Details

sample32.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify14.0ms

Calls

1 calls:

Slowest

13.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize8.0ms

Local error

Found 1 expressions with local error:

14.5b

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

rewrite2.0ms

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

2.0ms

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

series49.0ms

Calls

1 calls:

Slowest

49.0ms

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

simplify565.0ms

Calls

8 calls:

Slowest

267.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
84.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
80.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
61.0ms	(- (+ x (pow x 5)) (pow x 3))
34.0ms	(- (* x x) 1)

prune134.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

14.4b	(sqrt (+ (* x x) 1))
14.4b	(sqrt (+ (* x x) 1))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
0.0b	(/ x (sqrt (+ (* x x) 1)))

rewrite20.0ms

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

9.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
3.0ms	(/ x (sqrt (+ (* x x) 1)))
3.0ms	(sqrt (+ (* x x) 1))
2.0ms	(sqrt (+ (* x x) 1))

series204.0ms

Calls

4 calls:

Slowest

82.0ms	(/ x (sqrt (+ (* x x) 1)))
48.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
41.0ms	(sqrt (+ (* x x) 1))
34.0ms	(sqrt (+ (* x x) 1))

simplify8.6s

Calls

118 calls:

Slowest

377.0ms	(/ (* (* (/ 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))))
343.0ms	(sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))
319.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (cbrt (+ (* x x) 1))))
317.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (+ (* x x) 1)))
315.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (sqrt (+ (* x x) 1)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

14.5b

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

1 calls:

Slowest

10.0ms

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

series51.0ms

Calls

1 calls:

Slowest

51.0ms

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

simplify1.2s

Calls

36 calls:

Slowest

268.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
177.0ms	(/ (* (* (/ x 1) (/ x 1)) (/ x 1)) (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)))
94.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
87.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
77.0ms	(- (+ x (pow x 5)) (pow x 3))

prune251.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

18.6b	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
0.3b	(/ 1 (pow x 5))
0.1b	(/ (/ 1 x) x)
0.1b	(/ (/ (/ 1 x) x) x)

rewrite27.0ms

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

11.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
10.0ms	(/ (/ (/ 1 x) x) x)
4.0ms	(/ (/ 1 x) x)
1.0ms	(/ 1 (pow x 5))

series291.0ms

Calls

4 calls:

Slowest

165.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
54.0ms	(/ 1 (pow x 5))
54.0ms	(/ (/ (/ 1 x) x) x)
19.0ms	(/ (/ 1 x) x)

simplify830.0ms

Calls

29 calls:

Slowest

151.0ms	(- (* 1 x) (* (pow x 5) (/ (/ 1 x) x)))
73.0ms	(/ (exp (/ 1 (pow x 5))) (exp (/ (/ (/ 1 x) x) x)))
70.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))
64.0ms	(+ (sqrt (/ 1 (pow x 5))) (sqrt (/ (/ (/ 1 x) x) x)))
57.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

prune747.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes53.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch116.0ms

end0.0ms

sample661.0ms

Algorithm

intervals

Results

519.0ms

8000×

body

valid