Average Error: 10.0 → 10.0
Time: 23.1s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - z \cdot a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - z \cdot a}
double f(double x, double y, double z, double t, double a) {
        double r34319128 = x;
        double r34319129 = y;
        double r34319130 = z;
        double r34319131 = r34319129 * r34319130;
        double r34319132 = r34319128 - r34319131;
        double r34319133 = t;
        double r34319134 = a;
        double r34319135 = r34319134 * r34319130;
        double r34319136 = r34319133 - r34319135;
        double r34319137 = r34319132 / r34319136;
        return r34319137;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r34319138 = x;
        double r34319139 = y;
        double r34319140 = z;
        double r34319141 = r34319139 * r34319140;
        double r34319142 = r34319138 - r34319141;
        double r34319143 = t;
        double r34319144 = a;
        double r34319145 = r34319140 * r34319144;
        double r34319146 = r34319143 - r34319145;
        double r34319147 = r34319142 / r34319146;
        return r34319147;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.0
Target1.8
Herbie10.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.0

    \[\frac{x - y \cdot z}{t - a \cdot z}\]
  2. Using strategy rm

  3. Applied clear-num10.4

    \[\leadsto \color{blue}{\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity10.4

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

  6. Applied *-un-lft-identity10.4

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

  7. Applied times-frac10.4

    \[\leadsto \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{t - a \cdot z}{x - y \cdot z}}}\]

  8. Applied add-cube-cbrt10.4

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{t - a \cdot z}{x - y \cdot z}}\]

  9. Applied times-frac10.4

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{t - a \cdot z}{x - y \cdot z}}}\]

  10. Simplified10.4

    \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{t - a \cdot z}{x - y \cdot z}}\]

  11. Simplified10.0

    \[\leadsto 1 \cdot \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}}\]

  12. Final simplification10.0

    \[\leadsto \frac{x - y \cdot z}{t - z \cdot a}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))