Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[1 \cdot z + x \cdot \left(y - z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
1 \cdot z + x \cdot \left(y - z\right)
double f(double x, double y, double z) {
        double r150375 = x;
        double r150376 = y;
        double r150377 = r150375 * r150376;
        double r150378 = 1.0;
        double r150379 = r150378 - r150375;
        double r150380 = z;
        double r150381 = r150379 * r150380;
        double r150382 = r150377 + r150381;
        return r150382;
}
↓
double f(double x, double y, double z) {
        double r150383 = 1.0;
        double r150384 = z;
        double r150385 = r150383 * r150384;
        double r150386 = x;
        double r150387 = y;
        double r150388 = r150387 - r150384;
        double r150389 = r150386 * r150388;
        double r150390 = r150385 + r150389;
        return r150390;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt31.7

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

  4. Applied associate-*r*31.7

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

  5. Simplified31.7

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

  6. Taylor expanded around 0 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))