Details

Time bar (total: 2.1m)

sample93.0ms

Algorithm
intervals
Results
56.0ms256×body80valid
12.0ms256×pre80true

simplify5.0s

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.5b

localize56.0ms

Local error

Found 4 expressions with local error:

48.7b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
38.2b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite645.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×*-un-lft-identity add-cube-cbrt
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×associate-*l* pow-prod-down insert-posit16 add-log-exp
3×swap-sqr
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×pow2 pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 204
Calls
4 calls:
Slowest
236.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
153.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
125.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
124.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
261.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
187.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
90.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify3.5s

Counts
216 → 216

prune3.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.8b

localize39.0ms

Local error

Found 4 expressions with local error:

38.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
38.0b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite528.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
1×flip3-- flip--
Counts
4 → 256
Calls
4 calls:
Slowest
200.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
138.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
129.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
56.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
445.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
390.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
166.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
110.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.6s

Counts
268 → 268

prune4.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.8b

localize94.0ms

Local error

Found 4 expressions with local error:

38.2b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.2b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.0b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
9.1b
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))

rewrite575.0ms

Algorithm
rewrite-expression-head
Rules
11777×times-frac
6537×add-sqr-sqrt
5431×*-un-lft-identity
4327×add-cube-cbrt
3150×sqrt-prod
1104×difference-of-squares
552×distribute-lft-out--
313×div-inv
302×associate-/r/
152×associate-/r*
142×flip3-+ flip-+
39×add-exp-log
30×add-cbrt-cube
26×div-exp
23×associate-/l*
17×cbrt-undiv
6×pow1
4×sqrt-div insert-posit16 add-log-exp
3×1-exp associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/
1×prod-exp cbrt-unprod
Counts
4 → 3535
Calls
4 calls:
Slowest
205.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
65.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
12.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series712.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
111.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
74.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
69.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify13.9s

Counts
3547 → 3547

prune1.3m

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.8b

localize77.0ms

Local error

Found 4 expressions with local error:

38.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
0.2b
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite882.0ms

Algorithm
rewrite-expression-head
Rules
324×times-frac
300×*-un-lft-identity
219×add-sqr-sqrt
146×add-cube-cbrt
90×associate-*r*
69×distribute-lft-out
32×difference-of-squares
30×associate-/r/
23×associate-/l*
22×add-cbrt-cube add-exp-log
16×flip3-+ sqrt-prod flip-+ distribute-lft-out--
15×div-inv
12×associate-/r*
8×cbrt-undiv div-exp
6×pow1
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l* prod-exp cbrt-unprod unswap-sqr
1×flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 314
Calls
4 calls:
Slowest
366.0ms
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
263.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
147.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
95.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
451.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
320.0ms
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
148.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
109.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

simplify903.0ms

Counts
326 → 326

prune5.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.1b

regimes360.0ms

Accuracy

47.5% (8.7b remaining)

Error of 10.8b against oracle of 2.1b and baseline of 18.6b

bsearch130.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.5s8000×body80valid
448.0ms8000×pre80true