Details

sample122.0ms

Algorithm

intervals

Results

47.0ms	234×	body	160	nan
34.0ms	505×	body	80	nan
22.0ms	256×	body	80	valid

simplify151.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

151.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize29.0ms

Local error

Found 2 expressions with local error:

29.5b	(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)))
2.0ms	(sqrt (fma x x -1))

series191.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

108.0ms	(+ x (sqrt (fma x x -1)))
83.0ms	(sqrt (fma x x -1))

simplify1.6s

Counts

15 → 40

Calls

15 calls:

Slowest

406.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
277.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
249.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
238.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
171.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune376.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

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)))

rewrite51.0ms

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

29.0ms	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
20.0ms	(/ (/ -1/8 x) (* x x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

55.0ms	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
49.0ms	(/ (/ -1/8 x) (* x x))

simplify2.6s

Counts

56 → 74

Calls

56 calls:

Slowest

220.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
220.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
193.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
162.0ms	(* (exp (fma 2 x (/ -1/2 x))) (exp (/ (/ -1/8 x) (* x x))))
157.0ms	(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) x)

prune654.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	7567×	body	160	nan
1.3s	16256×	body	80	nan
732.0ms	8000×	body	80	valid