Details

sample172.0ms

Algorithm

intervals

Results

77.0ms	75×	body	1280	valid
32.0ms	50×	body	640	valid
17.0ms	11×	body	160	valid
17.0ms	20×	body	2560	valid
10.0ms	25×	body	320	valid
8.0ms	75×	body	80	valid

simplify21.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize27.0ms

Local error

Found 3 expressions with local error:

14.3b	(sqrt (+ (* x x) 1))
2.6b	(log (+ x (sqrt (+ (* x x) 1))))
0.6b	(+ x (sqrt (+ (* x x) 1)))

rewrite69.0ms

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

33.0ms	(+ x (sqrt (+ (* x x) 1)))
22.0ms	(log (+ x (sqrt (+ (* x x) 1))))
13.0ms	(sqrt (+ (* x x) 1))

series241.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

137.0ms	(log (+ x (sqrt (+ (* x x) 1))))
55.0ms	(sqrt (+ (* x x) 1))
49.0ms	(+ x (sqrt (+ (* x x) 1)))

simplify733.0ms

Counts: 63 → 54

prune492.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

18.2b	(+ (* 3/40 (pow x 5)) (* -1/6 (* (* x x) x)))
0.1b	(* -1/6 (* (* x x) x))
0.1b	(* (* x x) x)
0.1b	(* 3/40 (pow x 5))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
23×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`associate-r`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`associate-l`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `pow-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `flip3-+` `pow3` `pow-exp` `flip-+`

Counts

4 → 89

Calls

4 calls:

Slowest

71.0ms	(* -1/6 (* (* x x) x))
28.0ms	(* (* x x) x)
17.0ms	(* 3/40 (pow x 5))
16.0ms	(+ (* 3/40 (pow x 5)) (* -1/6 (* (* x x) x)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

197.0ms	(+ (* 3/40 (pow x 5)) (* -1/6 (* (* x x) x)))
61.0ms	(* 3/40 (pow x 5))
53.0ms	(* -1/6 (* (* x x) x))
52.0ms	(* (* x x) x)

simplify354.0ms

Counts: 102 → 101

prune967.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite454.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`*-un-lft-identity` `add-exp-log`
18×	`add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`distribute-lft-out`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `flip3-+` `pow-sqr` `flip-+`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `frac-add` `log-pow` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

Slowest

357.0ms	(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
63.0ms	(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))
19.0ms	(/ -1/8 (* (* x x) x))
14.0ms	(* (* x x) x)

series403.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))
144.0ms	(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
56.0ms	(/ -1/8 (* (* x x) x))
54.0ms	(* (* x x) x)

simplify571.0ms

Counts: 109 → 97

prune842.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

21.0b	(+ (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))
10.5b	(log (+ (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ -1/16 (pow x 5))))
0.4b	(/ 1/8 (* x x))
0.3b	(/ -1/16 (pow x 5))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
30×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
9×	`add-log-exp`
8×	`associate-/r*` `frac-add`
6×	`log-div` `log-prod` `distribute-lft-out` `associate-/l*`
5×	`pow1` `div-exp`
4×	`insert-posit16` `distribute-lft-out--` `sqr-pow`
3×	`cbrt-undiv`
2×	`associate-+l+` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `frac-sub` `flip-+` `div-inv` `flip--` `sub-div`
1×	`pow-to-exp` `+-commutative` `sub-neg` `diff-log` `rem-log-exp` `pow-exp` `prod-exp` `log-pow` `associate-+l-` `cbrt-unprod`

Counts

4 → 113

Calls

4 calls:

Slowest

158.0ms	(+ (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))
96.0ms	(log (+ (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ -1/16 (pow x 5))))
10.0ms	(/ 1/8 (* x x))
5.0ms	(/ -1/16 (pow x 5))

series351.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(log (+ (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ -1/16 (pow x 5))))
91.0ms	(/ -1/16 (pow x 5))
76.0ms	(+ (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))
56.0ms	(/ 1/8 (* x x))

simplify730.0ms

Counts: 167 → 125

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes98.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch143.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.3s	2320×	body	1280	valid
863.0ms	1625×	body	640	valid
511.0ms	793×	body	2560	valid
243.0ms	753×	body	320	valid
183.0ms	2116×	body	80	valid
109.0ms	393×	body	160	valid