Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	56×	body	1280	valid
17.0ms	45×	body	640	valid
11.0ms	122×	body	80	valid
6.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify285.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize13.0ms

Local error

Found 3 expressions with local error:

3.6b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

Slowest

62.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
26.0ms	(/ (+ x 1) (- x 1))
12.0ms	(/ x (+ x 1))

series149.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

96.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
27.0ms	(/ (+ x 1) (- x 1))
25.0ms	(/ x (+ x 1))

simplify905.0ms

Counts: 762 → 762

prune7.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

6.8b	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
0.2b	(/ 1 (* x x))
0.1b	(/ 3 (* x (* x x)))
0.1b	(* x (* x x))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
26×	`pow1`
23×	`*-un-lft-identity` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`times-frac` `prod-exp` `add-log-exp`
8×	`distribute-lft-out`
7×	`div-exp` `cbrt-unprod`
6×	`fma-def` `pow-prod-up` `div-inv` `pow-flip` `associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-l`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `pow-plus` `distribute-rgt-out` `1-exp` `pow-sqr` `flip-+`
1×	`+-commutative` `associate-+l+` `cube-unmult` `associate-r` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

Slowest

160.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
17.0ms	(* x (* x x))
12.0ms	(/ 3 (* x (* x x)))
9.0ms	(/ 1 (* x x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

54.0ms	(/ 3 (* x (* x x)))
43.0ms	(* x (* x x))
36.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
25.0ms	(/ 1 (* x x))

simplify2.3s

Counts: 129 → 129

prune855.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 x) (/ 1 x))
0.2b	(* (/ 1 x) (fma (* (/ 1 x) (/ 1 x)) 3 (+ (/ 1 x) 3)))
0.1b	(fma (* (/ 1 x) (/ 1 x)) 3 (+ (/ 1 x) 3))
0.0b	(+ (/ 1 x) 3)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
68×	`times-frac`
59×	`*-un-lft-identity`
53×	`add-exp-log`
47×	`add-cube-cbrt`
26×	`associate-l`
21×	`pow1` `add-cbrt-cube`
20×	`prod-exp`
18×	`div-exp`
16×	`associate-r`
15×	`swap-sqr`
13×	`fma-def`
12×	`unswap-sqr`
9×	`rec-exp` `1-exp` `div-inv`
8×	`pow-flip` `inv-pow`
6×	`cbrt-unprod` `add-log-exp`
5×	`cbrt-undiv` `pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`pow-sqr` `fma-udef`
2×	`associate-l/` `-commutative` `distribute-lft-out`
1×	`pow2` `distribute-rgt-in` `frac-times` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `pow-plus` `associate-*r/` `un-div-inv` `flip-+`

Counts

4 → 178

Calls

4 calls:

Slowest

18.0ms	(* (/ 1 x) (/ 1 x))
11.0ms	(* (/ 1 x) (fma (* (/ 1 x) (/ 1 x)) 3 (+ (/ 1 x) 3)))
9.0ms	(+ (/ 1 x) 3)
0.0ms	(fma (* (/ 1 x) (/ 1 x)) 3 (+ (/ 1 x) 3))

series100.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

48.0ms	(* (/ 1 x) (fma (* (/ 1 x) (/ 1 x)) 3 (+ (/ 1 x) 3)))
24.0ms	(* (/ 1 x) (/ 1 x))
14.0ms	(fma (* (/ 1 x) (/ 1 x)) 3 (+ (/ 1 x) 3))
14.0ms	(+ (/ 1 x) 3)

simplify557.0ms

Counts: 190 → 190

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

3.6b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

Slowest

111.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
16.0ms	(/ (+ x 1) (- x 1))
7.0ms	(/ x (+ x 1))

series149.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

93.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
30.0ms	(/ (+ x 1) (- x 1))
26.0ms	(/ x (+ x 1))

simplify1.0s

Counts: 762 → 762

prune7.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.7b

bsearch150.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

925.0ms	1758×	body	1280	valid
446.0ms	1295×	body	640	valid
387.0ms	4020×	body	80	valid
184.0ms	615×	body	320	valid
78.0ms	312×	body	160	valid