Details

Time bar (total: 18.1s)

sample34.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
4.0ms256×pre80true

simplify72.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b
(/ (/ (+ (+ (+ 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))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

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:
155.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
495.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
723.0ms
(/ (/ (/ (+ (+ (+ 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))
446.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series547.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
173.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
219.0ms
(/ (/ (/ (+ (+ (+ 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))
132.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify142.0ms

Counts
477 → 477

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
13.7b
(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
149×times-frac
101×*-un-lft-identity
87×associate-*r*
86×add-sqr-sqrt
77×add-cube-cbrt
49×cbrt-prod
30×cbrt-div
25×add-exp-log
19×flip3-+ flip-+
17×add-cbrt-cube
16×frac-times
12×associate-*l/ distribute-lft-out
9×pow1 prod-exp cbrt-unprod
8×associate-/r/
6×cbrt-undiv div-exp
5×associate-*r/
4×div-inv add-log-exp unswap-sqr
3×pow1/3 pow-prod-down
1×associate-*l* *-commutative
Counts
4 → 173
Calls
4 calls:
95.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
81.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
101.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.1s
(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
97.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
104.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
237.0ms
(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify61.0ms

Counts
185 → 185

prune954.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
3.4b
(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
1659×times-frac
1185×*-un-lft-identity
689×add-sqr-sqrt add-cube-cbrt
672×cbrt-prod
306×unpow-prod-down cube-prod
248×distribute-lft-out
145×associate-/l*
82×associate-/r/
42×flip3-+ flip-+
41×div-inv
17×cube-mult unpow3 sqr-pow
14×add-exp-log
13×add-cbrt-cube
7×associate-/r*
5×pow1 cbrt-undiv div-exp
4×add-log-exp
3×pow-unpow associate-/l/
2×cube-div frac-2neg pow-exp clear-num rem-cube-cbrt
1×pow-to-exp cbrt-div pow-pow pow1/3 rem-cbrt-cube
Counts
4 → 869
Calls
4 calls:
1.1s
(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
323.0ms
(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
252.0ms
(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
450.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series720.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
292.0ms
(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
119.0ms
(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
95.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify359.0ms

Counts
881 → 881

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b
(cbrt (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
36×times-frac
31×add-sqr-sqrt add-cube-cbrt
12×distribute-lft-out associate-/l*
10×add-exp-log add-cbrt-cube
9×associate-/r*
6×flip3-+ associate-/r/ flip-+ associate-/l/
4×pow1 add-log-exp
3×cbrt-undiv cbrt-div frac-2neg div-exp clear-num div-inv
1×cbrt-prod frac-times pow1/3 associate-*r/ associate-*l/
Counts
4 → 117
Calls
4 calls:
276.0ms
(cbrt (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
407.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
427.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
490.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(cbrt (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
106.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
107.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify58.0ms

Counts
129 → 129

prune784.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes125.0ms

Accuracy

-37.8% (3.4b remaining)

Error of 4.6b against oracle of 1.2b and baseline of 3.7b

bsearch425.0ms

Steps
ItersRangePoint
9
1.0650552711972757e+190
8.323418002339559e+195
3.282863536225363e+192
11
3.6813986932727994e+142
8.927873837486984e+161
3.719788790667249e+142
7
7.793074025213934e+96
6.077651646637727e+98
5.943357097504654e+98

simplify113.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s8000×body80valid
261.0ms8000×pre80true