Details

sample203.0ms

Algorithm

intervals

Results

79.0ms	748×	body	80	nan
22.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify62.0ms

Calls

1 calls:

Slowest

61.0ms

(* (sqrt (- x 1)) (sqrt x))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (- x 1)) (sqrt x))
0.0b	(sqrt (- x 1))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt` `sqrt-prod`
4×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`pow1/2` `associate-r`
2×	`expm1-log1p-u` `flip3--` `pow-prod-down` `associate-*l/` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

2 calls:

Slowest

13.0ms	(* (sqrt (- x 1)) (sqrt x))
2.0ms	(sqrt (- x 1))

series126.0ms

Calls

2 calls:

Slowest

94.0ms	(* (sqrt (- x 1)) (sqrt x))
32.0ms	(sqrt (- x 1))

simplify873.0ms

Calls

27 calls:

Slowest

315.0ms	(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
136.0ms	(+ (* 1/2 (/ x (sqrt -1))) (+ (* 1/8 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
114.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
62.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt x))
29.0ms	(sqrt (- (* x x) (* 1 1)))

prune359.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(- x (- 1/2 (/ -1/8 x)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`sub-neg` `associate--r+`
1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `flip3--` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `flip--` `associate--r-` `add-log-exp`

Calls

1 calls:

Slowest

1.0ms

(- x (- 1/2 (/ -1/8 x)))

series27.0ms

Calls

1 calls:

Slowest

27.0ms

(- x (- 1/2 (/ -1/8 x)))

simplify306.0ms

Calls

6 calls:

Slowest

99.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
92.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
81.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
13.0ms	(- (/ -1/8 x))
13.0ms	(- (/ -1/8 x))

prune115.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

30.4b	(sqrt (fma x x -1))
18.5b	(/ (* (sqrt (fma x x -1)) (sqrt x)) (sqrt (+ x 1)))
0.2b	(* (sqrt (fma x x -1)) (sqrt x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `times-frac` `associate-l*`
5×	`pow1`
3×	`expm1-log1p-u` `pow1/2` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `sqrt-unprod` `sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`

Calls

3 calls:

Slowest

9.0ms	(/ (* (sqrt (fma x x -1)) (sqrt x)) (sqrt (+ x 1)))
5.0ms	(* (sqrt (fma x x -1)) (sqrt x))
1.0ms	(sqrt (fma x x -1))

series256.0ms

Calls

3 calls:

Slowest

113.0ms	(/ (* (sqrt (fma x x -1)) (sqrt x)) (sqrt (+ x 1)))
74.0ms	(* (sqrt (fma x x -1)) (sqrt x))
68.0ms	(sqrt (fma x x -1))

simplify3.0s

Calls

52 calls:

Slowest

403.0ms	(* (* (* (sqrt (fma x x -1)) (sqrt (fma x x -1))) (sqrt (fma x x -1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
351.0ms	(sqrt (sqrt (+ x 1)))
249.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
238.0ms	(/ (* (* (* (sqrt (fma x x -1)) (sqrt (fma x x -1))) (sqrt (fma x x -1))) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
185.0ms	(/ (* (* (* (sqrt (fma x x -1)) (sqrt x)) (* (sqrt (fma x x -1)) (sqrt x))) (* (sqrt (fma x x -1)) (sqrt x))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune719.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

30.4b

(sqrt (* x (- x 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`sqrt-div` `associate-*r/`
1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`

Calls

1 calls:

Slowest

3.0ms

(sqrt (* x (- x 1)))

series46.0ms

Calls

1 calls:

Slowest

46.0ms

(sqrt (* x (- x 1)))

simplify307.0ms

Calls

6 calls:

Slowest

96.0ms	(sqrt (* x (- (* x x) (* 1 1))))
80.0ms	(- (+ (* 1/8 (/ 1 x)) 1/2) x)
65.0ms	(sqrt (* x (- (pow x 3) (pow 1 3))))
64.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
1.0ms	(sqrt x)

prune81.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.7s	23560×	body	80	nan
565.0ms	7995×	body	80	valid
1.0ms	5×	body	160	valid