Details

Time bar (total: 2.1m)

sample66.0ms

Algorithm
intervals
Results
34.0ms256×body80valid
10.0ms256×pre80true

simplify5.3s

Counts
1 → 1

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.5b

localize39.0ms

Local error

Found 4 expressions with local error:

46.0b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
36.8b
(/ (/ (* (* 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)))

rewrite614.0ms

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
239.0ms
(/ (/ (* (* 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)))
139.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
75.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.5s

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))
241.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
152.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
94.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify4.3s

Counts
224 → 224

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 35.6b

localize45.0ms

Local error

Found 4 expressions with local error:

37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
36.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-cbrt-cube add-exp-log
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r/
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 376
Calls
4 calls:
Slowest
718.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
253.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
82.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series4.4s

Counts
4 → 12
Calls
4 calls:
Slowest
3.6s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
450.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
186.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
126.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts
388 → 388

prune6.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.6b

localize87.0ms

Local error

Found 4 expressions with local error:

37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
36.9b
(/ (* 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 (sqrt 1.0)) (sqrt (+ (+ alpha beta) (* 2 i))))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))))

rewrite1.2s

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
648.0ms
(* (/ 1 (+ (sqrt (sqrt 1.0)) (sqrt (+ (+ alpha beta) (* 2 i))))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))))
291.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
177.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
58.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series56.9s

Counts
4 → 12
Calls
4 calls:
Slowest
48.5s
(* (/ 1 (+ (sqrt (sqrt 1.0)) (sqrt (+ (+ alpha beta) (* 2 i))))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0)))))
8.1s
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
161.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
127.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify4.0s

Counts
519 → 519

prune10.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.6b

localize91.0ms

Local error

Found 4 expressions with local error:

36.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
26.0b
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))) (/ (/ 1 (+ (+ alpha beta) (* 2 i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
16.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
3.4b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
328×times-frac
298×add-exp-log
259×add-sqr-sqrt
214×*-un-lft-identity
196×add-cbrt-cube
174×associate-*r*
156×sqrt-prod
152×add-cube-cbrt
141×div-exp
106×prod-exp
86×cbrt-undiv
68×cbrt-unprod
44×difference-of-squares
43×associate-*l*
36×associate-/r/
22×distribute-lft-out--
18×div-inv
17×flip3-+ flip-+
12×associate-/r*
11×pow1
9×rec-exp 1-exp distribute-lft-out
6×frac-times sqrt-div associate-*l/ associate-*r/ unswap-sqr
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u associate-/l* add-log-exp associate-/l/
3×flip3-- flip--
2×clear-num frac-2neg *-commutative
Counts
4 → 432
Calls
4 calls:
Slowest
998.0ms
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))) (/ (/ 1 (+ (+ alpha beta) (* 2 i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
672.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
247.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
74.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series10.0s

Counts
4 → 12
Calls
4 calls:
Slowest
4.6s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
3.5s
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))) (/ (/ 1 (+ (+ alpha beta) (* 2 i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
1.8s
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
124.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify3.0s

Counts
444 → 444

prune8.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 35.6b

regimes275.0ms

Accuracy

36.9% (1.8b remaining)

Error of 35.7b against oracle of 34.0b and baseline of 36.8b

bsearch88.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.0s8000×body80valid
377.0ms8000×pre80true