Average Error: 7.5 → 2.0
Time: 27.3s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x}}{\frac{y - z}{\sqrt[3]{x}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x}}{\frac{y - z}{\sqrt[3]{x}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}}{t - z}
double code(double x, double y, double z, double t) {
	return (x / ((y - z) * (t - z)));
}
↓
double code(double x, double y, double z, double t) {
	return ((cbrt(x) / ((y - z) / cbrt(x))) * ((cbrt((cbrt(x) * cbrt(x))) * cbrt(cbrt(x))) / (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

Original7.5
Target8.3
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.5

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

  3. Applied add-cube-cbrt8.0

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

  4. Applied times-frac1.9

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

  5. Simplified1.9

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

  7. Applied add-cube-cbrt1.9

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

  8. Applied cbrt-prod2.0

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

  9. Final simplification2.0

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(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 (* (- y z) (- t z)))))

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