Details

sample392.0ms

Algorithm

intervals

Results

195.0ms	83×	body	1280	valid
104.0ms	93×	body	2560	valid
31.0ms	263×	body	80	nan
22.0ms	41×	body	640	valid
13.0ms	14×	body	320	valid
7.0ms	8×	body	80	valid
5.0ms	17×	body	160	valid

simplify255.0ms

Calls

1 calls:

Slowest

255.0ms

(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.5b	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b	(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-/r*` `add-cbrt-cube` `difference-of-sqr-1` `add-exp-log`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`

Calls

2 calls:

Slowest

12.0ms	(/ (fma -5 (* v v) 1) (- (* v v) 1))
2.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series47.0ms

Calls

2 calls:

Slowest

42.0ms	(/ (fma -5 (* v v) 1) (- (* v v) 1))
5.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify6.4s

Calls

40 calls:

Slowest

435.0ms	(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
378.0ms	(- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1)
370.0ms	(/ (* (* (fma -5 (* v v) 1) (fma -5 (* v v) 1)) (fma -5 (* v v) 1)) (* (* (- (* v v) 1) (- (* v v) 1)) (- (* v v) 1)))
309.0ms	(acos (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))
286.0ms	(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))

prune815.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (/ (sqrt (fma -5 (* v v) 1)) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1)))))
0.0b	(/ (sqrt (fma -5 (* v v) 1)) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1))))
0.0b	(sqrt (fma -5 (* v v) 1))
0.0b	(sqrt (fma -5 (* v v) 1))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

336×	`times-frac`
177×	`sqrt-prod`
171×	`add-sqr-sqrt`
169×	`*-un-lft-identity` `add-cube-cbrt`
42×	`difference-of-sqr-1`
28×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `pow1/2`
1×	`acos-asin` `clear-num` `frac-2neg` `associate-/r/`

Calls

4 calls:

Slowest

19.0ms	(/ (sqrt (fma -5 (* v v) 1)) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1))))
2.0ms	(sqrt (fma -5 (* v v) 1))
2.0ms	(acos (/ (sqrt (fma -5 (* v v) 1)) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1)))))
2.0ms	(sqrt (fma -5 (* v v) 1))

series312.0ms

Calls

4 calls:

Slowest

234.0ms	(sqrt (fma -5 (* v v) 1))
37.0ms	(sqrt (fma -5 (* v v) 1))
35.0ms	(/ (sqrt (fma -5 (* v v) 1)) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1))))
6.0ms	(acos (/ (sqrt (fma -5 (* v v) 1)) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1)))))

simplify1.7m

Calls

394 calls:

Slowest

1.0s	(/ (sqrt (cbrt (fma -5 (* v v) 1))) (/ (- (* v v) 1) (sqrt (cbrt (fma -5 (* v v) 1)))))
928.0ms	(/ (cbrt (sqrt (fma -5 (* v v) 1))) (/ (sqrt (- (* v v) 1)) (sqrt (sqrt (fma -5 (* v v) 1)))))
920.0ms	(/ (cbrt (sqrt (fma -5 (* v v) 1))) (/ (- (* v v) 1) (sqrt (sqrt (fma -5 (* v v) 1)))))
866.0ms	(/ (sqrt (sqrt (fma -5 (* v v) 1))) (/ (sqrt (- (* v v) 1)) (sqrt (fma -5 (* v v) 1))))
843.0ms	(/ (sqrt (sqrt (fma -5 (* v v) 1))) (/ (- (* v v) 1) (sqrt (fma -5 (* v v) 1))))

prune3.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 2 expressions with local error:

0.5b	(acos (/ (fma (* v v) -5 1) (fma v v -1)))
0.0b	(/ (fma (* v v) -5 1) (fma v v -1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Calls

2 calls:

Slowest

9.0ms	(/ (fma (* v v) -5 1) (fma v v -1))
2.0ms	(acos (/ (fma (* v v) -5 1) (fma v v -1)))

series43.0ms

Calls

2 calls:

Slowest

38.0ms	(/ (fma (* v v) -5 1) (fma v v -1))
5.0ms	(acos (/ (fma (* v v) -5 1) (fma v v -1)))

simplify3.8s

Calls

31 calls:

Slowest

601.0ms	(/ (* (* (fma (* v v) -5 1) (fma (* v v) -5 1)) (fma (* v v) -5 1)) (* (* (fma v v -1) (fma v v -1)) (fma v v -1)))
308.0ms	(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
284.0ms	(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
227.0ms	(acos (/ (fma (pow v 2) -5 1) (fma v v -1)))
216.0ms	(- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1)

prune571.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
1.0b	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
1.0b	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
0.5b	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
6×	`add-cbrt-cube` `pow1/2` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow-prod-down` `pow-prod-up`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

13.0ms	(* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
2.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
2.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
2.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series60.0ms

Calls

4 calls:

Slowest

26.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
23.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
6.0ms	(* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
5.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify7.4s

Calls

42 calls:

Slowest

308.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
286.0ms	(sqrt (* (cbrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
278.0ms	(sqrt (cbrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
277.0ms	(sqrt (* (cbrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
266.0ms	(* (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))) (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))

prune991.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

regimes183.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample9.6s

Algorithm

intervals

Results

3.5s	3016×	body	2560	valid
2.4s	2537×	body	1280	valid
2.0s	7916×	body	80	nan
824.0ms	1246×	body	640	valid
324.0ms	575×	body	320	valid
122.0ms	413×	body	160	valid
34.0ms	213×	body	80	valid