Average Error: 0.7 → 0.7
Time: 9.6s
Precision: binary64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \left(\sqrt[3]{x} \cdot \frac{\sqrt[3]{x}}{y - z}\right) \cdot \frac{\sqrt[3]{x}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \left(\sqrt[3]{x} \cdot \frac{\sqrt[3]{x}}{y - z}\right) \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 0.7

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

  3. Applied add-cube-cbrt_binary64_14770.9

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

  4. Applied times-frac_binary64_14480.7

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

  5. Simplified0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2021176 
(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)))))