Average Error: 0.7 → 0.7
Time: 6.7s
Precision: binary64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)} \]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}

(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))
↓
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y t) (- y z)))))
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 - (x / ((y - t) * (y - 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

Derivation

  1. Initial program 0.7

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

  2. Applied add-cube-cbrt_binary640.9

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

  3. Applied times-frac_binary640.6

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

  4. Applied *-un-lft-identity_binary640.6

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

  5. Applied associate-*l*_binary640.6

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

  6. Simplified0.7

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

  7. Final simplification0.7

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

Reproduce

herbie shell --seed 2022097 
(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)))))