Details

Time bar (total: 55.9s)

sample91.0ms

Algorithm
intervals
Results
50.0ms256×body80valid
15.0ms256×pre80true

simplify5.3s

Counts
1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.7b

localize49.0ms

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))))
37.8b
(/ (/ (* (* 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)))

rewrite506.0ms

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
196.0ms
(/ (/ (* (* 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))
129.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
98.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
75.0ms
(* (* 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))
254.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
141.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
100.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify3.5s

Counts
224 → 224

prune3.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.5b

localize86.0ms

Local error

Found 4 expressions with local error:

37.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.0b
(/ (+ (* beta alpha) (* 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
680.0ms
(* (/ (/ (* 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))))
306.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
157.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
51.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series4.0s

Counts
4 → 12
Calls
4 calls:
Slowest
3.2s
(* (/ (/ (* 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))))
436.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
179.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
121.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.4s

Counts
388 → 388

prune6.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.5b

localize70.0ms

Local error

Found 4 expressions with local error:

37.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.0b
(/ (+ (* beta alpha) (* 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))))
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)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
85×add-cbrt-cube add-exp-log
79×times-frac
63×*-un-lft-identity
61×add-sqr-sqrt
42×associate-*l*
41×add-cube-cbrt
40×cbrt-undiv div-exp
21×prod-exp cbrt-unprod
18×associate-/r/
15×associate-*r*
12×associate-/r*
10×flip3-+ flip-+
9×div-inv distribute-lft-out
7×associate-/l/
6×pow1
5×associate-/l*
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp difference-of-squares unswap-sqr
3×clear-num frac-2neg
2×frac-times associate-*l/ sqrt-prod distribute-lft-out--
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 203
Calls
4 calls:
Slowest
446.0ms
(* (/ (/ (* 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))))
301.0ms
(/ (* (/ (/ (* 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)))
192.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
66.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series4.3s

Counts
4 → 12
Calls
4 calls:
Slowest
3.1s
(/ (* (/ (/ (* 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)))
847.0ms
(* (/ (/ (* 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))))
170.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
128.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.9s

Counts
215 → 215

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.5b

localize49.0ms

Local error

Found 4 expressions with local error:

37.0b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
0.2b
(* (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
0.1b
(* (/ (/ i 1) 1) (* (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
0.1b
(/ (* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
554×add-exp-log
326×div-exp
266×add-cbrt-cube
243×times-frac
220×*-un-lft-identity
188×prod-exp
143×add-sqr-sqrt
133×associate-*l*
128×cbrt-undiv
114×add-cube-cbrt
84×cbrt-unprod
70×1-exp
57×distribute-lft-out
16×associate-*r* associate-/r/
12×div-inv
11×frac-times pow1 associate-*r/
9×associate-/r* associate-/l/
8×flip3-+ flip-+
7×associate-*l/
6×unswap-sqr
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u associate-/l* add-log-exp difference-of-squares
2×clear-num frac-2neg *-commutative sqrt-prod distribute-lft-out--
1×flip3-- flip--
Counts
4 → 413
Calls
4 calls:
Slowest
456.0ms
(* (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
452.0ms
(/ (* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))
329.0ms
(* (/ (/ i 1) 1) (* (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
147.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.4s

Counts
4 → 12
Calls
4 calls:
Slowest
2.9s
(/ (* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))
797.0ms
(* (/ (/ i 1) 1) (* (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
470.0ms
(* (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
180.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.0s

Counts
425 → 425

prune7.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.5b

regimes229.0ms

Accuracy

44.6% (9.3b remaining)

Error of 11.3b against oracle of 2.0b and baseline of 18.8b

bsearch291.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.8s8000×body80valid
377.0ms8000×pre80true