

Calls

2 calls:

Slowest

28.0ms	(* (/ b a) (/ b a))
23.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify8.2s

Calls

263 calls:

Slowest

439.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
434.0ms	(* (/ a (cbrt b)) (/ a b))
223.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
175.0ms	(* (/ b (sqrt a)) (/ b (* (cbrt a) (cbrt a))))
174.0ms	(* (/ b (* (cbrt a) (cbrt a))) (* (cbrt b) (cbrt b)))

prune2.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.8b

localize40.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
81×	`frac-times`
76×	`*-un-lft-identity`
75×	`add-cube-cbrt`
61×	`associate-/l*`
60×	`associate-/r*`
40×	`times-frac`
21×	`clear-num`
20×	`frac-2neg`
16×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
9×	`associate-l/` `associate-r/` `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`
2×	`un-div-inv`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Calls

4 calls:

Slowest

28.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series85.0ms

Calls

4 calls:

Slowest

30.0ms	(* (/ b a) (/ b a))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
17.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
15.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify9.1s

Calls

279 calls:

Slowest

498.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
207.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
179.0ms	(* (/ b (sqrt a)) (/ b (* (cbrt a) (cbrt a))))
164.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
162.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune3.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 7.8b

localize28.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0b	(log1p (expm1 (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
0.5b	(expm1 (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
0.4b	(* (/ b a) (/ b a))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
81×	`frac-times`
74×	`*-un-lft-identity`
73×	`add-cube-cbrt`
61×	`associate-/l*`
60×	`associate-/r*`
40×	`times-frac`
21×	`clear-num`
20×	`frac-2neg`
16×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
9×	`associate-l/` `associate-r/`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`log1p-expm1` `un-div-inv`
1×	`pow2` `rem-sqrt-square` `log1p-udef` `expm1-log1p` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `expm1-udef`

Calls

4 calls:

Slowest

17.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.0ms	(log1p (expm1 (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
0.0ms	(expm1 (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))

series176.0ms

Calls

4 calls:

Slowest

71.0ms	(log1p (expm1 (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
43.0ms	(expm1 (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
39.0ms	(* (/ b a) (/ b a))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify8.6s

Calls

272 calls:

Slowest

407.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
246.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
174.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
167.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))
164.0ms	(* (/ b (* (cbrt a) (cbrt a))) (/ b a))

prune2.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 7.8b

regimes50.0ms

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

854.0ms	8000×	body	80	valid
366.0ms	8000×	pre	80	true