Details

sample52.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify318.0ms

Calls

1 calls:

Slowest

318.0ms

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.9b

localize27.0ms

Local error

Found 3 expressions with local error:

6.0b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))
0.0b	(- 1 (* (/ b a) (/ b a)))

rewrite40.0ms

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--`

Calls

3 calls:

Slowest

26.0ms	(* (/ b a) (/ b a))
9.0ms	(- 1 (* (/ b a) (/ b a)))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series132.0ms

Calls

3 calls:

Slowest

53.0ms	(* (/ b a) (/ b a))
53.0ms	(- 1 (* (/ b a) (/ b a)))
26.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.2s

Calls

94 calls:

Slowest

407.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
278.0ms	(/ (exp 1) (exp (* (/ b a) (/ b a))))
227.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
215.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
163.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (* (/ b a) b) a)
6.0b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
0.2b	(* (/ b a) b)
0.0b	(- 1 (/ (* (/ b a) b) a))

rewrite36.0ms

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/`

Calls

4 calls:

Slowest

13.0ms	(* (/ b a) b)
12.0ms	(/ (* (/ b a) b) a)
8.0ms	(- 1 (/ (* (/ b a) b) a))
1.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series171.0ms

Calls

4 calls:

Slowest

64.0ms	(- 1 (/ (* (/ b a) b) a))
48.0ms	(/ (* (/ b a) b) a)
34.0ms	(* (/ b a) b)
24.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify3.8s

Calls

62 calls:

Slowest

510.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
325.0ms	(/ (* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b)) (* (* a a) a))
249.0ms	(/ (* (* (* (/ b a) b) (* (/ b a) b)) (* (/ b a) b)) (* (* a a) a))
229.0ms	(/ (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b)) (* (* a a) a))
229.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.8b

localize22.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (* (/ b a) b) a)
6.4b	(/ (* (/ b a) b) a)
6.0b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
6.0b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`cbrt-undiv` `div-exp`
6×	`pow1` `associate-/r*` `times-frac` `sqrt-prod`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `div-inv` `associate-/l` `associate-/l/`

Calls

4 calls:

Slowest

23.0ms	(/ (* (/ b a) b) a)
17.0ms	(/ (* (/ b a) b) a)
2.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
2.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series126.0ms

Calls

4 calls:

Slowest

44.0ms	(/ (* (/ b a) b) a)
37.0ms	(/ (* (/ b a) b) a)
23.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
21.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify4.1s

Calls

54 calls:

Slowest

343.0ms	(/ (* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b)) (* (* a a) a))
323.0ms	(/ (* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b)) (* (* a a) a))
236.0ms	(/ (* (* (* (/ b a) b) (* (/ b a) b)) (* (/ b a) b)) (* (* a a) a))
220.0ms	(/ (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b)) (* (* a a) a))
195.0ms	(/ (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b)) (* (* a a) a))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 5.8b

localize42.0ms

Local error

Found 4 expressions with local error:

48.8b	(posit16->real (real->posit16 (* (/ b a) b)))
6.4b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
6.0b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
0.2b	(* (/ b a) b)

rewrite17.0ms

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`

Calls

4 calls:

Slowest

10.0ms	(* (/ b a) b)
4.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
1.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series101.0ms

Calls

4 calls:

Slowest

29.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
27.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
23.0ms	(* (/ b a) b)
22.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))

simplify2.7s

Calls

65 calls:

Slowest

436.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
221.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))
184.0ms	(/ (* (* (posit16->real (real->posit16 (* (/ b a) b))) (posit16->real (real->posit16 (* (/ b a) b)))) (posit16->real (real->posit16 (* (/ b a) b)))) (* (* a a) a))
124.0ms	(fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a)))
121.0ms	(sqrt (* (cbrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a)))) (cbrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))))

prune2.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

regimes209.0ms

Accuracy

0% (0.1b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

755.0ms	8000×	body	80	valid
337.0ms	8000×	pre	80	true