Details

sample137.0ms

Algorithm

intervals

Results

70.0ms	83×	body	1280	valid
27.0ms	50×	body	640	valid
18.0ms	24×	body	2560	valid
6.0ms	19×	body	320	valid
6.0ms	69×	body	80	valid
2.0ms	11×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.2b

localize43.0ms

Local error

Found 3 expressions with local error:

14.2b	(sqrt (+ (* x x) 1))
2.4b	(log (+ x (sqrt (+ (* x x) 1))))
1.0b	(+ x (sqrt (+ (* x x) 1)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 45

Calls

3 calls:

Slowest

13.0ms	(+ x (sqrt (+ (* x x) 1)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1))))
10.0ms	(sqrt (+ (* x x) 1))

series260.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

143.0ms	(log (+ x (sqrt (+ (* x x) 1))))
58.0ms	(sqrt (+ (* x x) 1))
58.0ms	(+ x (sqrt (+ (* x x) 1)))

simplify1.8s

Counts: 54 → 54

prune479.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

19.4b	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (* (* x x) (* (* x x) x))))
0.1b	(* (* (* x x) x) 1/6)
0.1b	(* 3/40 (* (* x x) (* (* x x) x)))
0.1b	(* (* x x) x)

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
47×	`add-cbrt-cube` `add-exp-log`
31×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up`
5×	`associate-l`
4×	`insert-posit16`
3×	`*-commutative`
2×	`pow2` `associate-+l+` `sum-log` `pow-sqr`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `pow3` `associate-+l-` `flip-+` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

Slowest

185.0ms	(* 3/40 (* (* x x) (* (* x x) x)))
59.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (* (* x x) (* (* x x) x))))
46.0ms	(* (* (* x x) x) 1/6)
14.0ms	(* (* x x) x)

series254.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

78.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (* (* x x) (* (* x x) x))))
69.0ms	(* 3/40 (* (* x x) (* (* x x) x)))
60.0ms	(* (* x x) x)
48.0ms	(* (* (* x x) x) 1/6)

simplify2.6s

Counts: 113 → 113

prune915.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

19.5b	(- (/ -1/16 (* (* x x) (* (* x x) x))) (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))
10.9b	(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
0.2b	(/ -1/16 (* (* x x) (* (* x x) x)))
0.1b	(/ 1/8 (* (* x x) x))

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
42×	`add-cbrt-cube`
19×	`*-un-lft-identity`
18×	`prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
10×	`cbrt-undiv` `div-exp`
9×	`add-cube-cbrt` `add-log-exp`
8×	`frac-sub`
6×	`log-prod` `times-frac` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`flip3--` `insert-posit16` `flip--`
3×	`diff-log`
2×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `div-inv` `associate--r+` `difference-of-squares`
1×	`rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 100

Calls

4 calls:

Slowest

232.0ms	(- (/ -1/16 (* (* x x) (* (* x x) x))) (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))
214.0ms	(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
47.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
17.0ms	(/ 1/8 (* (* x x) x))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
67.0ms	(- (/ -1/16 (* (* x x) (* (* x x) x))) (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))
56.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
53.0ms	(/ 1/8 (* (* x x) x))

simplify833.0ms

Counts: 112 → 112

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

8.8b	(log (+ x (+ (+ (/ (/ -1/8 (* x x)) x) x) (/ 1/2 x))))
0.2b	(/ -1/8 (* x x))
0.1b	(/ (/ -1/8 (* x x)) x)
0.0b	(+ x (+ (+ (/ (/ -1/8 (* x x)) x) x) (/ 1/2 x)))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
36×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`add-log-exp`
12×	`distribute-lft-out`
10×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`log-prod` `sum-log` `div-inv`
5×	`pow1`
4×	`associate-/r*` `insert-posit16`
2×	`log-div` `clear-num` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
1×	`+-commutative` `associate-+r+` `rem-log-exp` `log-pow` `associate-/l/`

Counts

4 → 107

Calls

4 calls:

Slowest

314.0ms	(+ x (+ (+ (/ (/ -1/8 (* x x)) x) x) (/ 1/2 x)))
224.0ms	(log (+ x (+ (+ (/ (/ -1/8 (* x x)) x) x) (/ 1/2 x))))
11.0ms	(/ (/ -1/8 (* x x)) x)
6.0ms	(/ -1/8 (* x x))

series303.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(log (+ x (+ (+ (/ (/ -1/8 (* x x)) x) x) (/ 1/2 x))))
74.0ms	(+ x (+ (+ (/ (/ -1/8 (* x x)) x) x) (/ 1/2 x)))
67.0ms	(/ (/ -1/8 (* x x)) x)
32.0ms	(/ -1/8 (* x x))

simplify2.5s

Counts: 119 → 119

prune820.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch124.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	2268×	body	1280	valid
982.0ms	802×	body	2560	valid
806.0ms	1551×	body	640	valid
251.0ms	754×	body	320	valid
208.0ms	2236×	body	80	valid
68.0ms	389×	body	160	valid