Details

sample43.0ms

Algorithm

intervals

Results

15.0ms	198×	body	80	valid
7.0ms	256×	pre	80	true
5.0ms	23×	body	640	valid
5.0ms	18×	body	1280	valid
2.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify120.0ms

Calls

1 calls:

Slowest

120.0ms

(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize32.0ms

Local error

Found 3 expressions with local error:

1.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.0b	(+ (+ alpha beta) 2.0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `flip3-+` `flip-+` `insert-posit16` `associate-/l` `add-log-exp`
2×	`+-commutative` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Calls

3 calls:

Slowest

41.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.0ms	(+ (+ alpha beta) 2.0)

series93.0ms

Calls

3 calls:

Slowest

40.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
40.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(+ (+ alpha beta) 2.0)

simplify2.3s

Calls

40 calls:

Slowest

242.0ms	(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
224.0ms	(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
205.0ms	(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
169.0ms	(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
162.0ms	(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune635.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

49.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.0ms	(/ alpha (+ (+ alpha beta) 2.0))
4.0ms	(/ beta (+ (+ alpha beta) 2.0))

series199.0ms

Calls

4 calls:

Slowest

63.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
60.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
39.0ms	(/ alpha (+ (+ alpha beta) 2.0))
37.0ms	(/ beta (+ (+ alpha beta) 2.0))

simplify3.4s

Calls

30 calls:

Slowest

319.0ms	(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
311.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
307.0ms	(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
295.0ms	(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
264.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune909.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.3b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*`
5×	`pow1` `log-prod`
4×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `log-pow` `insert-posit16` `add-log-exp`
3×	`exp-prod`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `exp-sum` `flip-+` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `rem-log-exp` `flip--`

Calls

4 calls:

Slowest

29.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
7.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.0ms	(/ beta (+ (+ alpha beta) 2.0))
3.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series165.0ms

Calls

4 calls:

Slowest

50.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
44.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
37.0ms	(/ alpha (+ (+ alpha beta) 2.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))

simplify3.0s

Calls

32 calls:

Slowest

344.0ms	(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
335.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
278.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
269.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
259.0ms	(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune864.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.4b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/r/` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`rec-exp` `sub-neg` `flip3--` `pow-flip` `flip--` `inv-pow`

Calls

4 calls:

Slowest

13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(/ (+ (+ alpha beta) 2.0) beta)
5.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
2.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series121.0ms

Calls

4 calls:

Slowest

38.0ms	(/ alpha (+ (+ alpha beta) 2.0))
37.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
31.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
16.0ms	(/ (+ (+ alpha beta) 2.0) beta)

simplify2.6s

Calls

26 calls:

Slowest

559.0ms	(+ (pow (+ alpha beta) 3) (pow 2.0 3))
380.0ms	(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
285.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
285.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
245.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune720.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

regimes237.0ms

Accuracy

77.9% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 16.2b

bsearch100.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

878.0ms	903×	body	1280	valid
589.0ms	5772×	body	80	valid
353.0ms	8000×	pre	80	true
265.0ms	715×	body	640	valid
139.0ms	435×	body	320	valid
31.0ms	175×	body	160	valid