Average Error: 3.6 → 3.6
Time: 5.6s
Precision: binary64
\[\alpha > -1 \land \beta > -1\]
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]
↓
\[\frac{\frac{\left(\left(\left(\alpha + \beta\right) + \alpha \cdot \beta\right) + 1\right) \cdot \frac{1}{\alpha + \left(\beta + 1 \cdot 2\right)}}{\left(\alpha + \beta\right) + 1 \cdot 2}}{1 + \left(\left(\alpha + \beta\right) + 1 \cdot 2\right)}\]
\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}
↓
\frac{\frac{\left(\left(\left(\alpha + \beta\right) + \alpha \cdot \beta\right) + 1\right) \cdot \frac{1}{\alpha + \left(\beta + 1 \cdot 2\right)}}{\left(\alpha + \beta\right) + 1 \cdot 2}}{1 + \left(\left(\alpha + \beta\right) + 1 \cdot 2\right)}
(FPCore (alpha beta)
 :precision binary64
 (/
  (/
   (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
   (+ (+ alpha beta) (* 2.0 1.0)))
  (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
↓
(FPCore (alpha beta)
 :precision binary64
 (/
  (/
   (*
    (+ (+ (+ alpha beta) (* alpha beta)) 1.0)
    (/ 1.0 (+ alpha (+ beta (* 1.0 2.0)))))
   (+ (+ alpha beta) (* 1.0 2.0)))
  (+ 1.0 (+ (+ alpha beta) (* 1.0 2.0)))))
double code(double alpha, double beta) {
	return (((((double) (((double) (((double) (alpha + beta)) + ((double) (beta * alpha)))) + 1.0)) / ((double) (((double) (alpha + beta)) + ((double) (2.0 * 1.0))))) / ((double) (((double) (alpha + beta)) + ((double) (2.0 * 1.0))))) / ((double) (((double) (((double) (alpha + beta)) + ((double) (2.0 * 1.0)))) + 1.0)));
}
↓
double code(double alpha, double beta) {
	return ((((double) (((double) (((double) (((double) (alpha + beta)) + ((double) (alpha * beta)))) + 1.0)) * (1.0 / ((double) (alpha + ((double) (beta + ((double) (1.0 * 2.0))))))))) / ((double) (((double) (alpha + beta)) + ((double) (1.0 * 2.0))))) / ((double) (1.0 + ((double) (((double) (alpha + beta)) + ((double) (1.0 * 2.0)))))));
}

Error

Bits error versus alpha

Bits error versus beta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.6

    \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]
  2. Using strategy rm

  3. Applied div-inv3.6

    \[\leadsto \frac{\frac{\color{blue}{\left(\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1\right) \cdot \frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]

  4. Simplified3.6

    \[\leadsto \frac{\frac{\left(\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1\right) \cdot \color{blue}{\frac{1}{\alpha + \left(\beta + 1 \cdot 2\right)}}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]

  5. Final simplification3.6

    \[\leadsto \frac{\frac{\left(\left(\left(\alpha + \beta\right) + \alpha \cdot \beta\right) + 1\right) \cdot \frac{1}{\alpha + \left(\beta + 1 \cdot 2\right)}}{\left(\alpha + \beta\right) + 1 \cdot 2}}{1 + \left(\left(\alpha + \beta\right) + 1 \cdot 2\right)}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))