Details

sample113.0ms

Algorithm

intervals

Results

80.0ms	180×	body	1280	valid
11.0ms	278×	body	80	valid
9.0ms	37×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify39.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

39.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.9b

localize43.0ms

Local error

Found 3 expressions with local error:

2.2b	(- (- (exp x) 2) (/ -1 (exp x)))
0.0b	(/ -1 (exp x))
0.0b	(- (exp x) 2)

rewrite91.0ms

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

73.0ms	(- (- (exp x) 2) (/ -1 (exp x)))
8.0ms	(/ -1 (exp x))
8.0ms	(- (exp x) 2)

series121.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

80.0ms	(- (- (exp x) 2) (/ -1 (exp x)))
23.0ms	(- (exp x) 2)
17.0ms	(/ -1 (exp x))

simplify2.5s

Counts

53 → 75

Calls

53 calls:

Slowest

380.0ms	(/ (* (* -1 -1) -1) (* (* (exp x) (exp x)) (exp x)))
310.0ms	(- (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) -1))
211.0ms	(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
185.0ms	(- (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) -1))
169.0ms	(/ (exp (- (exp x) 2)) (exp (/ -1 (exp x))))

prune594.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) (* x x))
0.2b	(* (* x x) (* x x))
0.1b	(* 1/12 (* (* x x) (* x x)))
0.1b	(* (* (* (* x x) (* x x)) (* x x)) 1/360)

rewrite638.0ms

Algorithm

rewrite-expression-head

Rules

297×	`pow1`
101×	`pow-prod-down`
99×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-up`
71×	`prod-exp` `cbrt-unprod`
44×	`pow-sqr`
36×	`pow-plus`
26×	`pow2`
7×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `add-log-exp`
3×	`unswap-sqr`
2×	`swap-sqr`

Counts

4 → 203

Calls

4 calls:

Slowest

447.0ms	(* (* (* (* x x) (* x x)) (* x x)) 1/360)
111.0ms	(* 1/12 (* (* x x) (* x x)))
49.0ms	(* (* x x) (* x x))
26.0ms	(* (* x x) (* x x))

series231.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(* (* (* (* x x) (* x x)) (* x x)) 1/360)
52.0ms	(* 1/12 (* (* x x) (* x x)))
50.0ms	(* (* x x) (* x x))
36.0ms	(* (* x x) (* x x))

simplify15.5s

Counts

202 → 215

Calls

202 calls:

Slowest

735.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))))
647.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))))
464.0ms	(* (* (* (* x x) (* x x)) (* x x)) 1/360)
436.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
419.0ms	(* (* (* (* x x) (* x x)) (* x x)) 1/360)

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

2.2b	(- (- (exp x) 2) (/ -1 (exp x)))
0.0b	(/ -1 (exp x))
0.0b	(- (exp x) 2)

rewrite108.0ms

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

81.0ms	(- (- (exp x) 2) (/ -1 (exp x)))
16.0ms	(- (exp x) 2)
10.0ms	(/ -1 (exp x))

series115.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

78.0ms	(- (- (exp x) 2) (/ -1 (exp x)))
21.0ms	(- (exp x) 2)
16.0ms	(/ -1 (exp x))

simplify2.4s

Counts

53 → 75

Calls

53 calls:

Slowest

390.0ms	(/ (* (* -1 -1) -1) (* (* (exp x) (exp x)) (exp x)))
319.0ms	(- (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) -1))
291.0ms	(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
171.0ms	(- (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) -1))
149.0ms	(* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp x))

prune621.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))
0.3b	(/ (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x))) (* (+ (exp x) 2) (exp x)))
0.0b	(* (exp x) (exp x))
0.0b	(* (+ (exp x) 2) (exp x))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
9×	`add-exp-log` `add-log-exp`
8×	`associate-*r/` `frac-sub`
7×	`associate-l`
6×	`flip3-+` `flip3--` `associate-r` `flip-+` `flip--` `associate-/l/`
5×	`pow-prod-down`
4×	`associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`times-frac` `diff-log` `swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `div-exp` `associate--l+` `associate-/r/` `*-commutative` `associate--r+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in` `pow-plus` `div-sub` `div-inv` `distribute-lft-out` `associate--r-`

Counts

4 → 111

Calls

4 calls:

Slowest

103.0ms	(/ (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x))) (* (+ (exp x) 2) (exp x)))
46.0ms	(- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))
26.0ms	(* (+ (exp x) 2) (exp x))
13.0ms	(* (exp x) (exp x))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

229.0ms	(/ (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x))) (* (+ (exp x) 2) (exp x)))
91.0ms	(- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))
25.0ms	(* (+ (exp x) 2) (exp x))
23.0ms	(* (exp x) (exp x))

simplify13.9s

Counts

99 → 123

Calls

99 calls:

Slowest

931.0ms	(- (* (* (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))))
674.0ms	(- (* (* (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))))
616.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
592.0ms	(/ (* (* (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x))) (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))) (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))) (* (* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x))) (* (+ (exp x) 2) (exp x))))
589.0ms	(/ (* (* (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x))) (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))) (- (* (exp x) (+ (* (exp x) (exp x)) -4)) (- -2 (exp x)))) (* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x))))

prune1.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

63.6% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.6b

bsearch70.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.9s	5670×	body	1280	valid
607.0ms	8016×	body	80	valid
439.0ms	1233×	body	640	valid
122.0ms	612×	body	320	valid
39.0ms	304×	body	160	valid