Details

Time bar (total: 22.2s)

sample53.0ms

Algorithm
intervals
Results
12.0ms190×body80valid
10.0ms29×body1280valid
8.0ms256×pre80true
4.0ms15×body640valid
3.0ms17×body320valid
1.0ms5×body160valid

simplify154.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
154.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize37.0ms

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))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
19×distribute-lft-out
14×add-cube-cbrt
6×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 67
Calls
2 calls:
Slowest
117.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
37.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series143.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
57.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.5s

Counts
74 → 73
Calls
74 calls:
Slowest
248.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
243.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
227.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
202.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
176.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune684.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.8b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
31×times-frac
28×add-sqr-sqrt
24×distribute-lft-out
23×add-cube-cbrt
10×associate-/r*
7×add-cbrt-cube add-exp-log
6×associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ div-inv difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 92
Calls
3 calls:
Slowest
155.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms
(/ alpha (+ (+ alpha beta) 2.0))
23.0ms
(/ beta (+ (+ alpha beta) 2.0))

series257.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
132.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
67.0ms
(/ beta (+ (+ alpha beta) 2.0))
58.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify4.2s

Counts
97 → 101
Calls
97 calls:
Slowest
336.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
320.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
299.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
281.0ms
(/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
260.0ms
(/ (* (* beta beta) beta) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.6b
(cbrt beta)
0.6b
(cbrt beta)
0.6b
(cbrt beta)

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×cbrt-prod *-un-lft-identity
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/3
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 52
Calls
4 calls:
Slowest
186.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(cbrt beta)
309.0ms
(cbrt beta)
291.0ms
(cbrt beta)
102.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts
27 → 64
Calls
27 calls:
Slowest
187.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
164.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
158.0ms
(* (cbrt -1) (pow (* beta -1) 1/3))
141.0ms
(* (cbrt -1) (pow (* beta -1) 1/3))
136.0ms
(* (cbrt -1) (pow (* beta -1) 1/3))

prune774.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.5b

localize53.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.6b
(cbrt (cbrt beta))
0.6b
(cbrt (cbrt beta))
0.6b
(cbrt (cbrt beta))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
15×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/3
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 61
Calls
4 calls:
Slowest
143.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(cbrt (cbrt beta))
2.0ms
(cbrt (cbrt beta))
2.0ms
(cbrt (cbrt beta))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
380.0ms
(cbrt (cbrt beta))
351.0ms
(cbrt (cbrt beta))
343.0ms
(cbrt (cbrt beta))
116.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.4s

Counts
36 → 73
Calls
36 calls:
Slowest
854.0ms
(* (pow (cbrt -1) 1/3) (pow (* beta -1) 1/9))
815.0ms
(* (pow (cbrt -1) 1/3) (pow (* beta -1) 1/9))
795.0ms
(* (pow (cbrt -1) 1/3) (pow (* beta -1) 1/9))
167.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
155.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune971.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

regimes218.0ms

Accuracy

72.7% (3.5b remaining)

Error of 6.4b against oracle of 2.9b and baseline of 15.6b

bsearch253.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
983.0ms5893×body80valid
419.0ms811×body1280valid
330.0ms8000×pre80true
292.0ms712×body640valid
95.0ms371×body320valid
57.0ms213×body160valid