Average Error: 10.1 → 1.6
Time: 8.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{x}{z} \cdot \left(y + 1\right) - x\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{x}{z} \cdot \left(y + 1\right) - x
double f(double x, double y, double z) {
        double r545088 = x;
        double r545089 = y;
        double r545090 = z;
        double r545091 = r545089 - r545090;
        double r545092 = 1.0;
        double r545093 = r545091 + r545092;
        double r545094 = r545088 * r545093;
        double r545095 = r545094 / r545090;
        return r545095;
}
↓
double f(double x, double y, double z) {
        double r545096 = x;
        double r545097 = z;
        double r545098 = r545096 / r545097;
        double r545099 = y;
        double r545100 = 1.0;
        double r545101 = r545099 + r545100;
        double r545102 = r545098 * r545101;
        double r545103 = r545102 - r545096;
        return r545103;
}

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
Target0.5
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 10.1

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

  2. Simplified9.1

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

  4. Applied div-inv9.2

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

  5. Applied associate-*l*3.5

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

  6. Simplified3.4

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

  7. Taylor expanded around 0 3.5

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

  8. Simplified1.8

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

  9. Taylor expanded around 0 3.5

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

  10. Simplified1.6

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

  11. Final simplification1.6

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

Reproduce

herbie shell --seed 2019195 
(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))