Details

Time bar (total: 41.2s)

sample45.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
01753
16052
229548
3183248
done500048

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
39.4b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite927.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 208
Calls
4 calls:
202.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
135.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
366.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
206.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
170.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
245.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify796.0ms

Counts
220 → 220
Iterations

Useful iterations: done (781.0ms)

IterNodesCost
036612421
1137011478
done50019638

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 37.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))))
0.3b
(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
38.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
38.3b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
206×times-frac
165×*-un-lft-identity
153×add-sqr-sqrt
97×add-cube-cbrt
28×difference-of-squares
25×add-exp-log add-cbrt-cube
24×distribute-lft-out associate-/l*
17×associate-/r* div-inv
14×sqrt-prod distribute-lft-out--
11×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+
1×flip3-- flip--
Counts
4 → 238
Calls
4 calls:
121.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))))
24.0ms
(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
83.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

series1.1s

Counts
4 → 12
Calls
4 calls:
347.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))))
458.0ms
(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
177.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
139.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

simplify2.2s

Counts
250 → 250
Iterations

Useful iterations: 2 (766.0ms)

IterNodesCost
03579598
19469333
246078913
done50008913

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 37.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))) (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))))
0.3b
(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
38.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
38.3b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
206×times-frac
165×*-un-lft-identity
153×add-sqr-sqrt
97×add-cube-cbrt
28×difference-of-squares
25×add-exp-log add-cbrt-cube
24×distribute-lft-out
22×associate-/l*
19×associate-/r*
17×div-inv
14×sqrt-prod distribute-lft-out--
11×cbrt-undiv div-exp
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×associate-/r/
2×flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+
1×flip3-- flip--
Counts
4 → 238
Calls
4 calls:
88.0ms
(/ (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))) (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))))
22.0ms
(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
45.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

series851.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(/ (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))) (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))))
357.0ms
(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
131.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
104.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

simplify2.0s

Counts
250 → 250
Iterations

Useful iterations: 2 (605.0ms)

IterNodesCost
03589618
19669385
247408959
done50008959

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 37.3b

localize41.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) 1) (/ (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))))
38.1b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
38.1b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
38.3b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

rewrite714.0ms

Algorithm
rewrite-expression-head
Rules
11021×times-frac
6151×add-sqr-sqrt
5137×*-un-lft-identity
4125×add-cube-cbrt
2996×sqrt-prod
1012×difference-of-squares
506×distribute-lft-out--
301×div-inv
140×associate-/r*
39×add-exp-log
30×add-cbrt-cube
26×div-exp
24×associate-/r/
23×associate-/l*
17×cbrt-undiv
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×1-exp associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num
1×flip3-+ prod-exp cbrt-unprod flip-+
Counts
4 → 3257
Calls
4 calls:
107.0ms
(/ (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) 1) (/ (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
48.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

series739.0ms

Counts
4 → 12
Calls
4 calls:
466.0ms
(/ (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) 1) (/ (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta)))))
94.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
68.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
110.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

simplify2.3s

Counts
3269 → 3269
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02938286040
done5001266576

prune17.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 37.3b

regimes382.0ms

Accuracy

37.4% (2.4b remaining)

Error of 36.2b against oracle of 33.8b and baseline of 37.7b

bsearch84.0ms

Steps
ItersRangePoint
6
3.998441498091938e+207
4.743012469806171e+208
4.07062621862513e+207

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02874
13472
done3472

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8000×body80valid
380.0ms8000×pre80true