Average Error: 0.8 → 0.9
Time: 9.5s
Precision: binary64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[1 - x \cdot \frac{1}{\left(y - t\right) \cdot \left(y - z\right)} \]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - x \cdot \frac{1}{\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 (/ 1.0 (* (- 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 * (1.0 / ((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 0.8

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

  3. Applied div-inv_binary640.9

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

  4. Simplified0.9

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

  6. Applied add-sqr-sqrt_binary640.9

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

  7. Applied associate-/l*_binary640.9

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

  8. Simplified0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2021207 
(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)))))