Details

sample184.0ms

Algorithm

intervals

Results

130.0ms	176×	body	1280	valid
16.0ms	39×	body	640	valid
16.0ms	272×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify48.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

48.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.5b

localize23.0ms

Local error

Found 2 expressions with local error:

4.2b	(+ (- (exp x) 2) (exp (- x)))
0.0b	(- (exp x) 2)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`neg-sub0` `exp-neg` `pow1` `associate-+l+` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+` `difference-of-squares`

Counts

2 → 37

Calls

2 calls:

Slowest

62.0ms	(+ (- (exp x) 2) (exp (- x)))
8.0ms	(- (exp x) 2)

series105.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

90.0ms	(+ (- (exp x) 2) (exp (- x)))
15.0ms	(- (exp x) 2)

simplify2.6s

Counts

25 → 43

Calls

25 calls:

Slowest

494.0ms	(+ (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) (exp 0)))
308.0ms	(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) 1))
270.0ms	(+ (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))) (exp 0)))
170.0ms	(+ (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) 1))

prune352.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

866×	`pow1`
370×	`pow-prod-up`
188×	`pow-prod-down`
153×	`pow-sqr`
140×	`pow-plus`
99×	`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×	`cube-unmult`

Counts

4 → 349

Calls

4 calls:

Slowest

105.0ms	(* 1/12 (* (* x x) (* x x)))
73.0ms	(* (* x x) (* (* x x) (* x x)))
49.0ms	(* (* x x) (* x x))
22.0ms	(* (* x x) (* x x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(* 1/12 (* (* x x) (* x x)))
65.0ms	(* (* x x) (* (* x x) (* x x)))
59.0ms	(* (* x x) (* x x))
54.0ms	(* (* x x) (* x x))

simplify17.4s

Counts

407 → 361

Calls

407 calls:

Slowest

845.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))))
803.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))))
717.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))))
497.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
490.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))

prune2.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (exp (* (* x x) (* (* x x) (* x x)))))
0.2b	(* (* x x) (* x x))
0.2b	(* (* x x) (* x x))
0.1b	(* 1/12 (* (* x x) (* x x)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

245×	`pow1`
72×	`pow-prod-up`
59×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
44×	`pow-sqr`
36×	`pow-plus`
29×	`prod-exp` `cbrt-unprod`
26×	`pow2`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `associate-r` `log-pow` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 172

Calls

4 calls:

Slowest

72.0ms	(* 1/12 (* (* x x) (* x x)))
31.0ms	(* (* x x) (* x x))
24.0ms	(* (* x x) (* x x))
22.0ms	(log (exp (* (* x x) (* (* x x) (* x x)))))

series199.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(log (exp (* (* x x) (* (* x x) (* x x)))))
46.0ms	(* 1/12 (* (* x x) (* x x)))
45.0ms	(* (* x x) (* x x))
41.0ms	(* (* x x) (* x x))

simplify8.1s

Counts

172 → 184

Calls

172 calls:

Slowest

815.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x))))
731.0ms	(* (* (* 1/12 1/12) 1/12) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))))
508.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
497.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
478.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

4.3b	(+ (* (- (* (exp x) (exp x)) 3) (exp x)) 2)
0.0b	(* (- (* (exp x) (exp x)) 3) (exp x))
0.0b	(* (exp x) (exp x))
0.0b	(* (+ (exp x) 2) (exp x))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
15×	`pow1`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`associate-r`
6×	`pow-prod-down` `add-exp-log` `add-log-exp`
4×	`associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`swap-sqr` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `flip3--` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

Slowest

82.0ms	(* (- (* (exp x) (exp x)) 3) (exp x))
38.0ms	(+ (* (- (* (exp x) (exp x)) 3) (exp x)) 2)
26.0ms	(* (+ (exp x) 2) (exp x))
18.0ms	(* (exp x) (exp x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

97.0ms	(+ (* (- (* (exp x) (exp x)) 3) (exp x)) 2)
50.0ms	(* (- (* (exp x) (exp x)) 3) (exp x))
41.0ms	(* (+ (exp x) 2) (exp x))
24.0ms	(* (exp x) (exp x))

simplify5.3s

Counts

76 → 103

Calls

76 calls:

Slowest

571.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
398.0ms	(* (exp (* (- (* (exp x) (exp x)) 3) (exp x))) (exp 2))
339.0ms	(* (* (* (- (* (exp x) (exp x)) 3) (- (* (exp x) (exp x)) 3)) (- (* (exp x) (exp x)) 3)) (* (* (exp x) (exp x)) (exp x)))
337.0ms	(* (- (pow (* (exp x) (exp x)) 3) (pow 3 3)) (exp x))
320.0ms	(* (- (* (exp x) (exp x)) (* 2 2)) (exp x))

prune903.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch3.0ms

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.9s	5620×	body	1280	valid
863.0ms	8131×	body	80	valid
479.0ms	1251×	body	640	valid
184.0ms	653×	body	320	valid
38.0ms	289×	body	160	valid