Details

sample24.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify17.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize16.0ms

Local error

Found 1 expressions with local error:

12.0b

(/ 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))

series56.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

55.0ms

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

simplify1.1s

Counts: 33 → 33

prune291.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

11.9b	(sqrt (+ (* x x) 1))
11.9b	(sqrt (+ (* x x) 1))
0.0b	(/ x (sqrt (+ (* x x) 1)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 266

Calls

4 calls:

Slowest

31.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
15.0ms	(sqrt (+ (* x x) 1))
14.0ms	(sqrt (+ (* x x) 1))
11.0ms	(/ x (sqrt (+ (* x x) 1)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

84.0ms	(/ x (sqrt (+ (* x x) 1)))
79.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
32.0ms	(sqrt (+ (* x x) 1))
32.0ms	(sqrt (+ (* x x) 1))

simplify892.0ms

Counts: 278 → 278

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

15.9b	(* (/ x (- (* (* x x) (* x x)) 1)) (- (* x x) 1))
3.4b	(/ x (- (* (* x x) (* x x)) 1))
0.1b	(* (* x x) (* x x))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

116×	`pow1`
38×	`add-sqr-sqrt`
37×	`times-frac`
36×	`pow-prod-up`
33×	`*-un-lft-identity`
25×	`associate-l` `add-cube-cbrt`
24×	`pow-prod-down`
22×	`add-cbrt-cube` `add-exp-log` `pow-sqr`
18×	`pow-plus`
16×	`difference-of-squares`
13×	`pow2`
10×	`prod-exp` `cbrt-unprod`
8×	`difference-of-sqr-1`
7×	`associate-r`
6×	`associate-/r*`
4×	`flip3--` `associate-/r/` `flip--`
3×	`insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `associate-r/` `-commutative` `div-inv`
1×	`clear-num` `frac-2neg` `swap-sqr` `associate-*l/`

Counts

3 → 161

Calls

3 calls:

Slowest

223.0ms	(* (/ x (- (* (* x x) (* x x)) 1)) (- (* x x) 1))
63.0ms	(/ x (- (* (* x x) (* x x)) 1))
25.0ms	(* (* x x) (* x x))

series401.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

193.0ms	(/ x (- (* (* x x) (* x x)) 1))
145.0ms	(* (/ x (- (* (* x x) (* x x)) 1)) (- (* x x) 1))
63.0ms	(* (* x x) (* x x))

simplify909.0ms

Counts: 170 → 170

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

15.4b	(/ (sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1)) (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))))
12.8b	(- (* x x) (* (* x x) (* x x)))
11.9b	(sqrt (+ (* x x) 1))
7.0b	(sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1))

rewrite506.0ms

Algorithm

rewrite-expression-head

Rules

78×	`sqrt-prod`
63×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
54×	`times-frac`
40×	`add-cube-cbrt`
15×	`difference-of-squares`
9×	`associate-/r*`
8×	`sqrt-div`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 133

Calls

4 calls:

Slowest

314.0ms	(/ (sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1)) (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))))
170.0ms	(sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1))
11.0ms	(- (* x x) (* (* x x) (* x x)))
7.0ms	(sqrt (+ (* x x) 1))

series533.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

200.0ms	(sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1))
179.0ms	(/ (sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1)) (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))))
104.0ms	(- (* x x) (* (* x x) (* x x)))
50.0ms	(sqrt (+ (* x x) 1))

simplify1.7s

Counts: 145 → 145

prune1.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 23.6b

bsearch87.0ms

end0.0ms

sample609.0ms

Algorithm

intervals

Results

481.0ms

8000×

body

valid