Average Error: 52.6 → 37.9
Time: 5.1m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 2.2615941774648398 \cdot 10^{+145}:\\ \;\;\;\;\frac{\frac{i \cdot \left(i + \left(\alpha + \beta\right)\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\frac{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}{\frac{\beta \cdot \alpha + i \cdot \left(i + \left(\alpha + \beta\right)\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Error

Bits error versus alpha

Bits error versus beta

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if alpha < 2.2615941774648398e+145

    1. Initial program 50.5

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
    2. Using strategy rm

    3. Applied times-frac35.4

      \[\leadsto \frac{\color{blue}{\frac{i \cdot \left(\left(\alpha + \beta\right) + i\right)}{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \frac{\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]

    4. Applied associate-/l*35.4

      \[\leadsto \color{blue}{\frac{\frac{i \cdot \left(\left(\alpha + \beta\right) + i\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\frac{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}{\frac{\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}}}\]

    if 2.2615941774648398e+145 < alpha

    1. Initial program 62.5

      \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
    2. Using strategy rm

    3. Applied associate-/l*56.1

      \[\leadsto \frac{\color{blue}{\frac{i \cdot \left(\left(\alpha + \beta\right) + i\right)}{\frac{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}{\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)}}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]

    4. Taylor expanded around inf 49.5

      \[\leadsto \color{blue}{0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification37.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 2.2615941774648398 \cdot 10^{+145}:\\ \;\;\;\;\frac{\frac{i \cdot \left(i + \left(\alpha + \beta\right)\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\frac{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}{\frac{\beta \cdot \alpha + i \cdot \left(i + \left(\alpha + \beta\right)\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019018 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :pre (and (> alpha -1) (> beta -1) (> i 1))
  (/ (/ (* (* 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)))

Details

Time bar (total: 5.1m)Debug log

sample87.0ms

Algorithm
intervals
Results
53.0ms256×body80valid
12.0ms256×pre80true

simplify262.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
262.0ms
(/ (/ (* (* 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))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize64.0ms

Local error

Found 4 expressions with local error:

46.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
38.1b
(/ (/ (* (* 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))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×flip-+
43×flip3-+
42×associate-/r/
36×add-exp-log
36×add-cbrt-cube
28×associate-*r/
28×frac-times
24×add-cube-cbrt
24×*-un-lft-identity
24×add-sqr-sqrt
14×associate-/l*
14×associate-*l/
13×div-exp
13×cbrt-undiv
9×associate-/l/
9×cbrt-unprod
9×prod-exp
6×div-inv
6×associate-*r*
6×pow1
4×add-log-exp
4×associate-/r*
2×*-commutative
2×distribute-lft-in
2×frac-2neg
2×clear-num
2×distribute-rgt-in
1×flip--
1×pow-prod-down
1×associate-*l*
1×flip3--
Counts
4 → 155
Calls
4 calls:
Slowest
35.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
34.0ms
(/ (/ (* (* 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))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
4.0ms
(* i (+ (+ alpha beta) i))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
706.0ms
(/ (/ (* (* 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))
196.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
87.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
22.0ms
(* i (+ (+ alpha beta) i))

simplify35.1s

Counts
173 → 167
Calls
173 calls:
Slowest
819.0ms
(/ 1 (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
745.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) 1)
655.0ms
(/ (- (+ alpha beta) (* 2 i)) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
634.0ms
(/ (- (+ alpha beta) (* 2 i)) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
593.0ms
(/ (- (+ alpha beta) (* 2 i)) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 38.0b

localize12.0ms

Local error

Found 4 expressions with local error:

36.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
35.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
31.8b
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
4.9b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
1416×times-frac
530×add-cube-cbrt
530×*-un-lft-identity
530×add-sqr-sqrt
186×associate-/r/
99×div-inv
89×flip-+
89×flip3-+
71×associate-/r*
34×add-exp-log
34×add-cbrt-cube
20×div-exp
20×cbrt-undiv
16×associate-/l*
7×associate-/l/
4×add-log-exp
4×frac-2neg
4×clear-num
4×pow1
2×associate-*r/
1×flip--
1×div-sub
1×flip3--
Counts
4 → 668
Calls
4 calls:
Slowest
44.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
27.0ms
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
16.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
8.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
740.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
547.0ms
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
104.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
78.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify3.1m

