Details

sample115.0ms

Algorithm

intervals

Results

38.0ms	237×	body	160	nan
33.0ms	493×	body	80	nan
21.0ms	256×	body	80	valid

simplify128.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

128.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize13.0ms

Local error

Found 2 expressions with local error:

29.6b	(sqrt (fma x x -1))
0.0b	(+ x (sqrt (fma x x -1)))

rewrite6.0ms

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

5.0ms	(+ x (sqrt (fma x x -1)))
1.0ms	(sqrt (fma x x -1))

series145.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

84.0ms	(+ x (sqrt (fma x x -1)))
62.0ms	(sqrt (fma x x -1))

simplify1.7s

Counts

15 → 40

Calls

15 calls:

Slowest

467.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
308.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
246.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
224.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
185.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune349.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

Slowest

21.0ms	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
20.0ms	(/ (/ -1/8 x) (* x x))
17.0ms	(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))

series240.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

111.0ms	(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))
74.0ms	(/ (/ -1/8 x) (* x x))
55.0ms	(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))

simplify4.4s

Counts

66 → 95

Calls

66 calls:

Slowest

374.0ms	(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
342.0ms	(log (- (* (fma 2 x (/ -1/2 x)) (fma 2 x (/ -1/2 x))) (* (/ (/ -1/8 x) (* x x)) (/ (/ -1/8 x) (* x x)))))
260.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
247.0ms	(- (+ (log -1/8) (* 4 (pow x 2))) (+ (* 24 (pow x 4)) (* 3 (log x))))
226.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune807.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	7793×	body	160	nan
1.3s	8000×	body	80	valid
1.2s	16305×	body	80	nan