Details

sample66.0ms

Algorithm

intervals

Results

16.0ms	47×	body	1280	valid
13.0ms	245×	body	80	nan
10.0ms	44×	body	640	valid
7.0ms	130×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize18.0ms

Local error

Found 1 expressions with local error:

3.2b	(- (sqrt (+ x 1)) (sqrt x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

1 → 71

Calls

1 calls:

Slowest

54.0ms

(- (sqrt (+ x 1)) (sqrt x))

series73.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

72.0ms

(- (sqrt (+ x 1)) (sqrt x))

simplify1.3s

Counts: 74 → 74

prune568.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
15×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `associate-/r/` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 72

Calls

2 calls:

Slowest

28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms	(+ (sqrt (+ x 1)) (sqrt x))

series190.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

107.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
83.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify988.0ms

Counts: 78 → 78

prune672.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
17×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`add-exp-log`
7×	`fma-def`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u` `pow1`
4×	`insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `log1p-udef` `expm1-log1p` `clear-num` `sum-log` `frac-2neg` `1-exp` `log1p-expm1` `div-inv` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 96

Calls

4 calls:

Slowest

46.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms	(+ (sqrt (+ x 1)) (sqrt x))
1.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

219.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
148.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
100.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
87.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts: 108 → 108

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(expm1 (expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))))
0.0b	(expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
17×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`add-exp-log`
7×	`fma-def`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16`
3×	`associate-/l*`
2×	`expm1-log1p` `flip3-+` `div-exp` `associate-/r/` `flip-+` `expm1-udef`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 96

Calls

4 calls:

Slowest

36.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
31.0ms	(+ (sqrt (+ x 1)) (sqrt x))
0.0ms	(expm1 (expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))))
0.0ms	(expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

Slowest

952.0ms	(expm1 (expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))))
555.0ms	(expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
96.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
67.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify2.4s

Counts: 108 → 108

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

649.0ms	4016×	body	80	valid
630.0ms	1783×	body	1280	valid
503.0ms	7827×	body	80	nan
278.0ms	1284×	body	640	valid
127.0ms	588×	body	320	valid
68.0ms	329×	body	160	valid