Counts
1143 → 680
Calls
1143 calls:
Slowest
956.0ms
(/ (/ i (sqrt (+ (+ alpha beta) (* 2 i)))) (/ (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) 1))
927.0ms
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (cbrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
889.0ms
(/ (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (cbrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
790.0ms
(/ (/ i 1) (/ 1 (/ (* (cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))))))
781.0ms
(/ (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (+ (+ alpha beta) (* 2 i)))))

prune11.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 38.0b

localize12.0ms

Local error

Found 4 expressions with local error:

42.0b
(/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.1b
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
3.3b
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
0.0b
(* i (+ (+ alpha beta) i))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
38×add-cube-cbrt
38×*-un-lft-identity
38×add-sqr-sqrt
32×add-exp-log
32×add-cbrt-cube
21×associate-/r/
16×associate-/l*
16×div-exp
16×cbrt-undiv
15×flip-+
15×flip3-+
15×associate-/r*
13×div-inv
11×associate-/l/
6×associate-*r/
4×add-log-exp
4×pow1
4×frac-times
3×cbrt-unprod
3×prod-exp
3×associate-*r*
3×frac-2neg
3×clear-num
2×associate-*l/
1×flip--
1×*-commutative
1×flip3--
1×distribute-lft-in
1×distribute-rgt-in
Counts
4 → 164
Calls
4 calls:
Slowest
30.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
23.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
20.0ms
(/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
10.0ms
(* i (+ (+ alpha beta) i))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
812.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
165.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
141.0ms
(/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
24.0ms
(* i (+ (+ alpha beta) i))

simplify31.6s

Counts
190 → 176
Calls
190 calls:
Slowest
891.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
818.0ms
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
714.0ms
(- (log (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (log (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
577.0ms
(* (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))
572.0ms
(/ 1 (* (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))))

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 38.0b

localize35.0ms

Local error

Found 4 expressions with local error:

38.1b
(/ (/ (* i (+ (+ alpha beta) i)) (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
36.5b
(sqrt (* (+ beta i) (+ alpha i)))
36.5b
(sqrt (* (+ beta i) (+ alpha i)))
3.3b
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i))))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log
47×add-cbrt-cube
29×times-frac
24×div-exp
24×cbrt-undiv
17×add-cube-cbrt
17×associate-/r/
17×*-un-lft-identity
17×add-sqr-sqrt
16×sqrt-div
13×flip-+
13×flip3-+
13×frac-times
11×associate-*r/
9×associate-/l*
9×associate-*l/
8×cbrt-unprod
8×prod-exp
6×div-inv
4×add-log-exp
4×associate-/r*
4×pow1
3×associate-/l/
2×sqrt-prod
2×pow1/2
2×frac-2neg
2×clear-num
1×flip--
1×flip3--
Counts
4 → 122
Calls
4 calls:
Slowest
29.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i))))))
29.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
1.0ms
(sqrt (* (+ beta i) (+ alpha i)))
1.0ms
(sqrt (* (+ beta i) (+ alpha i)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
765.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
184.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i))))))
58.0ms
(sqrt (* (+ beta i) (+ alpha i)))
35.0ms
(sqrt (* (+ beta i) (+ alpha i)))

simplify24.1s

Counts
121 → 134
Calls
121 calls:
Slowest
772.0ms
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i))))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i))))) (* (* (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i))))) (/ (+ (* 2 i) (+ beta alpha)) (sqrt (* (+ beta i) (+ alpha i)))))))
553.0ms
(/ (sqrt (* (+ beta i) (+ alpha i))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
548.0ms
(sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
537.0ms
(/ 1 (* (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))))
522.0ms
(/ (* (sqrt (* (+ beta i) (+ alpha i))) (sqrt (* (+ beta i) (+ alpha i)))) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))

prune2.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 38.0b

regimes224.0ms

Accuracy

43.7% (1.5b remaining)

Error of 37.9b against oracle of 36.4b and baseline of 39.1b

bsearch90.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.5s8000×body80valid
326.0ms8000×pre80true