Details

sample254.0ms

Algorithm

intervals

Results

92.0ms	88×	body	1280	valid
90.0ms	103×	body	2560	valid
27.0ms	263×	body	80	nan
16.0ms	30×	body	640	valid
7.0ms	17×	body	320	valid
4.0ms	14×	body	160	valid
0.0ms	4×	body	80	valid

simplify190.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

190.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b	(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
8×	`difference-of-squares`
6×	`associate-/r*`
4×	`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--`

Counts

2 → 55

Calls

2 calls:

Slowest

22.0ms	(/ (fma -5 (* v v) 1) (- (* v v) 1))
2.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series85.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

82.0ms	(/ (fma -5 (* v v) 1) (- (* v v) 1))
3.0ms	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify4.5s

Counts

54 → 61

Calls

54 calls:

Slowest

290.0ms	(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
208.0ms	(- (log (fma -5 (* v v) 1)) (log (- (* v v) 1)))
200.0ms	(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
185.0ms	(/ (sqrt (fma -5 (* v v) 1)) (sqrt (- (* v v) 1)))
184.0ms	(/ (* (cbrt (fma -5 (* v v) 1)) (cbrt (fma -5 (* v v) 1))) (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))))

prune483.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
0.0b	(fma (* v v) (* v v) (* v v))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`acos-asin` `fma-udef`

Counts

2 → 22

Calls

2 calls:

Slowest

1.0ms	(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
0.0ms	(fma (* v v) (* v v) (* v v))

series153.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

147.0ms	(fma (* v v) (* v v) (* v v))
5.0ms	(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))

simplify213.0ms

Counts

6 → 28

Calls

6 calls:

Slowest

63.0ms	(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
42.0ms	(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
42.0ms	(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
28.0ms	(+ (pow v 4) (pow v 2))
24.0ms	(+ (pow v 4) (pow v 2))

prune288.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
0.0b	(fma (* v v) (* v v) (* v v))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`acos-asin` `fma-udef`

Counts

2 → 22

Calls

2 calls:

Slowest

1.0ms	(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
0.0ms	(fma (* v v) (* v v) (* v v))

series161.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

158.0ms	(fma (* v v) (* v v) (* v v))
3.0ms	(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))

simplify280.0ms

Counts

6 → 28

Calls

6 calls:

Slowest

80.0ms	(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
79.0ms	(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
72.0ms	(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
20.0ms	(+ (pow v 4) (pow v 2))
14.0ms	(+ (pow v 4) (pow v 2))

prune275.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize45.0ms

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))))
0.2b	(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

rewrite26.0ms

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

18.0ms	(* (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)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

20.0ms	(sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))
17.0ms	(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)))

simplify10.6s

Counts

82 → 107

Calls

82 calls:

Slowest

545.0ms	(* (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
272.0ms	(* (* (* (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))))))
239.0ms	(* (* (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)))))))
191.0ms	(+ (log (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (log (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
189.0ms	(sqrt (sqrt (acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))))

prune879.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes81.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.9s	3032×	body	2560	valid
2.3s	2478×	body	1280	valid
1.2s	8130×	body	80	nan
695.0ms	1243×	body	640	valid
345.0ms	628×	body	320	valid
101.0ms	415×	body	160	valid
27.0ms	204×	body	80	valid