Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify2.9s

Counts: 1 → 1

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.8b

localize15.0ms

Local error

Found 2 expressions with local error:

8.8b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite15.0ms

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

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

series65.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

45.0ms	(* (/ b a) (/ b a))
20.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.7s

Counts: 92 → 92

prune876.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.8b

localize16.0ms

Local error

Found 3 expressions with local error:

8.8b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
6.6b	(/ (* (/ b a) b) a)
0.2b	(* (/ b a) b)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac` `associate-l`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `associate-r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-*l/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

3 → 78

Calls

3 calls:

Slowest

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

series78.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

33.0ms	(* (/ b a) b)
32.0ms	(/ (* (/ b a) b) a)
13.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify1.6s

Counts: 87 → 87

prune832.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.6b

localize19.0ms

Local error

Found 4 expressions with local error:

16.2b	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
8.8b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 169

Calls

4 calls:

Slowest

21.0ms	(* (/ b a) (/ b a))
13.0ms	(* (/ b a) (/ b a))
8.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

45.0ms	(* (/ b a) (/ b a))
34.0ms	(* (/ b a) (/ b a))
24.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.7s

Counts: 181 → 181

prune2.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 8.6b

localize41.0ms

Local error

Found 4 expressions with local error:

45.7b	(posit16->real (real->posit16 (* (/ b a) b)))
8.8b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
6.6b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.2b	(* (/ b a) b)

rewrite32.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 92

Calls

4 calls:

Slowest

19.0ms	(* (/ 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

39.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
34.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
22.0ms	(* (/ b a) b)
21.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))

simplify873.0ms

Counts: 104 → 104

prune1.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.6b

regimes138.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

703.0ms	8000×	body	80	valid
310.0ms	8000×	pre	80	true