Average Error: 0.7 → 0.6
Time: 3.3s
Precision: binary64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y - z}{\sqrt[3]{x}} \cdot \left(y - t\right)}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y - z}{\sqrt[3]{x}} \cdot \left(y - t\right)}
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))
↓
(FPCore (x y z t)
 :precision binary64
 (- 1.0 (/ (* (cbrt x) (cbrt x)) (* (/ (- y z) (cbrt x)) (- y t)))))
double code(double x, double y, double z, double t) {
	return ((double) (1.0 - (x / ((double) (((double) (y - z)) * ((double) (y - t)))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (1.0 - (((double) (((double) cbrt(x)) * ((double) cbrt(x)))) / ((double) ((((double) (y - z)) / ((double) cbrt(x))) * ((double) (y - t)))))));
}

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

Derivation

  1. Initial program Error: 0.7 bits

    \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
  2. Using strategy rm

  3. Applied add-cube-cbrtError: 0.9 bits

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

  4. Applied associate-/l*Error: 0.9 bits

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

  5. SimplifiedError: 0.6 bits

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

  6. Final simplificationError: 0.6 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))