Details

sample226.0ms

Algorithm

intervals

Results

110.0ms	105×	body	2560	valid
49.0ms	76×	body	1280	valid
24.0ms	257×	body	80	nan
19.0ms	36×	body	640	valid
8.0ms	20×	body	320	valid
3.0ms	14×	body	160	valid
1.0ms	5×	body	80	valid

simplify179.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

179.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 1 expressions with local error:

0.6b	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`acos-asin` `add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

Slowest

1.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

3.0ms

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

simplify312.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

117.0ms	(acos (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))
97.0ms	(acos (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))
97.0ms	(acos (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))

prune189.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize23.0ms

Local error

Found 1 expressions with local error:

0.6b	(acos (/ (fma (* v v) -5 1) (fma v v -1)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`acos-asin` `add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

Slowest

1.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

3.0ms

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

simplify211.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

84.0ms	(acos (/ (fma (pow v 2) -5 1) (fma v v -1)))
69.0ms	(acos (/ (fma (pow v 2) -5 1) (fma v v -1)))
57.0ms	(acos (/ (fma (pow v 2) -5 1) (fma v v -1)))

prune136.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

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))))
0.6b	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

Slowest

10.0ms	(* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
1.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
1.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
1.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

24.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
15.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
4.0ms	(* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
3.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify11.1s

Counts

82 → 107

Calls

82 calls:

Slowest

359.0ms	(* (* (* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (* (* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
280.0ms	(* (* (cbrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (cbrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (cbrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (cbrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))))
216.0ms	(* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
204.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
204.0ms	(sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))

prune820.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

451×	`sqrt-pow1`
342×	`pow1`
244×	`pow-prod-up`
227×	`pow1/2`
102×	`pow-sqr`
71×	`pow-prod-down`
18×	`pow-plus`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`prod-exp` `cbrt-unprod`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`sqrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
1×	`rem-square-sqrt` `swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 228

Calls

4 calls:

Slowest

104.0ms	(* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (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	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

22.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
18.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
15.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
8.0ms	(* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))))

simplify36.5s

Counts

344 → 240

Calls

344 calls:

Slowest

529.0ms	(* (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
521.0ms	(* (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
516.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
514.0ms	(* (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
405.0ms	(* (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))) (* (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (* (* (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))) (sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes130.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.4s	2997×	body	2560	valid
1.8s	2516×	body	1280	valid
1.3s	7762×	body	80	nan
732.0ms	1235×	body	640	valid
294.0ms	661×	body	320	valid
103.0ms	414×	body	160	valid
23.0ms	177×	body	80	valid