Average Error: 10.1 → 1.5
Time: 2.1s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{x}{z} \cdot \left(1 + y\right) - x\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{x}{z} \cdot \left(1 + y\right) - x
double f(double x, double y, double z) {
        double r712063 = x;
        double r712064 = y;
        double r712065 = z;
        double r712066 = r712064 - r712065;
        double r712067 = 1.0;
        double r712068 = r712066 + r712067;
        double r712069 = r712063 * r712068;
        double r712070 = r712069 / r712065;
        return r712070;
}
↓
double f(double x, double y, double z) {
        double r712071 = x;
        double r712072 = z;
        double r712073 = r712071 / r712072;
        double r712074 = 1.0;
        double r712075 = y;
        double r712076 = r712074 + r712075;
        double r712077 = r712073 * r712076;
        double r712078 = r712077 - r712071;
        return r712078;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.1
Target0.4
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 10.1

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

  2. Taylor expanded around 0 3.8

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

  3. Taylor expanded around 0 3.8

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

  4. Simplified1.5

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

  5. Final simplification1.5

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

Reproduce

herbie shell --seed 2020020 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))