Details

sample47.0ms

Algorithm

intervals

Results

13.0ms	60×	body	1280	valid
8.0ms	276×	body	80	nan
5.0ms	43×	body	640	valid
4.0ms	122×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	7×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize6.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite60.0ms

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:

59.0ms

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

series69.0ms

Counts

1 → 3

Calls

1 calls:

69.0ms

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

simplify792.0ms

Counts: 22 → 22

prune58.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

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)))

rewrite132.0ms

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:

49.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
78.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series250.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
172.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify544.0ms

Counts: 61 → 61

prune226.0ms

Pruning

9 alts after pruning (8 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))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
74×	`*-un-lft-identity`
32×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `add-log-exp` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

44.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
74.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
255.0ms	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
164.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
193.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
71.0ms	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.2s

Counts: 147 → 147

prune389.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.4b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

74.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
61.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
58.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
328.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

482.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
232.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
214.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
224.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.0s

Counts: 262 → 262

prune807.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify23.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

622.0ms	1230×	body	640	valid
429.0ms	1812×	body	1280	valid
379.0ms	8109×	body	80	nan
208.0ms	4052×	body	80	valid
61.0ms	616×	body	320	valid
20.0ms	290×	body	160	valid