Average Error: 1.6 → 0.6
Time: 3.6s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{x + 4}{y} - \sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot z\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{x + 4}{y} - \sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot z\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right|
double f(double x, double y, double z) {
        double r32110 = x;
        double r32111 = 4.0;
        double r32112 = r32110 + r32111;
        double r32113 = y;
        double r32114 = r32112 / r32113;
        double r32115 = r32110 / r32113;
        double r32116 = z;
        double r32117 = r32115 * r32116;
        double r32118 = r32114 - r32117;
        double r32119 = fabs(r32118);
        return r32119;
}
↓
double f(double x, double y, double z) {
        double r32120 = x;
        double r32121 = 4.0;
        double r32122 = r32120 + r32121;
        double r32123 = y;
        double r32124 = r32122 / r32123;
        double r32125 = cbrt(r32120);
        double r32126 = r32125 * r32125;
        double r32127 = cbrt(r32123);
        double r32128 = r32127 * r32127;
        double r32129 = r32126 / r32128;
        double r32130 = sqrt(r32129);
        double r32131 = r32125 / r32127;
        double r32132 = fabs(r32131);
        double r32133 = z;
        double r32134 = r32132 * r32133;
        double r32135 = r32134 * r32131;
        double r32136 = r32130 * r32135;
        double r32137 = r32124 - r32136;
        double r32138 = fabs(r32137);
        return r32138;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.9

    \[\leadsto \left|\frac{x + 4}{y} - \frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot z\right|\]

  4. Applied add-cube-cbrt2.0

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot z\right|\]

  5. Applied times-frac2.0

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} \cdot z\right|\]

  6. Applied associate-*l*0.6

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)}\right|\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.6

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}\right)} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  9. Applied associate-*l*0.6

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right)}\right|\]

  10. Simplified0.6

    \[\leadsto \left|\frac{x + 4}{y} - \sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \color{blue}{\left(\left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot z\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)}\right|\]

  11. Final simplification0.6

    \[\leadsto \left|\frac{x + 4}{y} - \sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot z\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right|\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))