Average Error: 2.1 → 1.1
Time: 13.1s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\]
\frac{x - y}{z - y} \cdot t
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}
double f(double x, double y, double z, double t) {
        double r449193 = x;
        double r449194 = y;
        double r449195 = r449193 - r449194;
        double r449196 = z;
        double r449197 = r449196 - r449194;
        double r449198 = r449195 / r449197;
        double r449199 = t;
        double r449200 = r449198 * r449199;
        return r449200;
}
↓
double f(double x, double y, double z, double t) {
        double r449201 = 1.0;
        double r449202 = cbrt(r449201);
        double r449203 = r449202 * r449202;
        double r449204 = z;
        double r449205 = y;
        double r449206 = r449204 - r449205;
        double r449207 = cbrt(r449206);
        double r449208 = r449207 * r449207;
        double r449209 = x;
        double r449210 = r449209 - r449205;
        double r449211 = cbrt(r449210);
        double r449212 = r449211 * r449211;
        double r449213 = r449208 / r449212;
        double r449214 = r449203 / r449213;
        double r449215 = t;
        double r449216 = r449207 / r449211;
        double r449217 = r449215 / r449216;
        double r449218 = r449214 * r449217;
        return r449218;
}

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

Original2.1
Target2.1
Herbie1.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.1

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

  3. Applied clear-num2.3

    \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \cdot t\]
  4. Using strategy rm

  5. Applied add-cube-cbrt3.3

    \[\leadsto \frac{1}{\frac{z - y}{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}} \cdot t\]

  6. Applied add-cube-cbrt2.9

    \[\leadsto \frac{1}{\frac{\color{blue}{\left(\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}\right) \cdot \sqrt[3]{z - y}}}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}} \cdot t\]

  7. Applied times-frac2.9

    \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}} \cdot t\]

  8. Applied add-cube-cbrt2.9

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}} \cdot t\]

  9. Applied times-frac2.8

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\right)} \cdot t\]

  10. Applied associate-*l*1.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \left(\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}} \cdot t\right)}\]

  11. Simplified1.1

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \color{blue}{\frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}}\]

  12. Final simplification1.1

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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