Details

sample51.0ms

Algorithm

intervals

Results

14.0ms	55×	body	1280	valid
10.0ms	218×	body	80	nan
7.0ms	35×	body	640	valid
6.0ms	133×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

simplify34.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize20.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 92

Calls

2 calls:

Slowest

32.0ms	(- (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series102.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

71.0ms	(- (sqrt (+ x 1)) (sqrt x))
31.0ms	(sqrt (+ x 1))

simplify1.6s

Counts: 98 → 98

prune832.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 93

Calls

3 calls:

Slowest

37.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms	(+ (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series192.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

90.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
65.0ms	(+ (sqrt (+ x 1)) (sqrt x))
38.0ms	(sqrt (+ x 1))

simplify1.3s

Counts: 102 → 102

prune853.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(log1p (expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite72.0ms

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×	`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

35.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
34.0ms	(+ (sqrt (+ x 1)) (sqrt x))
1.0ms	(expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.0ms	(log1p (expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

275.0ms	(log1p (expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
148.0ms	(expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
86.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
64.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.6s

Counts: 108 → 108

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))))
0.2b	(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
0.1b	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))
0.1b	(sqrt (sqrt (+ x 1)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`sqrt-prod`
9×	`times-frac`
8×	`add-exp-log`
7×	`pow1`
6×	`add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `sqrt-pow1` `sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `pow1/2` `div-exp`
1×	`cbrt-undiv` `rec-exp` `expm1-log1p` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `fma-udef` `div-inv` `pow-flip` `distribute-lft-out` `inv-pow` `expm1-udef`

Counts

4 → 82

Calls

4 calls:

Slowest

9.0ms	(sqrt (sqrt (+ x 1)))
4.0ms	(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
0.0ms	(expm1 (/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))))
0.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))

series576.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

254.0ms	(expm1 (/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))))
160.0ms	(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
125.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))
37.0ms	(sqrt (sqrt (+ x 1)))

simplify3.5s

Counts: 94 → 94

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

957.0ms	1666×	body	1280	valid
378.0ms	7729×	body	80	nan
326.0ms	4208×	body	80	valid
299.0ms	1214×	body	640	valid
125.0ms	618×	body	320	valid
32.0ms	294×	body	160	valid