Details

Time bar (total: 16.8s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms256×pre80true

simplify989.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211035
348035
4239835
done500135

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize12.0ms

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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite674.0ms

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:
55.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
174.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
259.0ms
(/ (/ (/ (+ (+ (+ 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))
150.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
136.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify584.0ms

Counts
477 → 477
Iterations

Useful iterations: done (550.0ms)

IterNodesCost
060325954
1149125182
done500225025

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite474.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
129×*-un-lft-identity
81×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
24×distribute-lft-out
19×difference-of-squares
16×associate-/r/
13×add-exp-log add-cbrt-cube add-log-exp
11×associate-/r*
9×flip3-+ flip-+
8×div-inv
6×sum-log
5×cbrt-undiv div-exp associate-/l/
4×pow1
3×frac-2neg clear-num
2×flip3-- flip--
1×+-commutative associate-+l+ div-sub
Counts
4 → 197
Calls
4 calls:
56.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
93.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
171.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
42.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
158.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.3s

Counts
209 → 209
Iterations

Useful iterations: 2 (585.0ms)

IterNodesCost
03498472
19358281
235577909
done50007909

prune835.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.9b
(* (/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
2.9b
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
3553×times-frac
2088×*-un-lft-identity
1654×add-sqr-sqrt
1436×add-cube-cbrt
1370×sqrt-prod
615×associate-*r*
326×distribute-lft-out
126×associate-/r/
87×associate-/l*
65×flip3-+ flip-+
63×div-inv
55×associate-*l*
45×add-exp-log add-cbrt-cube unswap-sqr
22×cbrt-undiv div-exp
10×sqrt-div
8×pow1 prod-exp cbrt-unprod
7×associate-/r*
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1497
Calls
4 calls:
238.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.1s
(* (/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
48.0ms
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))
63.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series893.0ms

Counts
4 → 12
Calls
4 calls:
382.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
414.0ms
(* (/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
51.0ms
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.5s

Counts
1509 → 1509
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01385103646
1434096503
done500196497

prune3.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))))
3.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
16×add-exp-log
15×flip3-+ flip-+
13×*-un-lft-identity
12×cbrt-prod
8×frac-times associate-/r/ add-cbrt-cube associate-/l/
7×add-sqr-sqrt add-cube-cbrt
4×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp
3×pow1/3 distribute-lft-out
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
92.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))))
33.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
30.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series340.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))))
63.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
63.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify631.0ms

Counts
91 → 91
Iterations

Useful iterations: done (628.0ms)

IterNodesCost
01693033
14972890
214162517
done50002368

prune356.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.7b

regimes97.0ms

Accuracy

92.6% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 3.6b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
030116
142116
done42116

end0.0ms

sample527.0ms

Algorithm
intervals
Results
291.0ms8000×body80valid
93.0ms8000×pre80true