Details

Time bar (total: 57.9s)

sample96.0ms

Algorithm
intervals
Results
64.0ms256×body80valid
14.0ms256×pre80true

simplify5.1s

Counts
1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.3b

localize37.0ms

Local error

Found 4 expressions with local error:

43.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
33.2b
(/ (/ (* (* 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
(* i (+ (+ alpha beta) i))

rewrite647.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-out
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 201
Calls
4 calls:
Slowest
275.0ms
(/ (/ (* (* 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))
205.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
108.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
56.0ms
(* i (+ (+ alpha beta) i))

series1.5s

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))
216.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
170.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
27.0ms
(* i (+ (+ alpha beta) i))

simplify3.9s

Counts
213 → 213

prune3.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 31.4b

localize47.0ms

Local error

Found 4 expressions with local error:

32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
32.2b
(/ (* 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)))

rewrite663.0ms

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×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
1×flip3-- flip--
Counts
4 → 264
Calls
4 calls:
Slowest
247.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
171.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
151.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
89.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series998.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
388.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
316.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
173.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
120.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.7s

Counts
276 → 276

prune4.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 31.4b

localize98.0ms

Local error

Found 4 expressions with local error:

32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.4b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite640.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
176×*-un-lft-identity
92×add-sqr-sqrt add-cube-cbrt
42×distribute-lft-out
32×sqrt-prod
30×associate-/r/
28×associate-/l*
25×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
15×associate-/r* div-inv
11×cbrt-undiv div-exp
6×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
Counts
4 → 248
Calls
4 calls:
Slowest
282.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
169.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
132.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
48.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series8.0s

Counts
4 → 12
Calls
4 calls:
Slowest
7.4s
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
322.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
139.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
118.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.6s

Counts
260 → 260

prune4.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 31.4b

localize109.0ms

Local error

Found 4 expressions with local error:

32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
0.4b
(/ (/ i 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.3b
(* (/ (/ i 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
823×times-frac
586×*-un-lft-identity
559×add-sqr-sqrt
343×add-cube-cbrt
237×sqrt-prod
153×associate-*r*
111×distribute-lft-out
97×associate-*l*
66×add-exp-log
52×add-cbrt-cube
38×associate-/r/
36×div-exp
35×unswap-sqr
34×div-inv
32×difference-of-squares
31×associate-/l*
25×cbrt-undiv
19×flip3-+ flip-+
16×associate-/r* distribute-lft-out--
12×prod-exp
9×cbrt-unprod
6×pow1 sqrt-div
4×expm1-log1p-u 1-exp insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg
1×frac-times flip3-- pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 618
Calls
4 calls:
Slowest
599.0ms
(* (/ (/ i 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
308.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
139.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
113.0ms
(/ (/ i 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
605.0ms
(/ (/ i 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
472.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
358.0ms
(* (/ (/ i 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
176.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.3s

Counts
630 → 630

prune11.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.1b

regimes280.0ms

Accuracy

48.3% (8.2b remaining)

Error of 10.3b against oracle of 2.1b and baseline of 17.9b

bsearch118.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.9s8000×body80valid
353.0ms8000×pre80true