Details

Time bar (total: 27.5s)

sample86.0ms

Algorithm
intervals
Results
20.0ms180×body80valid
17.0ms256×pre80true
15.0ms26×body1280valid
13.0ms29×body640valid
5.0ms14×body320valid
1.0ms7×body160valid

simplify164.0ms

Calls
1 calls:
Slowest
164.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize25.0ms

Local error

Found 2 expressions with local error:

1.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 add-log-exp associate-/l/
1×cbrt-undiv +-commutative clear-num frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Calls
2 calls:
Slowest
41.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
7.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series80.0ms

Calls
2 calls:
Slowest
40.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
39.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Calls
37 calls:
Slowest
302.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
215.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
200.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
187.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
175.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune467.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.1b

localize25.0ms

Local error

Found 3 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-/r*
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-/r/
3×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×clear-num frac-2neg flip3-+ flip-+ div-inv
1×sub-neg flip3-- flip--
Calls
3 calls:
Slowest
13.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.0ms
(/ beta (+ (+ alpha beta) 2.0))
4.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series119.0ms

Calls
3 calls:
Slowest
44.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
38.0ms
(/ beta (+ (+ alpha beta) 2.0))
37.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify2.2s

Calls
19 calls:
Slowest
360.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
325.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
324.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
292.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
273.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize29.0ms

Local error

Found 4 expressions with local error:

8.1b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.1b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.1b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/r/
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
1×sub-neg flip3-- flip--
Calls
4 calls:
Slowest
7.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
2.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
2.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series424.0ms

Calls
4 calls:
Slowest
133.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
120.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
118.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
53.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.7s

Calls
33 calls:
Slowest
555.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
525.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
459.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
308.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
267.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune787.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.0b
(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
9×pow1
8×add-cbrt-cube add-exp-log associate-/r/
6×associate-/r* associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×flip3-+ flip-+ insert-posit16 div-inv associate-/l*
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×pow2 frac-times cbrt-undiv sub-neg pow-plus diff-log div-sub div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
25.0ms
(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
6.0ms
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
5.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
4.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series213.0ms

Calls
4 calls:
Slowest
89.0ms
(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
61.0ms
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
35.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
28.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify11.7s

Calls
77 calls:
Slowest
796.0ms
(+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
537.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
517.0ms
(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (cbrt (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
515.0ms
(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (sqrt (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
414.0ms
(/ (exp (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (exp (* 1.0 1.0)))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

regimes212.0ms

Accuracy

77.9% (2.9b remaining)

Error of 5.8b against oracle of 2.9b and baseline of 16.0b

bsearch79.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
592.0ms5814×body80valid
409.0ms858×body1280valid
345.0ms8000×pre80true
290.0ms713×body640valid
239.0ms424×body320valid
36.0ms191×body160valid