Average Error: 10.2 → 1.6
Time: 3.7s
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 r687198 = x;
        double r687199 = y;
        double r687200 = z;
        double r687201 = r687199 - r687200;
        double r687202 = 1.0;
        double r687203 = r687201 + r687202;
        double r687204 = r687198 * r687203;
        double r687205 = r687204 / r687200;
        return r687205;
}
↓
double f(double x, double y, double z) {
        double r687206 = x;
        double r687207 = z;
        double r687208 = r687206 / r687207;
        double r687209 = 1.0;
        double r687210 = y;
        double r687211 = r687209 + r687210;
        double r687212 = r687208 * r687211;
        double r687213 = r687212 - r687206;
        return r687213;
}

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

Original10.2
Target0.5
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 10.2

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

  3. Applied associate-/l*3.3

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

  4. Taylor expanded around 0 3.6

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

  5. Taylor expanded around 0 3.6

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

  6. Simplified1.6

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

  7. Final simplification1.6

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

Reproduce

herbie shell --seed 2019354 
(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))