Average Error: 10.5 → 1.6
Time: 8.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\left(y \cdot \frac{x}{z} - x\right) + \frac{1 \cdot x}{z}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\left(y \cdot \frac{x}{z} - x\right) + \frac{1 \cdot x}{z}
double f(double x, double y, double z) {
        double r785156 = x;
        double r785157 = y;
        double r785158 = z;
        double r785159 = r785157 - r785158;
        double r785160 = 1.0;
        double r785161 = r785159 + r785160;
        double r785162 = r785156 * r785161;
        double r785163 = r785162 / r785158;
        return r785163;
}
↓
double f(double x, double y, double z) {
        double r785164 = y;
        double r785165 = x;
        double r785166 = z;
        double r785167 = r785165 / r785166;
        double r785168 = r785164 * r785167;
        double r785169 = r785168 - r785165;
        double r785170 = 1.0;
        double r785171 = r785170 * r785165;
        double r785172 = r785171 / r785166;
        double r785173 = r785169 + r785172;
        return r785173;
}

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

Original10.5
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 10.5

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

  2. Taylor expanded around 0 3.9

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

  3. Simplified1.8

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

  5. Applied div-inv1.8

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

  6. Simplified1.6

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

  7. Final simplification1.6

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))