Average Error: 7.7 → 2.3
Time: 22.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{z}{t \cdot z - x} \cdot y - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{z}{t \cdot z - x} \cdot y - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r434000 = x;
        double r434001 = y;
        double r434002 = z;
        double r434003 = r434001 * r434002;
        double r434004 = r434003 - r434000;
        double r434005 = t;
        double r434006 = r434005 * r434002;
        double r434007 = r434006 - r434000;
        double r434008 = r434004 / r434007;
        double r434009 = r434000 + r434008;
        double r434010 = 1.0;
        double r434011 = r434000 + r434010;
        double r434012 = r434009 / r434011;
        return r434012;
}
↓
double f(double x, double y, double z, double t) {
        double r434013 = x;
        double r434014 = z;
        double r434015 = t;
        double r434016 = r434015 * r434014;
        double r434017 = r434016 - r434013;
        double r434018 = r434014 / r434017;
        double r434019 = y;
        double r434020 = r434018 * r434019;
        double r434021 = r434013 / r434017;
        double r434022 = r434020 - r434021;
        double r434023 = r434013 + r434022;
        double r434024 = 1.0;
        double r434025 = r434013 + r434024;
        double r434026 = r434023 / r434025;
        return r434026;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
Target0.4
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.7

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
  2. Using strategy rm

  3. Applied div-sub7.7

    \[\leadsto \frac{x + \color{blue}{\left(\frac{y \cdot z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}}{x + 1}\]

  4. Simplified2.3

    \[\leadsto \frac{x + \left(\color{blue}{\frac{z}{t \cdot z - x} \cdot y} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
  5. Using strategy rm

  6. Applied pow12.3

    \[\leadsto \color{blue}{{\left(\frac{x + \left(\frac{z}{t \cdot z - x} \cdot y - \frac{x}{t \cdot z - x}\right)}{x + 1}\right)}^{1}}\]

  7. Final simplification2.3

    \[\leadsto \frac{x + \left(\frac{z}{t \cdot z - x} \cdot y - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))