Details

sample26.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify15.0ms

Calls

1 calls:

Slowest

15.0ms

(/ x (+ (* x x) 1))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize22.0ms

Local error

Found 1 expressions with local error:

16.5b

(/ x (+ (* x x) 1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-/r*`
2×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/` `add-cube-cbrt`
1×	`pow1` `clear-num` `frac-2neg` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Calls

1 calls:

Slowest

3.0ms

(/ x (+ (* x x) 1))

series44.0ms

Calls

1 calls:

Slowest

44.0ms

(/ x (+ (* x x) 1))

simplify588.0ms

Calls

8 calls:

Slowest

294.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
117.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
62.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
52.0ms	(- (+ x (pow x 5)) (pow x 3))
21.0ms	(- (* x x) 1)

prune116.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

16.4b	(sqrt (+ (* x x) 1))
16.4b	(sqrt (+ (* x x) 1))
0.0b	(/ x (sqrt (+ (* x x) 1)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
31×	`add-sqr-sqrt`
30×	`sqrt-prod`
29×	`*-un-lft-identity` `add-cube-cbrt`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`div-inv`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`pow1` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `pow1/2`
1×	`cbrt-undiv` `div-exp` `associate-/l/`

Calls

4 calls:

Slowest

7.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
2.0ms	(sqrt (+ (* x x) 1))
2.0ms	(sqrt (+ (* x x) 1))
2.0ms	(/ x (sqrt (+ (* x x) 1)))

series210.0ms

Calls

4 calls:

Slowest

70.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
64.0ms	(/ x (sqrt (+ (* x x) 1)))
43.0ms	(sqrt (+ (* x x) 1))
33.0ms	(sqrt (+ (* x x) 1))

simplify8.2s

Calls

118 calls:

Slowest

348.0ms	(/ (* (* (/ x (sqrt (+ (* x x) 1))) (/ x (sqrt (+ (* x x) 1)))) (/ x (sqrt (+ (* x x) 1)))) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1))))
332.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (sqrt (+ (* x x) 1))))
319.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (+ (* x x) 1)))
289.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (+ (* x x) 1)))
279.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (cbrt (+ (* x x) 1))))

prune977.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

16.3b	(* x (/ 1 (+ 1 (* x x))))
0.2b	(/ 1 (+ 1 (* x x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-r`
4×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/` `add-cube-cbrt`
3×	`pow1` `associate-/r*` `add-exp-log`
2×	`flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `div-inv` `add-log-exp`
1×	`rec-exp` `clear-num` `frac-2neg` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Calls

2 calls:

Slowest

1.0ms	(* x (/ 1 (+ 1 (* x x))))
1.0ms	(/ 1 (+ 1 (* x x)))

series108.0ms

Calls

2 calls:

Slowest

62.0ms	(* x (/ 1 (+ 1 (* x x))))
46.0ms	(/ 1 (+ 1 (* x x)))

simplify2.0s

Calls

20 calls:

Slowest

823.0ms	(+ (* 1 1) (- (* (* x x) (* x x)) (* 1 (* x x))))
490.0ms	(+ (* 1 1) (- (* (* x x) (* x x)) (* 1 (* x x))))
119.0ms	(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (/ 1 (pow x 4)))
113.0ms	(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (/ 1 (pow x 4)))
112.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune291.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

20.2b	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
0.2b	(/ (/ 1 x) x)
0.1b	(/ 1 (pow x 5))
0.1b	(/ (/ (/ 1 x) x) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`associate-/l*`
7×	`add-cube-cbrt`
6×	`div-inv` `add-log-exp`
5×	`add-exp-log`
4×	`pow1` `add-cbrt-cube` `insert-posit16`
3×	`clear-num` `associate-/r*` `frac-2neg`
2×	`rec-exp` `distribute-lft-out--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow` `difference-of-squares`

Calls

4 calls:

Slowest

7.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
5.0ms	(/ (/ (/ 1 x) x) x)
3.0ms	(/ (/ 1 x) x)
1.0ms	(/ 1 (pow x 5))

series265.0ms

Calls

4 calls:

Slowest

143.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
60.0ms	(/ 1 (pow x 5))
44.0ms	(/ (/ (/ 1 x) x) x)
17.0ms	(/ (/ 1 x) x)

simplify854.0ms

Calls

29 calls:

Slowest

203.0ms	(- (* 1 x) (* (pow x 5) (/ (/ 1 x) x)))
71.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
66.0ms	(/ (exp (/ 1 (pow x 5))) (exp (/ (/ (/ 1 x) x) x)))
57.0ms	(- (sqrt (/ 1 (pow x 5))) (sqrt (/ (/ (/ 1 x) x) x)))
52.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

prune728.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch75.0ms

end0.0ms

sample725.0ms

Algorithm

intervals

Results

622.0ms

8000×

body

valid