Details

Time bar (total: 22.8s)

sample92.0ms

Algorithm
intervals
Results
32.0ms182×body80valid
13.0ms24×body1280valid
12.0ms256×pre80true
10.0ms22×body640valid
7.0ms21×body320valid
2.0ms7×body160valid

simplify140.0ms

Calls
1 calls:
Slowest
140.0ms
(/ (+ (/ (- 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

localize26.0ms

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))

rewrite25.0ms

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
18.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
6.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series98.0ms

Calls
2 calls:
Slowest
56.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
42.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify2.3s

Calls
37 calls:
Slowest
255.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
206.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
192.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
180.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
164.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))

prune469.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize25.0ms

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))

rewrite37.0ms

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
19.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
13.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(/ beta (+ (+ alpha beta) 2.0))
2.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series172.0ms

Calls
4 calls:
Slowest
58.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
38.0ms
(/ beta (+ (+ alpha beta) 2.0))
38.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
37.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify3.8s

Calls
32 calls:
Slowest
384.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
343.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
320.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
295.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
293.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune787.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize13.0ms

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)

rewrite14.0ms

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
11.0ms
(- (/ 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)))

series426.0ms

Calls
4 calls:
Slowest
142.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
121.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
106.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
57.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify5.2s

Calls
33 calls:
Slowest
943.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
496.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
461.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
284.0ms
(- (+ (* (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))))
271.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune837.0ms

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))

rewrite55.0ms

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
27.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
16.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
6.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.0ms
(/ beta (+ (+ alpha beta) 2.0))

series215.0ms

Calls
4 calls:
Slowest
82.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
54.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
43.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
36.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify4.8s

Calls
41 calls:
Slowest
372.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
334.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
302.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
272.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
261.0ms
(exp (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))))))

prune991.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

regimes247.0ms

Accuracy

99.1% (0.1b remaining)

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

bsearch10.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
624.0ms5851×body80valid
394.0ms824×body1280valid
326.0ms718×body640valid
315.0ms8000×pre80true
133.0ms395×body320valid
63.0ms212×body160valid