Details

Time bar (total: 12.8s)

sample56.0ms

Algorithm
intervals
Results
11.0ms37×body1280valid
10.0ms174×body80valid
6.0ms256×pre80true
5.0ms21×body640valid
3.0ms16×body320valid
1.0ms8×body160valid

simplify18.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite306.0ms

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-exp-log add-cbrt-cube add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ associate-/l/
1×cbrt-undiv +-commutative associate-+l- flip3-- frac-2neg div-exp clear-num sum-log flip-- div-inv
Counts
2 → 65
Calls
2 calls:
57.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
247.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series152.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
76.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify92.0ms

Counts
71 → 71

prune253.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
61×add-sqr-sqrt
56×times-frac
36×add-cube-cbrt
24×distribute-lft-out
13×associate-/r* associate-/l* distribute-lft-out--
10×add-exp-log add-cbrt-cube difference-of-squares
6×add-log-exp
4×pow1 associate-/r/ associate-/l/
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ frac-sub flip-+
1×sub-neg diff-log div-sub
Counts
4 → 137
Calls
4 calls:
1.4s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
47.0ms
(/ beta (+ (+ alpha beta) 2.0))
47.0ms
(/ alpha (+ (+ alpha beta) 2.0))
249.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series336.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
76.0ms
(/ beta (+ (+ alpha beta) 2.0))
58.0ms
(/ alpha (+ (+ alpha beta) 2.0))
106.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify67.0ms

Counts
149 → 149

prune439.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b
(/ (- (* 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)))) (* (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)) 2.0))
1.8b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
245×*-un-lft-identity
141×times-frac
131×add-sqr-sqrt
123×associate-*r/
90×distribute-lft-out
83×flip3-+ flip-+
73×add-cube-cbrt associate-*l/
71×frac-times
66×frac-add associate-/l/
64×frac-sub
39×unpow-prod-down cube-prod swap-sqr
38×associate-/r/
28×add-exp-log add-cbrt-cube
26×flip3-- flip--
24×difference-of-squares
21×associate-*r* associate-*l*
12×pow1
11×sqr-pow
8×cbrt-undiv div-exp
7×prod-exp cbrt-unprod div-inv
6×add-log-exp
5×distribute-lft-out--
4×unswap-sqr
3×pow-unpow associate-/l*
2×pow-exp rem-cube-cbrt
1×difference-cubes cube-div pow2 cube-mult pow-to-exp sub-neg pow-pow frac-2neg pow-plus diff-log unpow3 div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up
Counts
4 → 329
Calls
4 calls:
242.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
80.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
819.0ms
(/ (- (* 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)))) (* (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)) 2.0))
608.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series1.0s

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
122.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
629.0ms
(/ (- (* 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)))) (* (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)) 2.0))
162.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify143.0ms

Counts
341 → 341

prune2.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

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-exp-log add-cbrt-cube
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- times-frac diff-log flip-- distribute-lft-out--
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
206.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series958.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(cbrt beta)
275.0ms
(cbrt beta)
319.0ms
(cbrt beta)
99.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify85.0ms

Counts
60 → 60

prune234.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.4b

regimes91.0ms

Accuracy

74.4% (3.3b remaining)

Error of 6.0b against oracle of 2.7b and baseline of 15.6b

bsearch59.0ms

Steps
ItersRangePoint
5
879064267.884121
3030780229.4257846
1845090834.437638

simplify88.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
713.0ms844×body1280valid
419.0ms5878×body80valid
188.0ms697×body640valid
163.0ms8000×pre80true
141.0ms381×body320valid
20.0ms200×body160valid