Details

sample54.0ms

Algorithm

intervals

Results

19.0ms	69×	body	640	valid
15.0ms	132×	body	80	valid
6.0ms	27×	body	320	valid
4.0ms	12×	body	1280	valid
2.0ms	16×	body	160	valid

simplify632.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize39.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

Slowest

227.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
61.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
12.0ms	(/ 1 (- x 1))
10.0ms	(/ 1 (+ x 1))

series186.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
21.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))

simplify1.8s

Counts: 153 → 153

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

6.6b	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
0.1b	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
0.0b	(sqrt (/ 1 (+ x 1)))
0.0b	(sqrt (/ 1 (+ x 1)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod`
129×	`*-un-lft-identity`
112×	`add-sqr-sqrt`
104×	`times-frac`
60×	`add-cube-cbrt`
31×	`pow1` `swap-sqr`
30×	`sqrt-pow1`
26×	`distribute-lft-out`
21×	`associate-r` `associate-l`
16×	`unswap-sqr`
12×	`associate-/r/`
10×	`pow1/2` `sqrt-div` `pow-flip` `inv-pow`
9×	`pow-prod-up` `div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`rem-sqrt-square` `add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `frac-add` `pow-sqr`
4×	`insert-posit16`
3×	`frac-sub`
2×	`frac-times` `associate-+l+` `sum-log` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip--`

Counts

4 → 217

Calls

4 calls:

Slowest

209.0ms	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
46.0ms	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
6.0ms	(sqrt (/ 1 (+ x 1)))
6.0ms	(sqrt (/ 1 (+ x 1)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
59.0ms	(sqrt (/ 1 (+ x 1)))
44.0ms	(sqrt (/ 1 (+ x 1)))
24.0ms	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))

simplify903.0ms

Counts: 229 → 229

prune2.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (pow x 5))
0.2b	(/ 2 (pow x 7))
0.1b	(/ (/ 2 x) (* x x))
0.0b	(+ (/ 2 (pow x 7)) (/ 2 (pow x 5)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

79×	`times-frac`
60×	`*-un-lft-identity`
52×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`add-exp-log`
24×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`associate-/l*`
15×	`associate-/r*`
12×	`div-exp`
8×	`cbrt-undiv` `sqr-pow`
7×	`div-inv`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `frac-add` `flip-+` `associate-/l/`

Counts

4 → 157

Calls

4 calls:

Slowest

29.0ms	(+ (/ 2 (pow x 7)) (/ 2 (pow x 5)))
12.0ms	(/ 2 (pow x 7))
12.0ms	(/ (/ 2 x) (* x x))
10.0ms	(/ 2 (pow x 5))

series494.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

244.0ms	(+ (/ 2 (pow x 7)) (/ 2 (pow x 5)))
96.0ms	(/ 2 (pow x 5))
88.0ms	(/ 2 (pow x 7))
65.0ms	(/ (/ 2 x) (* x x))

simplify685.0ms

Counts: 169 → 169

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (pow x 5))
0.2b	(/ 2 (pow x 7))
0.1b	(/ 2 (* x (* x x)))
0.0b	(* x (* x x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`pow1`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `pow-prod-up`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

Slowest

34.0ms	(/ 2 (* x (* x x)))
27.0ms	(* x (* x x))
10.0ms	(/ 2 (pow x 7))
6.0ms	(/ 2 (pow x 5))

series304.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(/ 2 (pow x 7))
83.0ms	(/ 2 (* x (* x x)))
65.0ms	(/ 2 (pow x 5))
56.0ms	(* x (* x x))

simplify2.2s

Counts: 153 → 153

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes45.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 25.1b

bsearch156.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

880.0ms	1859×	body	640	valid
710.0ms	567×	body	1280	valid
535.0ms	4169×	body	80	valid
371.0ms	946×	body	320	valid
140.0ms	459×	body	160	valid