Average Error: 0.7 → 0.7
Time: 7.6s
Precision: binary64
Cost: 20160
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{y - t}\]
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

Alternatives

Alternative 1
Error1.2
Cost704
\[1 - \frac{\frac{x}{y - z}}{y - t}\]
Alternative 2
Error5.7
Cost904
\[\begin{array}{l} \mathbf{if}\;z \leq -4.19096472920461 \cdot 10^{-118} \lor \neg \left(z \leq 8.136291538909425 \cdot 10^{-138}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array}\]
Alternative 3
Error5.2
Cost904
\[\begin{array}{l} \mathbf{if}\;z \leq -1.721968569026964 \cdot 10^{-87} \lor \neg \left(z \leq 7.187023508950631 \cdot 10^{-115}\right):\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array}\]
Alternative 4
Error5.1
Cost904
\[\begin{array}{l} \mathbf{if}\;t \leq -1.67938791701375 \cdot 10^{-25} \lor \neg \left(t \leq 5.977864496253995 \cdot 10^{-07}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array}\]
Alternative 5
Error7.9
Cost1218
\[\begin{array}{l} \mathbf{if}\;y \leq -181695747888231.47:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.184674480054839 \cdot 10^{-10}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 6
Error10.0
Cost1090
\[\begin{array}{l} \mathbf{if}\;y \leq -5.6725229094671797 \cdot 10^{-95}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6208172435325529 \cdot 10^{-152}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 7
Error13.6
Cost64
\[1\]

Error

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_76150.9

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

  4. Applied times-frac_binary64_75860.7

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

  5. Simplified0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2021044 
(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)))))