Details

Time bar (total: 16.9s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01435
13335
211135
355035
4408735
done500035

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
106.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
331.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
484.0ms
(/ (/ (/ (+ (+ (+ 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))
285.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
141.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
152.0ms
(/ (/ (/ (+ (+ (+ 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))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Counts
477 → 477
Iterations

Useful iterations: done (1.7s)

IterNodesCost
060325954
1144325182
2475424241
done500123501

prune972.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite820.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cube-cbrt add-cbrt-cube
28×div-exp
18×associate-*r*
16×prod-exp
15×cbrt-undiv associate-*l*
10×associate-/r* associate-/r/
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×flip3-+ flip-+ unswap-sqr
5×rec-exp 1-exp div-inv associate-/l/
4×add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 169
Calls
4 calls:
35.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
318.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))))
205.0ms
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
253.0ms
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))))
163.0ms
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.4s

Counts
181 → 181
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02495645
17315198
233454504
done50004500

prune368.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite746.0ms

Algorithm
rewrite-expression-head
Rules
624×times-frac
522×sqrt-prod
425×*-un-lft-identity
325×add-sqr-sqrt
323×add-cube-cbrt
55×associate-/l*
51×distribute-lft-out
24×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×sqrt-undiv associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 464
Calls
4 calls:
271.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
208.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
114.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
114.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series406.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
108.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
53.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.1s

Counts
476 → 476
Iterations

Useful iterations: done (1.0s)

IterNodesCost
045523023
1103220455
2218419368
done500018678

prune824.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 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)) 1.0))
1.3b
(/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.1b
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))
17.1b
(* (/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
271×times-frac
192×*-un-lft-identity
135×add-sqr-sqrt
126×add-cube-cbrt
78×associate-*l*
37×difference-of-squares
34×add-exp-log add-cbrt-cube
33×distribute-lft-out
26×associate-/r/
23×associate-/l*
14×cbrt-undiv div-exp
13×div-inv
12×flip3-+ flip-+
11×associate-/r*
8×associate-/l/
6×pow1 flip3-- prod-exp flip-- cbrt-unprod
4×frac-times associate-*r/ add-log-exp
3×distribute-rgt-in frac-2neg distribute-lft-in associate-*r* clear-num unswap-sqr
2×sub-neg associate-*l/ associate--l+
1×pow-prod-down *-commutative
Counts
4 → 290
Calls
4 calls:
254.0ms
(/ (* (/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 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)) 1.0))
309.0ms
(/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
251.0ms
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))
441.0ms
(* (/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))

series751.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(/ (* (/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 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)) 1.0))
172.0ms
(/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
81.0ms
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))
264.0ms
(* (/ (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))

simplify603.0ms

Counts
302 → 302
Iterations

Useful iterations: done (589.0ms)

IterNodesCost
042414592
1124314314
done500112372

prune897.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.6b

regimes88.0ms

Accuracy

53.2% (1.2b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.7b

bsearch64.0ms

Steps
ItersRangePoint
8
3.217179906409216e+160
4.6405531927643885e+163
5.4871944677191445e+162

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03284
14784
done4784

end0.0ms

sample757.0ms

Algorithm
intervals
Results
485.0ms8000×body80valid
87.0ms8000×pre80true