Average Error: 7.2 → 2.1
Time: 19.0s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(x + \frac{z}{t \cdot z - x} \cdot y\right) - \frac{x}{t \cdot z - x}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(x + \frac{z}{t \cdot z - x} \cdot y\right) - \frac{x}{t \cdot z - x}}{x + 1}
double f(double x, double y, double z, double t) {
        double r465068 = x;
        double r465069 = y;
        double r465070 = z;
        double r465071 = r465069 * r465070;
        double r465072 = r465071 - r465068;
        double r465073 = t;
        double r465074 = r465073 * r465070;
        double r465075 = r465074 - r465068;
        double r465076 = r465072 / r465075;
        double r465077 = r465068 + r465076;
        double r465078 = 1.0;
        double r465079 = r465068 + r465078;
        double r465080 = r465077 / r465079;
        return r465080;
}
↓
double f(double x, double y, double z, double t) {
        double r465081 = x;
        double r465082 = z;
        double r465083 = t;
        double r465084 = r465083 * r465082;
        double r465085 = r465084 - r465081;
        double r465086 = r465082 / r465085;
        double r465087 = y;
        double r465088 = r465086 * r465087;
        double r465089 = r465081 + r465088;
        double r465090 = r465081 / r465085;
        double r465091 = r465089 - r465090;
        double r465092 = 1.0;
        double r465093 = r465081 + r465092;
        double r465094 = r465091 / r465093;
        return r465094;
}

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

Original7.2
Target0.3
Herbie2.1
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.2

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

  3. Applied div-sub7.2

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

  4. Applied associate-+r-7.2

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

  5. Simplified4.3

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

  7. Applied associate-/r/2.1

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

  8. Final simplification2.1

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

Reproduce

herbie shell --seed 2019304 
(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)))