Details

sample42.0ms

Algorithm

intervals

Results

8.0ms	54×	body	1280	valid
8.0ms	251×	body	80	nan
5.0ms	135×	body	80	valid
4.0ms	37×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

8.0ms	(sqrt (+ x 1.0))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify91.0ms

Counts: 41 → 41

prune124.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

12.0ms	(sqrt (+ x 1.0))
42.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
59.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series334.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
96.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
202.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify98.0ms

Counts: 80 → 80

prune292.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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)))
0.1b	(/ 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))))

rewrite340.0ms

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:

40.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
157.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

232.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
191.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
433.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
166.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify148.0ms

Counts: 457 → 457

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

196×	`*-un-lft-identity`
181×	`sqrt-prod`
148×	`times-frac`
120×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
68×	`distribute-lft-out`
63×	`cbrt-prod`
60×	`associate-r`
32×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`associate-/r*`
15×	`associate-l` `unswap-sqr`
10×	`cbrt-undiv` `sqrt-div` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
7×	`pow1` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 250

Calls

4 calls:

57.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ (cbrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
59.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
292.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (cbrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

218.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
531.0ms	(/ (cbrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
552.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
229.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (cbrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify92.0ms

Counts: 262 → 262

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

628.0ms	1307×	body	640	valid
453.0ms	8028×	body	80	nan
325.0ms	1737×	body	1280	valid
197.0ms	4108×	body	80	valid
53.0ms	574×	body	320	valid
17.0ms	274×	body	160	valid