Details

sample58.0ms

Algorithm

intervals

Results

18.0ms	198×	body	80	valid
11.0ms	256×	pre	80	true
8.0ms	23×	body	640	valid
7.0ms	18×	body	1280	valid
3.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify134.0ms

Calls

1 calls:

Slowest

133.0ms

(/ (+ (/ (- 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

localize21.0ms

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)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`fma-def` `times-frac`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`+-commutative` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Calls

3 calls:

Slowest

19.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
6.0ms	(+ (+ alpha beta) 2.0)

series83.0ms

Calls

3 calls:

Slowest

38.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
32.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
12.0ms	(+ (+ alpha beta) 2.0)

simplify3.6s

Calls

56 calls:

Slowest

579.0ms	(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
257.0ms	(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
230.0ms	(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
218.0ms	(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
211.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))

prune805.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

localize22.0ms

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)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`associate-/r*` `fma-neg` `associate-/r/`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `flip-+` `flip--`
2×	`frac-sub`
1×	`sub-neg` `div-sub` `distribute-lft-out--` `difference-of-squares`

Calls

4 calls:

Slowest

60.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
8.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
5.0ms	(/ beta (+ (+ alpha beta) 2.0))
2.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series153.0ms

Calls

4 calls:

Slowest

57.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
50.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
24.0ms	(/ beta (+ (+ alpha beta) 2.0))
22.0ms	(/ alpha (+ (+ alpha beta) 2.0))

simplify4.6s

Calls

34 calls:

Slowest

554.0ms	(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
339.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
321.0ms	(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
321.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
290.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

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

9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `fma-neg` `associate-/r/`
5×	`pow1` `log-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `flip3-+` `flip-+` `div-inv`
2×	`clear-num` `sub-neg` `frac-2neg` `exp-sum`
1×	`log-div` `flip3--` `exp-diff` `rem-log-exp` `flip--`

Calls

4 calls:

Slowest

27.0ms	(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))
4.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series139.0ms

Calls

4 calls:

Slowest

51.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
41.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
23.0ms	(/ beta (+ (+ alpha beta) 2.0))
23.0ms	(/ alpha (+ (+ alpha beta) 2.0))

simplify4.3s

Calls

36 calls:

Slowest

571.0ms	(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
375.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
369.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
363.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
353.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

localize26.0ms

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))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-/r*`
6×	`fma-neg`
5×	`pow1` `add-exp-log` `associate-/r/` `div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-/l/`
1×	`rec-exp` `sub-neg` `flip3--` `pow-flip` `flip--` `inv-pow`

Calls

4 calls:

Slowest

14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(/ (+ (+ alpha beta) 2.0) beta)
2.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
2.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series123.0ms

Calls

4 calls:

Slowest

44.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
35.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
22.0ms	(/ alpha (+ (+ alpha beta) 2.0))
21.0ms	(/ (+ (+ alpha beta) 2.0) beta)

simplify3.6s

Calls

30 calls:

Slowest

526.0ms	(+ (pow (+ alpha beta) 3) (pow 2.0 3))
524.0ms	(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
396.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
360.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
298.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))

prune842.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

regimes171.0ms

Accuracy

77.8% (2.9b remaining)

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

bsearch65.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	5772×	body	80	valid
489.0ms	903×	body	1280	valid
332.0ms	8000×	pre	80	true
313.0ms	715×	body	640	valid
136.0ms	435×	body	320	valid
31.0ms	175×	body	160	valid