Details

sample72.0ms

Algorithm

intervals

Results

22.0ms	219×	body	160	nan
21.0ms	484×	body	80	nan
15.0ms	256×	body	80	valid

simplify108.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

108.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize19.0ms

Local error

Found 2 expressions with local error:

29.0b	(sqrt (fma x x -1))
0.0b	(log (+ x (sqrt (fma x x -1))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

Slowest

4.0ms	(log (+ x (sqrt (fma x x -1))))
1.0ms	(sqrt (fma x x -1))

series208.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

157.0ms	(log (+ x (sqrt (fma x x -1))))
51.0ms	(sqrt (fma x x -1))

simplify3.8s

Counts

46 → 40

Calls

46 calls:

Slowest

403.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
310.0ms	(log (+ (* x x) (- (* (sqrt (fma x x -1)) (sqrt (fma x x -1))) (* x (sqrt (fma x x -1))))))
260.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
242.0ms	(log (+ (pow x 3) (pow (sqrt (fma x x -1)) 3)))
241.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune338.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ (/ -1/8 x) (* x x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
6×	`cbrt-undiv` `div-exp`
3×	`div-inv`
2×	`prod-exp` `cbrt-unprod`
1×	`expm1-log1p-u` `pow1` `clear-num` `associate-/r*` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`

Counts

1 → 49

Calls

1 calls:

Slowest

20.0ms

(/ (/ -1/8 x) (* x x))

series68.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

68.0ms

(/ (/ -1/8 x) (* x x))

simplify3.0s

Counts

66 → 52

Calls

66 calls:

Slowest

400.0ms	(* (* (/ (/ -1/8 x) (* x x)) (/ (/ -1/8 x) (* x x))) (/ (/ -1/8 x) (* x x)))
172.0ms	(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
141.0ms	(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
136.0ms	(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) x)
133.0ms	(/ (* (* (/ -1/8 x) (/ -1/8 x)) (/ -1/8 x)) (* (* (* x x) x) (* (* x x) x)))

prune457.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (fma x x -1))
29.0b	(sqrt (fma x x -1))
0.0b	(sqrt (+ x (sqrt (fma x x -1))))
0.0b	(sqrt (+ x (sqrt (fma x x -1))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`sqrt-prod`
12×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

Slowest

10.0ms	(sqrt (+ x (sqrt (fma x x -1))))
6.0ms	(sqrt (+ x (sqrt (fma x x -1))))
1.0ms	(sqrt (fma x x -1))
1.0ms	(sqrt (fma x x -1))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(sqrt (+ x (sqrt (fma x x -1))))
96.0ms	(sqrt (+ x (sqrt (fma x x -1))))
83.0ms	(sqrt (fma x x -1))
76.0ms	(sqrt (fma x x -1))

simplify7.0s

Counts

92 → 86

Calls

92 calls:

Slowest

466.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
364.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
279.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
268.0ms	(+ (sqrt (sqrt -1)) (+ (* 1/8 (* (pow x 2) (sqrt (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (* x (sqrt (/ 1 (sqrt -1)))))))
264.0ms	(sqrt (- (* x x) (* (sqrt (fma x x -1)) (sqrt (fma x x -1)))))

prune942.0ms

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 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	7582×	body	160	nan
1.2s	8000×	body	80	valid
1.1s	16074×	body	80	nan