Details

Time bar (total: 1.8m)

sample63.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
11.0ms256×pre80true

simplify5.1s

Counts
1 → 1

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 55.4b

localize66.0ms

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)))

rewrite593.0ms

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×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u 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 → 212
Calls
4 calls:
Slowest
205.0ms
(/ (/ (* (* 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))
164.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
115.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
100.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (/ (* (* 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))
279.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
171.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
70.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify4.7s

Counts
224 → 224

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.8b

localize65.0ms

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)))

rewrite699.0ms

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
271.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
200.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
150.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
67.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
485.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
346.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
150.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
148.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.3s

Counts
276 → 276

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.8b

localize52.0ms

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)))
7.9b
(* (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) 1) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite465.0ms

Algorithm
rewrite-expression-head
Rules
502×times-frac
450×add-sqr-sqrt
257×*-un-lft-identity
173×add-cube-cbrt
150×associate-*r*
138×sqrt-prod
87×add-exp-log
70×associate-*l*
53×div-exp
48×difference-of-squares
45×add-cbrt-cube
44×unswap-sqr
24×distribute-lft-out--
22×prod-exp
20×cbrt-undiv
16×associate-/r/
15×1-exp
12×div-inv
10×flip3-+ cbrt-unprod flip-+
8×pow1
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*r/
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times clear-num frac-2neg flip3-- pow-prod-down associate-*l/ *-commutative flip-- associate-/l*
Counts
4 → 373
Calls
4 calls:
Slowest
367.0ms
(* (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) 1) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
57.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
14.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
6.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series811.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
469.0ms
(* (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) 1) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
128.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
111.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
101.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.2s

Counts
385 → 385

prune7.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 35.8b

localize88.0ms

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

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
618×add-sqr-sqrt
579×times-frac
355×*-un-lft-identity
347×sqrt-prod
216×add-cube-cbrt
186×difference-of-squares
171×associate-*r*
62×distribute-lft-out--
56×associate-/r/
55×add-exp-log
37×add-cbrt-cube
28×flip3-+ flip-+ div-inv
24×div-exp
21×associate-*l*
19×associate-/l*
17×associate-/r*
15×cbrt-undiv
13×prod-exp
9×unswap-sqr
7×cbrt-unprod
6×pow1 distribute-lft-out
5×associate-/l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp associate-*r/
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 507
Calls
4 calls:
Slowest
601.0ms
(* (/ 1 (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))))
227.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
120.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
59.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series56.1s

Counts
4 → 12
Calls
4 calls:
Slowest
47.9s
(* (/ 1 (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))))
7.5s
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
548.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
176.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify4.0s

Counts
519 → 519

prune10.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 35.8b

regimes355.0ms

Accuracy

44.1% (1.4b remaining)

Error of 35.7b against oracle of 34.2b and baseline of 36.8b

bsearch130.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.5s8000×body80valid
835.0ms8000×pre80true