Details

Time bar (total: 12.2s)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify83.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.3b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
31.0ms
(+ (+ alpha beta) (* beta alpha))
346.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
510.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
310.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ alpha beta) (* beta alpha))
151.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
163.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
87.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify129.0ms

Counts
475 → 475

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.3b
(/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite658.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
523×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
30.0ms
(+ (+ alpha beta) (* beta alpha))
160.0ms
(/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
312.0ms
(/ (/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
119.0ms
(/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ alpha beta) (* beta alpha))
154.0ms
(/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
167.0ms
(/ (/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
78.0ms
(/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Counts
475 → 475

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
4.3b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
297×times-frac
277×*-un-lft-identity
168×add-sqr-sqrt
138×add-cube-cbrt
78×associate-*r*
68×distribute-lft-out
54×add-exp-log
34×add-cbrt-cube
28×associate-/r/
25×associate-/l*
24×div-exp
15×flip3-+ associate-*l* flip-+
14×cbrt-undiv div-inv
12×prod-exp
10×associate-/r*
9×unswap-sqr
7×pow1
6×cbrt-unprod
4×rec-exp 1-exp add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 311
Calls
4 calls:
36.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
493.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
705.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
297.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
165.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
88.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify82.0ms

Counts
323 → 323

prune764.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
20.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
251×times-frac
206×*-un-lft-identity
147×add-sqr-sqrt
126×add-cube-cbrt
66×associate-*r*
40×distribute-lft-out
34×add-exp-log add-cbrt-cube
28×associate-/r/
22×associate-*l* associate-/l*
14×cbrt-undiv div-exp div-inv
13×flip3-+ flip-+
11×associate-/r*
9×difference-of-squares
6×pow1 prod-exp cbrt-unprod unswap-sqr
5×associate-/l/
4×add-log-exp
3×flip3-- frac-2neg div-sub clear-num flip--
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 287
Calls
4 calls:
98.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
228.0ms
(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
824.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
303.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
89.0ms
(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
242.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify79.0ms

Counts
299 → 299

prune941.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.1b

regimes64.0ms

Accuracy

58.3% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.7b

bsearch82.0ms

Steps
ItersRangePoint
9
2.4188886995094645e+186
6.2578256904215e+192
1.6384098757042544e+190

simplify1.0ms

end0.0ms

sample914.0ms

Algorithm
intervals
Results
503.0ms8000×body80valid
194.0ms8000×pre80true