Details

sample135.0ms

Algorithm

intervals

Results

52.0ms	263×	body	160	nan
38.0ms	533×	body	80	nan
22.0ms	256×	body	80	valid

simplify141.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

141.0ms

(log (+ x (sqrt (- (* x x) 1))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize24.0ms

Local error

Found 2 expressions with local error:

29.4b	(sqrt (fma x x -1))
0.0b	(+ x (sqrt (fma x x -1)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def` `sqrt-prod`
2×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

Slowest

10.0ms	(+ x (sqrt (fma x x -1)))
3.0ms	(sqrt (fma x x -1))

series141.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

74.0ms	(+ x (sqrt (fma x x -1)))
67.0ms	(sqrt (fma x x -1))

simplify1.9s

Counts

15 → 40

Calls

15 calls:

Slowest

547.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
268.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
256.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
255.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
236.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune363.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ -1/8 x) (* x x))
0.0b	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
19×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`fma-def` `div-inv`
2×	`expm1-log1p-u` `pow1` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip-+` `fma-udef` `distribute-lft-out` `associate-/l/`

Counts

2 → 68

Calls

2 calls:

Slowest

28.0ms	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
20.0ms	(/ (/ -1/8 x) (* x x))

series144.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

73.0ms	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
71.0ms	(/ (/ -1/8 x) (* x x))

simplify2.8s

Counts

56 → 74

Calls

56 calls:

Slowest

270.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
237.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
216.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
164.0ms	(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
162.0ms	(* (exp (fma 2 x (/ -1/2 x))) (exp (/ (/ -1/8 x) (* x x))))

prune708.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.7s	7715×	body	160	nan
1.6s	16362×	body	80	nan
708.0ms	8000×	body	80	valid