Average Error: 10.9 → 11.0
Time: 3.8s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r723974 = x;
        double r723975 = y;
        double r723976 = z;
        double r723977 = r723975 * r723976;
        double r723978 = r723974 - r723977;
        double r723979 = t;
        double r723980 = a;
        double r723981 = r723980 * r723976;
        double r723982 = r723979 - r723981;
        double r723983 = r723978 / r723982;
        return r723983;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r723984 = x;
        double r723985 = y;
        double r723986 = z;
        double r723987 = r723985 * r723986;
        double r723988 = r723984 - r723987;
        double r723989 = 1.0;
        double r723990 = t;
        double r723991 = a;
        double r723992 = r723991 * r723986;
        double r723993 = r723990 - r723992;
        double r723994 = r723989 / r723993;
        double r723995 = r723988 * r723994;
        return r723995;
}

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

Original10.9
Target1.8
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.9

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

  3. Applied div-inv11.0

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

  4. Final simplification11.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344) (- (/ 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))))