Average Error: 7.9 → 1.8
Time: 3.1s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}}
double code(double x, double y, double z, double t) {
	return ((double) (x / ((double) (((double) (y - z)) * ((double) (t - z))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (((double) cbrt(x)) * ((double) cbrt(x)))) / ((double) (y - z)))) * ((double) (((double) cbrt(((double) (((double) cbrt(x)) * ((double) cbrt(x)))))) / ((double) (((double) cbrt(((double) (t - z)))) * ((double) cbrt(((double) (t - z)))))))))) * ((double) (((double) cbrt(((double) cbrt(x)))) / ((double) cbrt(((double) (t - z))))))));
}

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

Original7.9
Target8.6
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.9

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

  3. Applied add-cube-cbrt8.4

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

  4. Applied times-frac1.7

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.9

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

  7. Applied add-cube-cbrt1.9

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

  8. Applied cbrt-prod1.9

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

  9. Applied times-frac1.9

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

  10. Applied associate-*r*1.8

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

  11. Final simplification1.8

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

Reproduce

herbie shell --seed 2020161 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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