Average Error: 6.9 → 2.2
Time: 14.7s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(y \cdot \frac{1}{\frac{t \cdot z - x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(y \cdot \frac{1}{\frac{t \cdot z - x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r766073 = x;
        double r766074 = y;
        double r766075 = z;
        double r766076 = r766074 * r766075;
        double r766077 = r766076 - r766073;
        double r766078 = t;
        double r766079 = r766078 * r766075;
        double r766080 = r766079 - r766073;
        double r766081 = r766077 / r766080;
        double r766082 = r766073 + r766081;
        double r766083 = 1.0;
        double r766084 = r766073 + r766083;
        double r766085 = r766082 / r766084;
        return r766085;
}
↓
double f(double x, double y, double z, double t) {
        double r766086 = x;
        double r766087 = y;
        double r766088 = 1.0;
        double r766089 = t;
        double r766090 = z;
        double r766091 = r766089 * r766090;
        double r766092 = r766091 - r766086;
        double r766093 = r766092 / r766090;
        double r766094 = r766088 / r766093;
        double r766095 = r766087 * r766094;
        double r766096 = r766086 / r766092;
        double r766097 = r766095 - r766096;
        double r766098 = r766086 + r766097;
        double r766099 = 1.0;
        double r766100 = r766086 + r766099;
        double r766101 = r766098 / r766100;
        return r766101;
}

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

Original6.9
Target0.3
Herbie2.2
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 6.9

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

  3. Applied div-sub6.9

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

  4. Simplified2.2

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

  6. Applied clear-num2.2

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

  7. Final simplification2.2

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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)))