Average Error: 10.4 → 10.8
Time: 16.9s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - a \cdot z}{x - z \cdot y}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - a \cdot z}{x - z \cdot y}}
double f(double x, double y, double z, double t, double a) {
        double r34515186 = x;
        double r34515187 = y;
        double r34515188 = z;
        double r34515189 = r34515187 * r34515188;
        double r34515190 = r34515186 - r34515189;
        double r34515191 = t;
        double r34515192 = a;
        double r34515193 = r34515192 * r34515188;
        double r34515194 = r34515191 - r34515193;
        double r34515195 = r34515190 / r34515194;
        return r34515195;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r34515196 = 1.0;
        double r34515197 = t;
        double r34515198 = a;
        double r34515199 = z;
        double r34515200 = r34515198 * r34515199;
        double r34515201 = r34515197 - r34515200;
        double r34515202 = x;
        double r34515203 = y;
        double r34515204 = r34515199 * r34515203;
        double r34515205 = r34515202 - r34515204;
        double r34515206 = r34515201 / r34515205;
        double r34515207 = r34515196 / r34515206;
        return r34515207;
}

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

Original10.4
Target1.7
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  3. Applied clear-num10.8

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

  4. Final simplification10.8

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

Reproduce

herbie shell --seed 2019168 
(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))))