Details

Time bar (total: 29.7s)

sample70.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
8.0ms256×pre80true

simplify876.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
31753
2282
158
017

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha))
7.0b
(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
29.3b
(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
37.4b
(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

rewrite815.0ms

Algorithm
rewrite-expression-head
Rules
394×times-frac
249×*-un-lft-identity
165×add-sqr-sqrt
144×add-cube-cbrt
55×distribute-lft-out
49×add-cbrt-cube add-exp-log
45×associate-/r/
33×div-inv
30×associate-/l*
26×cbrt-undiv div-exp
21×difference-of-squares
20×associate-*l/
18×associate-/r*
14×flip3-+ flip-+
7×associate-/l/
6×prod-exp cbrt-unprod
4×pow1 clear-num frac-2neg add-log-exp
1×flip3-- div-sub flip--
Counts
4 → 326
Calls
4 calls:
117.0ms
(/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha))
337.0ms
(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
208.0ms
(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
126.0ms
(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

series1.4s

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha))
532.0ms
(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
541.0ms
(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
186.0ms
(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

simplify691.0ms

Counts
338 → 338
Iterations
IterNodes
done5001
11744
0534

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.4b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (+ alpha (+ beta (* i 2.0))))
0.1b
(/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (* (/ (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))) (+ (+ i alpha) beta)) (+ alpha (+ beta (* i 2.0)))))
37.2b
(sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta)))
37.2b
(sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta)))

rewrite414.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt
27×add-cube-cbrt sqrt-prod
15×add-cbrt-cube add-exp-log
12×associate-/l*
8×sqrt-div
7×flip3-+ associate-/r/ flip-+ distribute-lft-out
6×pow1
5×cbrt-undiv associate-/r* div-exp
4×add-log-exp associate-/l/
2×frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp associate-*r/ cbrt-unprod div-inv
1×associate-*l/
Counts
4 → 116
Calls
4 calls:
112.0ms
(/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (+ alpha (+ beta (* i 2.0))))
163.0ms
(/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (* (/ (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))) (+ (+ i alpha) beta)) (+ alpha (+ beta (* i 2.0)))))
62.0ms
(sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta)))
73.0ms
(sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta)))

series1.4s

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (+ alpha (+ beta (* i 2.0))))
864.0ms
(/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (* (/ (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))) (+ (+ i alpha) beta)) (+ alpha (+ beta (* i 2.0)))))
180.0ms
(sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta)))
166.0ms
(sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta)))

simplify1.4s

Counts
128 → 128
Iterations
IterNodes
done5004
23144
1617
0218

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 35.4b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0)))))
0.0b
(/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))))
0.1b
(/ (* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))
37.4b
(/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
490×*-un-lft-identity
420×times-frac
216×add-sqr-sqrt
171×add-cube-cbrt distribute-lft-out
100×associate-*l*
97×add-cbrt-cube add-exp-log
52×cbrt-undiv div-exp
39×associate-/r/
34×associate-/r*
26×associate-*r*
24×flip3-+ flip-+
22×associate-/l*
18×prod-exp cbrt-unprod div-inv
12×distribute-lft-out-- difference-of-squares
8×frac-add
6×pow1 sqrt-prod unswap-sqr associate-/l/
4×add-log-exp
3×clear-num frac-2neg
2×frac-times associate-*l/ associate-*r/
1×pow-prod-down *-commutative
Counts
4 → 418
Calls
4 calls:
443.0ms
(* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0)))))
180.0ms
(/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))))
418.0ms
(/ (* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))
145.0ms
(/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

series4.8s

Counts
4 → 12
Calls
4 calls:
751.0ms
(* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0)))))
415.0ms
(/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))))
3.5s
(/ (* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))
136.0ms
(/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

simplify968.0ms

Counts
430 → 430
Iterations
IterNodes
done5000
11876
0534

prune3.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))
0.0b
(* (/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0)))))
0.0b
(/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))))
0.1b
(/ (* (/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))

rewrite952.0ms

Algorithm
rewrite-expression-head
Rules
163×*-un-lft-identity
118×times-frac
97×add-cbrt-cube add-exp-log
80×add-sqr-sqrt
53×distribute-lft-out
51×add-cube-cbrt
45×cbrt-undiv div-exp
34×associate-/r*
26×associate-*r*
25×prod-exp cbrt-unprod
17×associate-/r/
15×associate-*l*
13×flip3-+ flip-+
12×distribute-lft-out-- difference-of-squares
8×frac-add
7×div-inv associate-/l*
6×pow1 sqrt-prod
5×associate-/l/
4×add-log-exp
3×clear-num frac-2neg
2×frac-times associate-*l/ associate-*r/ unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 236
Calls
4 calls:
123.0ms
(/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))
364.0ms
(* (/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0)))))
97.0ms
(/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))))
357.0ms
(/ (* (/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))

series2.2s

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))
383.0ms
(* (/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0)))))
243.0ms
(/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))))
1.5s
(/ (* (/ (* i 0.5) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))

simplify781.0ms

Counts
248 → 248
Iterations
IterNodes
done5000
11397
0389

prune1.7s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 4.0b

regimes703.0ms

Accuracy

13.4% (7.6b remaining)

Error of 12.0b against oracle of 4.4b and baseline of 13.2b

bsearch364.0ms

Steps
ItersRangePoint
7
6.799596305326668e+197
7.2943904197803876e+199
3.1853129188408834e+198
6
4.3812592823287414e+156
2.226581515516614e+157
4.444149846130252e+156
8
8.093951090051452e+74
1.688752603979303e+79
1.647212354283295e+79

simplify18.0ms

Iterations
IterNodes
done94
394
288
179
060

end0.0ms

sample1.5s

Algorithm
intervals
Results
924.0ms8000×body80valid
248.0ms8000×pre80true