Details

sample114.0ms

Algorithm

intervals

Results

37.0ms	217×	body	160	nan
35.0ms	496×	body	80	nan
23.0ms	256×	body	80	valid

simplify159.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

159.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize11.0ms

Local error

Found 2 expressions with local error:

27.7b	(sqrt (fma x x -1))
0.0b	(+ x (sqrt (fma x x -1)))

rewrite7.0ms

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))

series149.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

81.0ms	(+ x (sqrt (fma x x -1)))
68.0ms	(sqrt (fma x x -1))

simplify1.5s

Counts

15 → 40

Calls

15 calls:

Slowest

432.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
221.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
204.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
189.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
177.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune334.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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

10.0ms

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

series46.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

46.0ms

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

simplify1.9s

Counts

48 → 52

Calls

48 calls:

Slowest

179.0ms	(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) x)
172.0ms	(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
161.0ms	(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
141.0ms	(/ (* (* (/ -1/8 x) (/ -1/8 x)) (/ -1/8 x)) (* (* (* x x) (* x x)) (* x x)))
124.0ms	(/ (* (* (/ -1/8 x) (/ -1/8 x)) (/ -1/8 x)) (* (* (* x x) x) (* (* x x) x)))

prune500.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma x x -1))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma x x -1))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series936.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

324.0ms	(cbrt x)
306.0ms	(cbrt x)
251.0ms	(cbrt x)
54.0ms	(sqrt (fma x x -1))

simplify2.0s

Counts

26 → 70

Calls

26 calls:

Slowest

585.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
541.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
245.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
168.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
139.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune812.0ms

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

sample4.0s

Algorithm

intervals

Results

1.7s	16300×	body	80	nan
1.2s	7539×	body	160	nan
691.0ms	8000×	body	80	valid