Details

sample16.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify9.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

9.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize8.0ms

Local error

Found 1 expressions with local error:

15.7b

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 30

Calls

1 calls:

Slowest

10.0ms

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

series53.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

53.0ms

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

simplify1.8s

Counts

30 → 33

Calls

30 calls:

Slowest

435.0ms	(/ (* (* x x) x) (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)))
322.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
228.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
209.0ms	(- (+ x (pow x 5)) (pow x 3))
199.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune245.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

15.6b	(sqrt (+ (* x x) 1))
15.6b	(sqrt (+ (* x x) 1))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
148×	`add-sqr-sqrt`
146×	`*-un-lft-identity` `add-cube-cbrt`
144×	`sqrt-prod`
24×	`associate-/l*`
20×	`sqrt-div`
16×	`associate-/r/`
10×	`flip3-+` `flip-+`
8×	`add-cbrt-cube` `add-exp-log` `div-inv`
6×	`associate-/r*`
5×	`pow1`
3×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

3 → 224

Calls

3 calls:

Slowest

51.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
13.0ms	(sqrt (+ (* x x) 1))
8.0ms	(sqrt (+ (* x x) 1))

series147.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

75.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
37.0ms	(sqrt (+ (* x x) 1))
34.0ms	(sqrt (+ (* x x) 1))

simplify24.3s

Counts

345 → 233

Calls

345 calls:

Slowest

751.0ms	(/ (sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))) (cbrt (sqrt (+ (* x x) 1))))
532.0ms	(/ (/ x (sqrt (+ (pow (* x x) 3) (pow 1 3)))) (sqrt (sqrt (+ (* x x) 1))))
494.0ms	(/ (/ (* (* x x) x) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1))))
494.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
473.0ms	(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

15.7b	(/ (+ (* x x) 1) x)
0.1b	(/ 1 (/ (+ (* x x) 1) x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `add-log-exp` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

2 → 107

Calls

2 calls:

Slowest

31.0ms	(/ (+ (* x x) 1) x)
22.0ms	(/ 1 (/ (+ (* x x) 1) x))

series167.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

101.0ms	(/ (+ (* x x) 1) x)
65.0ms	(/ 1 (/ (+ (* x x) 1) x))

simplify7.0s

Counts

132 → 113

Calls

132 calls:

Slowest

683.0ms	(/ (* (* 1 1) 1) (/ (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)) (* (* x x) x)))
510.0ms	(/ (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)) (* (* x x) x))
326.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))) (* (cbrt x) (cbrt x))))
321.0ms	(/ (sqrt 1) (/ (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))) (* (cbrt x) (cbrt x))))
274.0ms	(/ (* (* 1 1) 1) (* (* (/ (+ (* x x) 1) x) (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x)))

prune751.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ 1 (+ x (/ 1 x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`associate-/r*` `add-exp-log` `div-inv`
3×	`add-cbrt-cube` `associate-/l*`
2×	`pow1` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `insert-posit16` `pow-flip` `inv-pow` `add-log-exp`

Counts

1 → 42

Calls

1 calls:

Slowest

10.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

33.0ms

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

simplify1.8s

Counts

46 → 45

Calls

46 calls:

Slowest

480.0ms	(/ (* (* 1 1) 1) (* (* (+ x (/ 1 x)) (+ x (/ 1 x))) (+ x (/ 1 x))))
260.0ms	(- (+ x (pow x 5)) (pow x 3))
227.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
220.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
117.0ms	(+ (* x x) (- (* (/ 1 x) (/ 1 x)) (* x (/ 1 x))))

prune277.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample756.0ms

Algorithm

intervals

Results

622.0ms

8000×

body

valid