Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	195×	body	80	valid
7.0ms	256×	pre	80	true
6.0ms	21×	body	1280	valid
4.0ms	19×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify111.0ms

Calls

1 calls:

Slowest

111.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize365.0ms

Local error

Found 2 expressions with local error:

2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

39.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series179.0ms

Calls

2 calls:

Slowest

110.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
69.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.8s

Calls

51 calls:

Slowest

625.0ms	(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
288.0ms	(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
281.0ms	(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
231.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
219.0ms	(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune529.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize12.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (/ 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))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
14×	`associate-/r/`
12×	`fma-neg`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`clear-num` `frac-2neg` `frac-sub` `associate--r+`
1×	`diff-log` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Calls

4 calls:

Slowest

41.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.0ms	(/ beta (+ (+ alpha beta) 2.0))
4.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series344.0ms

Calls

4 calls:

Slowest

118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
81.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
77.0ms	(/ beta (+ (+ alpha beta) 2.0))
67.0ms	(/ alpha (+ (+ alpha beta) 2.0))

simplify11.3s

Calls

76 calls:

Slowest

615.0ms	(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
512.0ms	(/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
422.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
384.0ms	(* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
341.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize9.0ms

Local error

Found 4 expressions with local error:

10.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b	(/ beta (+ (+ alpha beta) 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

18.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
16.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
7.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.0ms	(/ beta (+ (+ alpha beta) 2.0))

series454.0ms

Calls

4 calls:

Slowest

179.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
79.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))

simplify6.2s

Calls

45 calls:

Slowest

586.0ms	(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
385.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
349.0ms	(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
341.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
324.0ms	(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

5.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/` `add-cube-cbrt`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip--`

Calls

4 calls:

Slowest

10.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series659.0ms

Calls

4 calls:

Slowest

213.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
185.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
179.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify7.0s

Calls

37 calls:

Slowest

782.0ms	(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
684.0ms	(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
612.0ms	(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
604.0ms	(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
599.0ms	(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))

prune958.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

regimes165.0ms

Accuracy

77.4% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.9b

bsearch124.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

583.0ms	5850×	body	80	valid
358.0ms	813×	body	1280	valid
336.0ms	8000×	pre	80	true
304.0ms	703×	body	640	valid
99.0ms	410×	body	320	valid
36.0ms	224×	body	160	valid