Average Error: 10.8 → 10.8
Time: 1.0m
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r15134176 = x;
        double r15134177 = y;
        double r15134178 = z;
        double r15134179 = r15134177 * r15134178;
        double r15134180 = r15134176 - r15134179;
        double r15134181 = t;
        double r15134182 = a;
        double r15134183 = r15134182 * r15134178;
        double r15134184 = r15134181 - r15134183;
        double r15134185 = r15134180 / r15134184;
        return r15134185;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15134186 = x;
        double r15134187 = y;
        double r15134188 = z;
        double r15134189 = r15134187 * r15134188;
        double r15134190 = r15134186 - r15134189;
        double r15134191 = t;
        double r15134192 = a;
        double r15134193 = r15134192 * r15134188;
        double r15134194 = r15134191 - r15134193;
        double r15134195 = r15134190 / r15134194;
        return r15134195;
}

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

Original10.8
Target1.7
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied *-un-lft-identity10.8

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

  4. Applied associate-/r*10.8

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

  5. Simplified10.8

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

  6. Final simplification10.8

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

Reproduce

herbie shell --seed 2019200 +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)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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