Details

Time bar (total: 32.5s)

sample39.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
5.0ms256×pre80true

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211135
355035
4408735
done500035

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize29.0ms

Local error

Found 3 expressions with local error:

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))
1.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 450
Calls
3 calls:
434.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
773.0ms
(/ (/ (/ (+ (+ (+ 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))
430.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series872.0ms

Counts
3 → 9
Calls
3 calls:
207.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
212.0ms
(/ (/ (/ (+ (+ (+ 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))
453.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.7s

Counts
459 → 459
Iterations

Useful iterations: done (2.6s)

IterNodesCost
058025719
1139524955
2462824032
done500023292

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b
(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 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))
1.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
3614×times-frac
2164×*-un-lft-identity
1424×add-sqr-sqrt add-cube-cbrt
370×distribute-lft-out
192×associate-/l*
152×associate-/r/
89×div-inv
84×associate-/r*
65×flip3-+ flip-+
64×add-exp-log
44×div-exp
34×add-cbrt-cube
20×cbrt-undiv
6×rec-exp 1-exp
5×pow1 associate-/l/
4×frac-2neg clear-num add-log-exp
1×pow-flip inv-pow
Counts
4 → 1332
Calls
4 calls:
287.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
311.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
756.0ms
(/ (/ 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))
440.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series806.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
241.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
240.0ms
(/ (/ 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))
113.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify4.1s

Counts
1344 → 1344
Iterations

Useful iterations: done (4.0s)

IterNodesCost
0158983763
1383078123
done500275998

prune3.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))))
0.1b
(/ (/ 1 (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ 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))
1.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.7b
(/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
502×times-frac
280×*-un-lft-identity
182×add-sqr-sqrt add-cube-cbrt
110×associate-/r/
97×add-exp-log
58×div-exp
55×associate-/l*
49×add-cbrt-cube distribute-lft-out
41×flip3-- flip--
40×frac-times associate-*r/
28×div-inv
26×cbrt-undiv
21×associate-/r* difference-of-squares
20×associate-*l/
14×prod-exp
8×rec-exp 1-exp
6×cbrt-unprod
5×pow1 associate-/l/
4×frac-2neg clear-num add-log-exp
3×flip3-+ flip-+
1×pow-flip div-sub inv-pow
Counts
4 → 407
Calls
4 calls:
389.0ms
(/ 1 (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))))
614.0ms
(/ (/ 1 (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ 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))
401.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
257.0ms
(/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
438.0ms
(/ 1 (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))))
343.0ms
(/ (/ 1 (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ 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))
114.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
461.0ms
(/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0))))

simplify1.2s

Counts
419 → 419
Iterations

Useful iterations: done (1.2s)

IterNodesCost
061127539
1158626050
done500020256

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (* (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (/ 1 (* (+ (+ alpha beta) (* 2.0 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) (* 2.0 1.0))))
15.8b
(* (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
34×add-cbrt-cube
24×prod-exp
23×flip3-+ flip-+
22×add-sqr-sqrt *-un-lft-identity
21×pow1
20×div-exp
18×associate-*r* associate-/r/
16×frac-times
15×add-cube-cbrt
12×times-frac
10×cbrt-undiv associate-*l/ cbrt-unprod
8×associate-*r/
7×associate-*l*
6×rec-exp pow-flip 1-exp associate-/l/
5×associate-/r*
4×associate-/l* add-log-exp unswap-sqr
3×swap-sqr pow-prod-down div-inv distribute-lft-out
2×pow2 frac-2neg pow-plus clear-num pow-sqr un-div-inv *-commutative pow-prod-up
1×distribute-rgt-in distribute-lft-in inv-pow
Counts
4 → 161
Calls
4 calls:
209.0ms
(* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
577.0ms
(/ (* (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
126.0ms
(/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
539.0ms
(* (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series570.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
235.0ms
(/ (* (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
86.0ms
(/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
223.0ms
(* (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (/ 1 (* (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify2.3s

Counts
173 → 173
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02435238
17144532
236063895
done50003480

prune562.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes61.0ms

Accuracy

66.3% (1.5b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 4.4b

bsearch101.0ms

Steps
ItersRangePoint
10
3.787217848124224e+152
3.104754081890425e+165
2.4580673707165206e+153

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03178
14378
done4378

end0.0ms

sample1.5s

Algorithm
intervals
Results
719.0ms8000×body80valid
527.0ms8000×pre80true