Details

Time bar (total: 1.7m)

sample30.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms256×pre80true

simplify579.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3554
2111
133
014

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize31.0ms

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

rewrite1.4s

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-cbrt-cube add-exp-log
13×add-log-exp
10×cbrt-undiv associate-/r* div-exp
6×sum-log
4×pow1 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
120.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
352.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
543.0ms
(/ (/ (/ (+ (+ (+ 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))
313.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
150.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
248.0ms
(/ (/ (/ (+ (+ (+ 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))
120.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify632.0ms

Counts
477 → 477
Iterations
IterNodes
done5001
11609
0602

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b
(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b
(/ (/ (/ 1 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))
3.6b
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
21211×times-frac
13116×*-un-lft-identity
7701×add-sqr-sqrt add-cube-cbrt
3071×distribute-lft-out
910×associate-/l*
738×div-inv
572×associate-/r/
245×flip3-+ flip-+
154×add-exp-log
134×div-exp
96×associate-/r*
61×add-cbrt-cube
41×cbrt-undiv
30×1-exp
12×rec-exp
6×associate-/l/
4×pow1 clear-num frac-2neg add-log-exp
Counts
4 → 5638
Calls
4 calls:
266.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0))))
247.0ms
(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))
758.0ms
(/ (/ (/ 1 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))
306.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

series806.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0))))
193.0ms
(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))
270.0ms
(/ (/ (/ 1 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))
142.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.0s

Counts
5650 → 5650
Iterations
IterNodes
done5275
05275

prune33.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b
(/ (/ 1 (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b
(/ (* (/ (/ 1 (sqrt 1)) (/ 1 1)) (/ (/ 1 (sqrt 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))
3.6b
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
5364×times-frac
3217×*-un-lft-identity
2369×add-exp-log
2098×add-sqr-sqrt add-cube-cbrt
2036×div-exp
671×distribute-lft-out
621×sqrt-prod
441×1-exp
377×prod-exp
285×rec-exp
270×add-cbrt-cube
186×cbrt-undiv
175×associate-/r/
169×div-inv
96×associate-/r*
77×flip3-+ flip-+
35×cbrt-unprod
31×associate-/l*
8×associate-/l/
4×pow1 clear-num frac-2neg add-log-exp
1×frac-times associate-*l/ associate-*r/
Counts
4 → 2197
Calls
4 calls:
227.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0))))
265.0ms
(/ (/ 1 (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))
462.0ms
(/ (* (/ (/ 1 (sqrt 1)) (/ 1 1)) (/ (/ 1 (sqrt 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))
391.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
247.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0))))
201.0ms
(/ (/ 1 (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))
246.0ms
(/ (* (/ (/ 1 (sqrt 1)) (/ 1 1)) (/ (/ 1 (sqrt 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))
522.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Counts
2209 → 2209
Iterations
IterNodes
done5001
02754

prune11.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ 1 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))
0.3b
(* (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))))
3.6b
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite15.9s

Algorithm
rewrite-expression-head
Rules
19598×times-frac
12974×*-un-lft-identity
8120×add-sqr-sqrt
6518×add-cube-cbrt
5994×sqrt-prod
3158×distribute-lft-out
1840×swap-sqr
892×associate-*r* associate-*l*
855×div-inv
402×associate-/r/
289×unswap-sqr
173×flip3-+ flip-+
19×pow1
15×add-cbrt-cube add-exp-log
11×associate-/l*
10×associate-/r*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/l/
5×pow-prod-up
4×cbrt-undiv div-exp add-log-exp
3×clear-num frac-2neg pow-prod-down pow-sqr
2×frac-times associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×pow2 rem-square-sqrt pow-plus sqrt-unprod *-commutative
Counts
4 → 4047
Calls
4 calls:
611.0ms
(/ (* (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ 1 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))
13.5s
(* (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))))
358.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))
328.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (* (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ 1 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))
207.0ms
(* (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))))))
107.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))
110.0ms
(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (+ (+ alpha beta) (* 2.0 1.0)))

simplify5.5s

Counts
4059 → 4059
Iterations
IterNodes
done5001
04904

prune20.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

58.7% (1.5b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 3.6b

bsearch108.0ms

Steps
ItersRangePoint
8
1.8081809151522212e+136
9.209084411088349e+140
4.082362444610108e+139

simplify9.0ms

Iterations
IterNodes
done42
142
030

end0.0ms

sample1.2s

Algorithm
intervals
Results
815.0ms8000×body80valid
183.0ms8000×pre80true