Average Error: 0.6 → 0.8
Time: 19.6s
Precision: binary64
\[[z, t]=\mathsf{sort}([z, t])\]
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{y - t} \]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{y - t}

(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 1.0 - (x / ((y - z) * (y - t)));
}
↓
double code(double x, double y, double z, double t) {
	return 1.0 - (((cbrt(x) * cbrt(x)) / (y - z)) * (cbrt(x) / (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 0.6

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

  2. Applied add-cube-cbrt_binary640.8

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

  3. Applied times-frac_binary640.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2021215 
(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)))))