Details

Time bar (total: 35.7s)

sample44.0ms

Algorithm
intervals
Results
11.0ms182×body80valid
7.0ms256×pre80true
7.0ms24×body1280valid
5.0ms22×body640valid
4.0ms21×body320valid
1.0ms7×body160valid

simplify143.0ms

Calls
1 calls:
Slowest
143.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize33.0ms

Local error

Found 2 expressions with local error:

2.2b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite30.0ms

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
23.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
6.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series80.0ms

Calls
2 calls:
Slowest
42.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
38.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.3s

Calls
51 calls:
Slowest
474.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
264.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
253.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
235.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
217.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))

prune685.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.3b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ 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))

rewrite43.0ms

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
23.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
14.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(/ beta (+ (+ alpha beta) 2.0))
2.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series176.0ms

Calls
4 calls:
Slowest
59.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
55.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
37.0ms
(/ alpha (+ (+ alpha beta) 2.0))
25.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify11.5s

Calls
76 calls:
Slowest
613.0ms
(/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
551.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
498.0ms
(fma (/ beta (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0))) (- (+ alpha beta) 2.0) (- (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
369.0ms
(* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
332.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize30.0ms

Local error

Found 4 expressions with local error:

7.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite21.0ms

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
15.0ms
(- (/ 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)))

series450.0ms

Calls
4 calls:
Slowest
145.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
133.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
130.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
42.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify6.3s

Calls
37 calls:
Slowest
651.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
611.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
608.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
572.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
403.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune967.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

11.7b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b
(- (/ 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))

rewrite46.0ms

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
19.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
15.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
8.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
3.0ms
(/ beta (+ (+ alpha beta) 2.0))

series233.0ms

Calls
4 calls:
Slowest
107.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
57.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
44.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
26.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify6.5s

Calls
45 calls:
Slowest
631.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
430.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
360.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
358.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
356.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

regimes268.0ms

Accuracy

99.1% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 16.0b

bsearch10.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
734.0ms718×body640valid
558.0ms5851×body80valid
496.0ms824×body1280valid
325.0ms8000×pre80true
108.0ms395×body320valid
36.0ms212×body160valid