Details

sample22.0ms

Algorithm

intervals

Results

10.0ms	241×	body	80	valid
1.0ms	5×	body	1280	valid
0.0ms	5×	body	320	valid
0.0ms	2×	body	2560	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid

simplify8.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r-` `flip3-+` `div-sub` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 13

Calls

1 calls:

22.0ms

(+ x (/ (- x y) 2.0))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(+ x (/ (- x y) 2.0))

simplify72.0ms

Counts: 16 → 16

prune38.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.2b	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity` `sqrt-prod`
28×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+r-` `pow-plus` `sqrt-unprod` `div-sub` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

22.0ms	(+ x (/ (- x y) 2.0))
37.0ms	(sqrt (+ x (/ (- x y) 2.0)))
38.0ms	(sqrt (+ x (/ (- x y) 2.0)))
174.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ x (/ (- x y) 2.0))
92.0ms	(sqrt (+ x (/ (- x y) 2.0)))
91.0ms	(sqrt (+ x (/ (- x y) 2.0)))
40.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

simplify189.0ms

Counts: 119 → 119

prune208.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
0.1b	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
0.2b	(* (sqrt (+ x (/ (- x y) 2.0))) (* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0))))))
0.3b	(* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0)))))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-div`
112×	`sqrt-prod`
91×	`sqrt-pow1`
69×	`pow1`
60×	`add-sqr-sqrt`
47×	`pow1/2`
42×	`*-un-lft-identity`
39×	`pow-prod-up`
35×	`flip3-+` `flip-+`
32×	`frac-times`
22×	`add-cube-cbrt`
20×	`swap-sqr`
17×	`associate-l`
16×	`associate-*r/`
12×	`pow-prod-down`
11×	`add-exp-log` `associate-r` `pow-sqr` `add-cbrt-cube` `unswap-sqr`
10×	`associate-*l/`
9×	`distribute-lft-out`
4×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`pow2` `pow-plus` `rem-square-sqrt`

Counts

4 → 205

Calls

4 calls:

39.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
39.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
250.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0))))))
177.0ms	(* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

440.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
453.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
46.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0))))))
91.0ms	(* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0)))))

simplify74.0ms

Counts: 217 → 217

prune395.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ x (/ (- x y) 2.0)))) (sqrt (+ x (/ (- x y) 2.0))))
0.2b	(* (* (fabs (cbrt (+ x (/ (- x y) 2.0)))) (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (cbrt (+ x (/ (- x y) 2.0)))))
0.6b	(cbrt (+ x (/ (- x y) 2.0)))
0.6b	(cbrt (+ x (/ (- x y) 2.0)))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`associate-r`
16×	`add-sqr-sqrt`
14×	`sqrt-div`
12×	`cbrt-prod` `add-cube-cbrt` `sqrt-prod`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`cbrt-div` `associate-*r/`
9×	`flip3-+` `flip-+`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out` `add-log-exp`
2×	`pow1/3` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

86.0ms	(* (fabs (cbrt (+ x (/ (- x y) 2.0)))) (sqrt (+ x (/ (- x y) 2.0))))
165.0ms	(* (* (fabs (cbrt (+ x (/ (- x y) 2.0)))) (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (cbrt (+ x (/ (- x y) 2.0)))))
19.0ms	(cbrt (+ x (/ (- x y) 2.0)))
20.0ms	(cbrt (+ x (/ (- x y) 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (fabs (cbrt (+ x (/ (- x y) 2.0)))) (sqrt (+ x (/ (- x y) 2.0))))
519.0ms	(* (* (fabs (cbrt (+ x (/ (- x y) 2.0)))) (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (cbrt (+ x (/ (- x y) 2.0)))))
451.0ms	(cbrt (+ x (/ (- x y) 2.0)))
445.0ms	(cbrt (+ x (/ (- x y) 2.0)))

simplify55.0ms

Counts: 98 → 98

prune328.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample518.0ms

Algorithm

intervals

Results

263.0ms	7418×	body	80	valid
24.0ms	237×	body	1280	valid
11.0ms	137×	body	640	valid
11.0ms	90×	body	2560	valid
5.0ms	79×	body	320	valid
2.0ms	42×	body	160	valid