Details

sample150.0ms

Algorithm

intervals

Results

96.0ms	192×	body	1280	valid
30.0ms	237×	body	80	valid
8.0ms	27×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify55.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

55.0ms

(+ (- (exp x) 2) (exp (- x)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.8b

localize23.0ms

Local error

Found 3 expressions with local error:

3.7b	(- (- (exp x) 2) (/ -1 (exp x)))
0.0b	(/ -1 (exp x))
0.0b	(- (exp x) 2)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`times-frac` `add-log-exp`
5×	`add-cbrt-cube`
4×	`diff-log` `add-exp-log` `distribute-lft-out--`
3×	`pow1` `associate-/r` `sub-neg` `flip3--` `insert-posit16` `flip--` `associate-/l` `difference-of-squares`
2×	`associate--l+` `frac-sub`
1×	`associate--l-` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 66

Calls

3 calls:

Slowest

72.0ms	(- (- (exp x) 2) (/ -1 (exp x)))
16.0ms	(- (exp x) 2)
10.0ms	(/ -1 (exp x))

series128.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

105.0ms	(- (- (exp x) 2) (/ -1 (exp x)))
12.0ms	(- (exp x) 2)
10.0ms	(/ -1 (exp x))

simplify2.2s

Counts

53 → 75

Calls

53 calls:

Slowest

315.0ms	(/ (* (* -1 -1) -1) (* (* (exp x) (exp x)) (exp x)))
252.0ms	(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
220.0ms	(- (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) -1))
166.0ms	(- (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) -1))
147.0ms	(* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp x))

prune580.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* 1/12 (* (* x x) (* x x)))
0.1b	(* (* (* x x) (* x x)) (* x x))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

909×	`pow1`
378×	`pow-prod-up`
203×	`pow-prod-down`
163×	`pow-plus`
159×	`pow-sqr`
102×	`pow2`
87×	`add-cbrt-cube` `add-exp-log`
60×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `associate-l`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`swap-sqr`
1×	`pow3`

Counts

4 → 366

Calls

4 calls:

Slowest

120.0ms	(* (* (* x x) (* x x)) (* x x))
107.0ms	(* 1/12 (* (* x x) (* x x)))
52.0ms	(* (* x x) (* x x))
45.0ms	(* (* x x) (* x x))

series234.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

62.0ms	(* 1/12 (* (* x x) (* x x)))
60.0ms	(* (* x x) (* x x))
59.0ms	(* (* x x) (* x x))
53.0ms	(* (* (* x x) (* x x)) (* x x))

simplify17.2s

Counts

425 → 378

Calls

425 calls:

Slowest

1.3s	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))
1.1s	(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) x) (* (* x x) x)))
1.0s	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))))
639.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))))
412.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))
0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (+ (* (exp x) (exp x)) -4))
0.0b	(* (+ (exp x) 2) (exp x))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
15×	`pow1`
10×	`add-cbrt-cube` `associate-l`
9×	`associate-r` `add-log-exp`
6×	`pow-prod-down` `associate-*r/` `add-exp-log`
4×	`flip3-+` `pow-sqr` `pow-prod-up` `frac-sub` `flip-+` `insert-posit16`
3×	`flip3--` `diff-log` `swap-sqr` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `associate--l+` `associate--r+`
1×	`pow2` `pow-plus` `distribute-lft-out` `associate--r-`

Counts

4 → 103

Calls

4 calls:

Slowest

76.0ms	(* (exp x) (+ (* (exp x) (exp x)) -4))
57.0ms	(- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))
54.0ms	(* (+ (exp x) 2) (exp x))
13.0ms	(* (exp x) (exp x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))
58.0ms	(* (exp x) (+ (* (exp x) (exp x)) -4))
22.0ms	(* (+ (exp x) 2) (exp x))
14.0ms	(* (exp x) (exp x))

simplify7.6s

Counts

91 → 115

Calls

91 calls:

