Details

sample112.0ms

Algorithm

intervals

Results

52.0ms	76×	body	1280	valid
21.0ms	50×	body	640	valid
16.0ms	27×	body	2560	valid
5.0ms	75×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.7b

localize27.0ms

Local error

Found 4 expressions with local error:

15.4b	(sqrt (+ (* x x) 1))
2.1b	(log (+ x (sqrt (+ (* x x) 1))))
1.1b	(+ x (sqrt (+ (* x x) 1)))
0.0b	(+ (* x x) 1)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

Slowest

31.0ms	(sqrt (+ (* x x) 1))
12.0ms	(+ x (sqrt (+ (* x x) 1)))
12.0ms	(log (+ x (sqrt (+ (* x x) 1))))
11.0ms	(+ (* x x) 1)

series308.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(log (+ x (sqrt (+ (* x x) 1))))
69.0ms	(+ (* x x) 1)
63.0ms	(+ x (sqrt (+ (* x x) 1)))
37.0ms	(sqrt (+ (* x x) 1))

simplify763.0ms

Counts: 69 → 69

prune592.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

19.8b	(+ (* (* (* x x) x) -1/6) (* 3/40 (pow x 5)))
0.1b	(* (* (* x x) x) -1/6)
0.1b	(* 3/40 (pow x 5))
0.0b	(* (* x x) x)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
23×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`associate-r`
12×	`prod-exp`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
5×	`associate-l`
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

59.0ms	(+ (* (* (* x x) x) -1/6) (* 3/40 (pow x 5)))
50.0ms	(* (* (* x x) x) -1/6)
28.0ms	(* (* x x) x)
10.0ms	(* 3/40 (pow x 5))

series429.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

229.0ms	(+ (* (* (* x x) x) -1/6) (* 3/40 (pow x 5)))
92.0ms	(* 3/40 (pow x 5))
60.0ms	(* (* (* x x) x) -1/6)
48.0ms	(* (* x x) x)

simplify2.0s

Counts: 101 → 101

prune919.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

10.2b	(log (+ (/ x 1/2) (- (/ 1/2 x) (/ (/ 1/8 x) (* x x)))))
0.1b	(/ (/ 1/8 x) (* x x))
0.0b	(- (/ 1/2 x) (/ (/ 1/8 x) (* x x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

Slowest

43.0ms	(log (+ (/ x 1/2) (- (/ 1/2 x) (/ (/ 1/8 x) (* x x)))))
29.0ms	(- (/ 1/2 x) (/ (/ 1/8 x) (* x x)))
19.0ms	(/ (/ 1/8 x) (* x x))

series315.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

139.0ms	(- (/ 1/2 x) (/ (/ 1/8 x) (* x x)))
107.0ms	(log (+ (/ x 1/2) (- (/ 1/2 x) (/ (/ 1/8 x) (* x x)))))
68.0ms	(/ (/ 1/8 x) (* x x))

simplify637.0ms

Counts: 97 → 97

prune897.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

19.9b	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 x) (* x x))))
11.2b	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 x) (* x x)))))
0.2b	(/ -1/16 (pow x 5))
0.1b	(/ (/ 1/8 x) (* x x))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

Slowest

79.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 x) (* x x))))
78.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 x) (* x x)))))
18.0ms	(/ (/ 1/8 x) (* x x))
9.0ms	(/ -1/16 (pow x 5))

series405.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

177.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 x) (* x x)))))
84.0ms	(/ -1/16 (pow x 5))
80.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 x) (* x x))))
63.0ms	(/ (/ 1/8 x) (* x x))

simplify981.0ms

Counts: 144 → 144

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.0b

bsearch145.0ms

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	2361×	body	1280	valid
832.0ms	1587×	body	640	valid
699.0ms	815×	body	2560	valid
268.0ms	757×	body	320	valid
195.0ms	2099×	body	80	valid
72.0ms	381×	body	160	valid