Average Error: 7.3 → 1.2
Time: 4.2s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z}}}{\sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{\sqrt[3]{t - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z}}}{\sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{\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) cbrt(((double) (t - z)))))) / ((double) cbrt(((double) (t - z)))))) * ((double) (((double) (((double) cbrt(x)) / ((double) (y - z)))) / ((double) cbrt(((double) (t - z))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.3
Target8.1
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.3

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

  3. Applied associate-/r*2.1

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

  5. Applied add-cube-cbrt2.7

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

  6. Applied *-un-lft-identity2.7

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

  7. Applied add-cube-cbrt2.8

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

  8. Applied times-frac2.8

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

  9. Applied times-frac1.2

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

  10. Simplified1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2020129 
(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))))