Details

Time bar (total: 2.0m)

sample64.0ms

Algorithm
intervals
Results
15.0ms171×body80valid
12.0ms28×body1280valid
11.0ms32×body640valid
10.0ms256×pre80true
4.0ms15×body320valid
2.0ms10×body160valid

simplify133.0ms

Calls
1 calls:
Slowest
132.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize33.0ms

Local error

Found 3 expressions with local error:

2.4b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.0b
(+ (+ alpha beta) 2.0)

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
38×distribute-lft-out
35×fma-def
27×add-cube-cbrt
11×distribute-lft-out-- difference-of-squares
10×add-log-exp
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×sum-log flip3-+ associate-/r/ flip-+
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×+-commutative div-sub div-inv associate-/l/
1×cbrt-undiv associate-+l+ clear-num frac-2neg flip3-- div-exp associate-+l- flip--
Calls
3 calls:
Slowest
172.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
37.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
25.0ms
(+ (+ alpha beta) 2.0)

series199.0ms

Calls
3 calls:
Slowest
95.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
81.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms
(+ (+ alpha beta) 2.0)

simplify5.2s

Calls
113 calls:
Slowest
276.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
269.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
262.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
255.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
246.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.1b

localize39.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ 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))

rewrite736.0ms

Algorithm
rewrite-expression-head
Rules
512×*-un-lft-identity
328×add-sqr-sqrt
263×times-frac
252×prod-diff
213×add-cube-cbrt
150×distribute-lft-out
65×associate--r+
46×difference-of-squares
42×fma-neg
32×associate-/r/
25×distribute-lft-out--
16×flip3-+ flip-+ div-inv
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×expm1-log1p-u pow1 diff-log insert-posit16 log1p-expm1-u
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp frac-sub
1×associate--r-
Calls
4 calls:
Slowest
512.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
146.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
33.0ms
(/ beta (+ (+ alpha beta) 2.0))
25.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series330.0ms

Calls
4 calls:
Slowest
118.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms
(/ alpha (+ (+ alpha beta) 2.0))
71.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify1.3m

Calls
593 calls:
Slowest
702.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt beta) (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
593.0ms
(fma (/ 1 (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ beta (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 1)))
520.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ 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))))))
508.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ 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))))))
489.0ms
(fma (/ (sqrt beta) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (sqrt beta) (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))

prune4.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize36.0ms

Local error

Found 4 expressions with local error:

2.4b
(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
48×times-frac
39×add-sqr-sqrt add-cube-cbrt
24×distribute-lft-out
13×log-prod associate-/r*
10×add-cbrt-cube
9×add-exp-log associate-/l*
5×pow1
4×expm1-log1p-u exp-prod div-exp associate-/r/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv clear-num frac-2neg
2×flip3-+ rem-log-exp log-pow flip-+ pow-div
1×log-div
Calls
4 calls:
Slowest
90.0ms
(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
71.0ms
(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))
34.0ms
(/ alpha (+ (+ alpha beta) 2.0))
23.0ms
(/ beta (+ (+ alpha beta) 2.0))

series550.0ms

Calls
4 calls:
Slowest
224.0ms
(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
161.0ms
(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))
86.0ms
(/ beta (+ (+ alpha beta) 2.0))
80.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify7.7s

Calls
138 calls:
Slowest
709.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
401.0ms
(- (+ (* 4.0 (/ 1 (pow alpha 2))) (log (/ E (exp 1.0)))) (* 2.0 (/ 1 alpha)))
361.0ms
(- (+ (* 4.0 (/ 1 (pow alpha 2))) (log (/ E (exp 1.0)))) (* 2.0 (/ 1 alpha)))
351.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
308.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize24.0ms

Local error

Found 4 expressions with local error:

10.3b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.8b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite700.0ms

Algorithm
rewrite-expression-head
Rules
166×*-un-lft-identity
89×add-sqr-sqrt
78×times-frac
74×add-cube-cbrt
63×prod-diff
48×distribute-lft-out
21×fma-neg
14×log-prod
10×associate-/r/
8×log-div
7×exp-sum add-exp-log distribute-lft-out--
6×pow1 add-cbrt-cube add-log-exp difference-of-squares
5×associate-/r* flip3-+ flip3-- flip-+ div-inv flip--
4×expm1-log1p-u exp-prod exp-diff frac-sub insert-posit16 log1p-expm1-u
3×associate-/l*
2×log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp rem-log-exp rem-exp-log
Calls
4 calls:
Slowest
279.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
266.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
126.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms
(/ beta (+ (+ alpha beta) 2.0))

series439.0ms

Calls
4 calls:
Slowest
168.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
121.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
77.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
72.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify17.7s

Calls
232 calls:
Slowest
567.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
489.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
419.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
362.0ms
(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)))))
345.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

regimes239.0ms

Accuracy

75.2% (3.2b remaining)

Error of 6.2b against oracle of 3.0b and baseline of 16.0b

bsearch43.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
904.0ms856×body1280valid
634.0ms5823×body80valid
299.0ms8000×pre80true
250.0ms721×body640valid
95.0ms384×body320valid
72.0ms216×body160valid