Average Error: 0.7 → 0.7
Time: 10.1s
Precision: binary64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y - z}{\frac{\sqrt[3]{x}}{\left(y - t\right) + t \cdot 0}}} \]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y - z}{\frac{\sqrt[3]{x}}{\left(y - t\right) + t \cdot 0}}}

(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) (* t 0.0)))))))
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) + (t * 0.0)))));
}

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 *-un-lft-identity_binary640.7

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

  3. Applied add-cube-cbrt_binary640.8

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

  4. Applied prod-diff_binary640.8

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

  5. Applied distribute-rgt-in_binary640.8

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

  6. Applied add-cube-cbrt_binary641.0

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

  7. Applied associate-/l*_binary641.0

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

  8. Simplified0.7

    \[\leadsto 1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\color{blue}{\frac{y - z}{\frac{\sqrt[3]{x}}{\left(y - t\right) + t \cdot 0}}}} \]

  9. Final simplification0.7

    \[\leadsto 1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y - z}{\frac{\sqrt[3]{x}}{\left(y - t\right) + t \cdot 0}}} \]

Reproduce

herbie shell --seed 2022077 
(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)))))