Slowest

650.0ms	(- (* (* (exp x) (+ (pow (* (exp x) (exp x)) 3) (pow -4 3))) (+ (* -2 -2) (+ (* (exp x) (exp x)) (* -2 (exp x))))) (* (+ (* (* (exp x) (exp x)) (* (exp x) (exp x))) (- (* -4 -4) (* (* (exp x) (exp x)) -4))) (- (pow -2 3) (pow (exp x) 3))))
496.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
481.0ms	(/ (exp (* (exp x) (+ (* (exp x) (exp x)) -4))) (exp (- -2 (exp x))))
405.0ms	(/ (exp (* (exp x) (+ (* (exp x) (exp x)) -4))) (/ (exp -2) (exp (exp x))))
352.0ms	(* (- (* (exp x) (exp x)) (* 2 2)) (exp x))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* (- (exp x) 2) (- (exp x) 2)) (* (/ -1 (exp x)) (/ -1 (exp x))))
0.3b	(/ (- (* (- (exp x) 2) (- (exp x) 2)) (* (/ -1 (exp x)) (/ -1 (exp x)))) (+ (- (exp x) 2) (/ -1 (exp x))))
0.0b	(* (- (exp x) 2) (- (exp x) 2))
0.0b	(/ -1 (exp x))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
48×	`frac-sub`
45×	`flip3--` `flip--`
44×	`frac-times`
37×	`add-sqr-sqrt`
30×	`associate-l/` `associate-r/`
29×	`times-frac`
27×	`add-cube-cbrt`
26×	`associate-/l/`
11×	`pow1` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `distribute-lft-out`
9×	`add-exp-log`
8×	`associate-/r*`
7×	`swap-sqr` `associate-/l*`
6×	`add-log-exp`
5×	`sub-neg` `associate-r` `associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `associate-/r/` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-add` `div-inv`
1×	`pow2` `flip3-+` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 189

Calls

4 calls:

Slowest

154.0ms	(/ (- (* (- (exp x) 2) (- (exp x) 2)) (* (/ -1 (exp x)) (/ -1 (exp x)))) (+ (- (exp x) 2) (/ -1 (exp x))))
60.0ms	(* (- (exp x) 2) (- (exp x) 2))
37.0ms	(- (* (- (exp x) 2) (- (exp x) 2)) (* (/ -1 (exp x)) (/ -1 (exp x))))
10.0ms	(/ -1 (exp x))

series437.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

244.0ms	(/ (- (* (- (exp x) 2) (- (exp x) 2)) (* (/ -1 (exp x)) (/ -1 (exp x)))) (+ (- (exp x) 2) (/ -1 (exp x))))
133.0ms	(- (* (- (exp x) 2) (- (exp x) 2)) (* (/ -1 (exp x)) (/ -1 (exp x))))
50.0ms	(* (- (exp x) 2) (- (exp x) 2))
10.0ms	(/ -1 (exp x))

simplify38.7s

Counts

221 → 201

Calls

221 calls:

Slowest

731.0ms	(* (* (+ (exp x) 2) (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2)))) (exp x))
720.0ms	(- (* (* (- (* (exp x) (exp x)) (* 2 2)) (- (* (exp x) (exp x)) (* 2 2))) (* (exp x) (exp x))) (* (* (+ (exp x) 2) (+ (exp x) 2)) (* -1 -1)))
693.0ms	(- (* (* (- (* (exp x) (exp x)) (* 2 2)) (- (* (exp x) (exp x)) (* 2 2))) (* (exp x) (exp x))) (* (* (+ (exp x) 2) (+ (exp x) 2)) (* -1 -1)))
660.0ms	(* (- (pow (exp x) 3) (pow 2 3)) (- (pow (exp x) 3) (pow 2 3)))
627.0ms	(* (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2)))) (exp x))

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch4.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

4.1s	5672×	body	1280	valid
509.0ms	7901×	body	80	valid
446.0ms	1245×	body	640	valid
137.0ms	627×	body	320	valid
39.0ms	286×	body	160	valid