Details

Time bar (total: 22.9s)

sample83.0ms

Algorithm
intervals
Results
24.0ms195×body80valid
13.0ms21×body1280valid
13.0ms256×pre80true
9.0ms19×body640valid
5.0ms12×body320valid
2.0ms9×body160valid

simplify122.0ms

Calls
1 calls:
Slowest
122.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize37.0ms

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))

rewrite47.0ms

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
34.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
12.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series146.0ms

Calls
2 calls:
Slowest
88.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
58.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify2.3s

Calls
37 calls:
Slowest
295.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
236.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
203.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
174.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
173.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune405.0ms

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))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity
6×associate-/r* add-cube-cbrt add-log-exp
4×pow1 add-cbrt-cube add-exp-log associate-/r/ insert-posit16
3×sub-neg flip3-- flip--
2×clear-num frac-2neg flip3-+ frac-sub flip-+ div-inv associate--r+
1×diff-log distribute-lft-out-- associate--r- difference-of-squares
Calls
4 calls:
Slowest
18.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
13.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
3.0ms
(/ beta (+ (+ alpha beta) 2.0))
2.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series313.0ms

Calls
4 calls:
Slowest
110.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
91.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
57.0ms
(/ alpha (+ (+ alpha beta) 2.0))
54.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify3.7s

Calls
32 calls:
Slowest
367.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
329.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
329.0ms
(- (* 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)))))
277.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune765.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize23.0ms

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))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×log-prod
8×log-div add-cube-cbrt
6×pow1
5×flip3-- exp-sum add-exp-log flip--
4×exp-prod add-cbrt-cube exp-diff frac-sub insert-posit16 add-log-exp
3×associate-/r*
2×associate-/r/ log-pow distribute-lft-out-- difference-of-squares
1×clear-num sub-neg frac-2neg flip3-+ rem-log-exp flip-+ div-inv rem-exp-log
Calls
4 calls:
Slowest
21.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
13.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
6.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(/ beta (+ (+ alpha beta) 2.0))

series452.0ms

Calls
4 calls:
Slowest
195.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
95.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
83.0ms
(/ beta (+ (+ alpha beta) 2.0))
79.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))

simplify4.9s

Calls
41 calls:
Slowest
379.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
345.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
276.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
273.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
266.0ms
(log (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))

prune917.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize20.0ms

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)

rewrite18.0ms

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
12.0ms
(- (/ 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)))

series750.0ms

Calls
4 calls:
Slowest
239.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
213.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
179.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
119.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.6s

Calls
33 calls:
Slowest
516.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
516.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
506.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
276.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
243.0ms
(- (+ (* (cbrt -1) (pow -1 1/3)) (* 0.8888888888888888 (* (/ (cbrt -1) (pow beta 2)) (pow -1 1/3)))) (* 0.6666666666666666 (* (/ (cbrt -1) beta) (pow -1 1/3))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

regimes154.0ms

Accuracy

77% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.7b

bsearch76.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
586.0ms5850×body80valid
401.0ms813×body1280valid
313.0ms8000×pre80true
282.0ms703×body640valid
131.0ms410×body320valid
38.0ms224×body160valid