Details

sample22.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify8.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize8.0ms

Local error

Found 1 expressions with local error:

14.3b

(/ 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))

series45.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

45.0ms

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

simplify1.0s

Counts: 33 → 33

prune224.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

14.2b	(sqrt (+ (* x x) 1))
14.2b	(sqrt (+ (* x x) 1))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
0.0b	(/ x (sqrt (+ (* x x) 1)))

rewrite57.0ms

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

28.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
10.0ms	(/ x (sqrt (+ (* x x) 1)))
7.0ms	(sqrt (+ (* x x) 1))
7.0ms	(sqrt (+ (* x x) 1))

series203.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(/ x (sqrt (+ (* x x) 1)))
44.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
40.0ms	(sqrt (+ (* x x) 1))
35.0ms	(sqrt (+ (* x x) 1))

simplify1.4s

Counts: 278 → 278

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (+ (* x x) 1))
14.7b	(cbrt (+ (* x x) 1))
14.2b	(sqrt (+ (* x x) 1))
0.1b	(/ x (sqrt (cbrt (+ (* x x) 1))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac` `sqrt-prod`
18×	`cbrt-prod`
9×	`associate-/r*`
6×	`cbrt-div` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+` `insert-posit16` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 98

Calls

4 calls:

Slowest

21.0ms	(/ x (sqrt (cbrt (+ (* x x) 1))))
6.0ms	(sqrt (+ (* x x) 1))
4.0ms	(cbrt (+ (* x x) 1))
4.0ms	(cbrt (+ (* x x) 1))

series489.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ x (sqrt (cbrt (+ (* x x) 1))))
150.0ms	(cbrt (+ (* x x) 1))
136.0ms	(cbrt (+ (* x x) 1))
50.0ms	(sqrt (+ (* x x) 1))

simplify1.0s

Counts: 110 → 110

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

15.3b	(- (* x x) (* (* x x) (* x x)))
14.3b	(/ (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))) (sqrt (+ (* x x) 1)))
14.2b	(sqrt (+ (* x x) 1))
14.1b	(* (/ x (sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1))) (/ (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))) (sqrt (+ (* x x) 1))))

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
164×	`sqrt-prod`
148×	`times-frac`
122×	`*-un-lft-identity`
83×	`add-cube-cbrt`
60×	`associate-r`
27×	`difference-of-squares`
24×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
15×	`unswap-sqr`
13×	`distribute-lft-out--`
10×	`sqrt-div`
9×	`associate-/l*`
7×	`pow1`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16`
3×	`div-inv`
2×	`flip3--` `flip--` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 237

Calls

4 calls:

Slowest

435.0ms	(* (/ x (sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1))) (/ (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))) (sqrt (+ (* x x) 1))))
87.0ms	(/ (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))) (sqrt (+ (* x x) 1)))
14.0ms	(- (* x x) (* (* x x) (* x x)))
12.0ms	(sqrt (+ (* x x) 1))

series481.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

223.0ms	(* (/ x (sqrt (+ (* (* (* x x) x) (* (* x x) x)) 1))) (/ (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))) (sqrt (+ (* x x) 1))))
110.0ms	(- (* x x) (* (* x x) (* x x)))
101.0ms	(/ (sqrt (- 1 (- (* x x) (* (* x x) (* x x))))) (sqrt (+ (* x x) 1)))
47.0ms	(sqrt (+ (* x x) 1))

simplify1.6s

Counts: 249 → 249

prune3.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes60.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.4b

bsearch99.0ms

end0.0ms

sample544.0ms

Algorithm

intervals

Results

448.0ms

8000×

body

valid