Details

sample58.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify280.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

280.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 3 expressions with local error:

7.4b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))
0.0b	(- 1 (* (/ b a) (/ b a)))

rewrite36.0ms

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

24.0ms	(* (/ b a) (/ b a))
8.0ms	(- 1 (* (/ b a) (/ b a)))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series109.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

48.0ms	(- 1 (* (/ b a) (/ b a)))
39.0ms	(* (/ b a) (/ b a))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.7s

Counts

94 → 106

Calls

94 calls:

Slowest

345.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
244.0ms	(/ (exp 1) (exp (* (/ b a) (/ b a))))
213.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
196.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
164.0ms	(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
4.5b	(/ (* (/ b a) b) a)
0.2b	(* (/ b a) b)
0.0b	(- 1 (/ (* (/ b a) b) a))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
15×	`add-cube-cbrt`
13×	`times-frac` `associate-l`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16`
3×	`associate-/r` `associate-r*` `sqrt-prod`
2×	`associate-*l/` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip--` `associate-/l` `distribute-lft-out--` `associate-/l/`

Counts

4 → 88

Calls

4 calls:

Slowest

11.0ms	(/ (* (/ b a) b) a)
10.0ms	(- 1 (/ (* (/ b a) b) a))
9.0ms	(* (/ b a) b)
1.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series150.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

62.0ms	(- 1 (/ (* (/ b a) b) a))
42.0ms	(/ (* (/ b a) b) a)
33.0ms	(* (/ b a) b)
13.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify3.1s

Counts

62 → 100

Calls

62 calls:

Slowest

405.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
267.0ms	(/ (* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b)) (* (* a a) a))
195.0ms	(/ (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b)) (* (* a a) a))
189.0ms	(/ (* (* (* (/ b a) b) (* (/ b a) b)) (* (/ b a) b)) (* (* a a) a))
184.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))

prune846.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.2b

localize42.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (- 1 (/ (* (/ b a) b) a)))
7.7b	(cbrt (- 1 (/ (* (/ b a) b) a)))
7.7b	(cbrt (- 1 (/ (* (/ b a) b) a)))
7.4b	(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod` `add-sqr-sqrt`
17×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`cbrt-div` `difference-of-squares`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3--` `pow1/3` `sqrt-prod` `flip--` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 65

Calls

4 calls:

Slowest

8.0ms	(cbrt (- 1 (/ (* (/ b a) b) a)))
6.0ms	(cbrt (- 1 (/ (* (/ b a) b) a)))
5.0ms	(cbrt (- 1 (/ (* (/ b a) b) a)))
2.0ms	(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

198.0ms	(cbrt (- 1 (/ (* (/ b a) b) a)))
183.0ms	(cbrt (- 1 (/ (* (/ b a) b) a)))
180.0ms	(cbrt (- 1 (/ (* (/ b a) b) a)))
14.0ms	(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

simplify3.9s

Counts

41 → 77

Calls

41 calls:

Slowest

275.0ms	(cbrt (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))))
271.0ms	(cbrt (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))))
263.0ms	(cbrt (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))))
239.0ms	(exp (* 1/3 (- (+ (* 2 (log (/ -1 a))) (log -1)) (* 2 (log (/ -1 b))))))
212.0ms	(exp (* 1/3 (- (+ (* 2 (log (/ 1 a))) (log -1)) (* 2 (log (/ 1 b))))))

prune922.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 7.2b

localize45.0ms

Local error

Found 4 expressions with local error:

50.5b	(posit16->real (real->posit16 (* (/ b a) b)))
7.4b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
4.5b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.2b	(* (/ b a) b)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `remove-posit16`

Counts

4 → 84

Calls

4 calls:

Slowest

23.0ms	(* (/ b a) b)
8.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
2.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
1.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

44.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
30.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
29.0ms	(* (/ b a) b)
12.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))

simplify2.7s

Counts

65 → 96

Calls

65 calls:

Slowest

491.0ms	(sqrt (sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a)))))
382.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
191.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))
158.0ms	(/ (* (* (posit16->real (real->posit16 (* (/ b a) b))) (posit16->real (real->posit16 (* (/ b a) b)))) (posit16->real (real->posit16 (* (/ b a) b)))) (* (* a a) a))
128.0ms	(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune2.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.2b

regimes123.0ms

Accuracy

0% (0.1b remaining)

Error of 7.3b against oracle of 7.2b and baseline of 7.3b

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

785.0ms	8000×	body	80	valid
333.0ms	8000×	pre	80	true