Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	255×	body	80	nan
6.0ms	53×	body	1280	valid
4.0ms	44×	body	640	valid
4.0ms	134×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	12×	body	160	valid

simplify25.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

76.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series81.0ms

Counts

1 → 3

Calls

1 calls:

81.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify748.0ms

Counts: 22 → 22

prune97.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

62.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
95.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series314.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
222.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify415.0ms

Counts: 61 → 61

prune160.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

48.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
62.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
63.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
188.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
210.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
436.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
199.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.4s

Counts: 457 → 457

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
0.2b	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
0.4b	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

rewrite774.0ms

Algorithm

rewrite-expression-head

Rules

1822×	`*-un-lft-identity`
1674×	`times-frac`
1600×	`sqrt-prod`
840×	`cbrt-prod`
702×	`add-sqr-sqrt` `add-cube-cbrt`
640×	`distribute-lft-out`
324×	`unpow-prod-down` `cube-prod`
90×	`associate-/l*`
36×	`cube-mult` `unpow3` `associate-/r*` `sqr-pow`
28×	`sqrt-div`
26×	`cube-div`
24×	`cbrt-div` `associate-/r/`
14×	`flip3-+` `flip-+`
12×	`add-exp-log` `div-inv`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 1096

Calls

4 calls:

186.0ms	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
323.0ms	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
47.0ms	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
56.0ms	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

series1.5s

Counts

4 → 12

Calls

4 calls:

518.0ms	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
174.0ms	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
245.0ms	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
541.0ms	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

simplify1.6s

Counts: 1108 → 1108

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify19.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

735.0ms	1748×	body	1280	valid
258.0ms	7985×	body	80	nan
162.0ms	4122×	body	80	valid
148.0ms	1238×	body	640	valid
47.0ms	611×	body	320	valid
15.0ms	281×	body	160	valid