Average Error: 10.0 → 10.4
Time: 18.8s
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 r34793457 = x;
        double r34793458 = y;
        double r34793459 = z;
        double r34793460 = r34793458 * r34793459;
        double r34793461 = r34793457 - r34793460;
        double r34793462 = t;
        double r34793463 = a;
        double r34793464 = r34793463 * r34793459;
        double r34793465 = r34793462 - r34793464;
        double r34793466 = r34793461 / r34793465;
        return r34793466;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r34793467 = 1.0;
        double r34793468 = t;
        double r34793469 = a;
        double r34793470 = z;
        double r34793471 = r34793469 * r34793470;
        double r34793472 = r34793468 - r34793471;
        double r34793473 = x;
        double r34793474 = y;
        double r34793475 = r34793470 * r34793474;
        double r34793476 = r34793473 - r34793475;
        double r34793477 = r34793472 / r34793476;
        double r34793478 = r34793467 / r34793477;
        return r34793478;
}

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

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. Final simplification10.4

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

Reproduce

herbie shell --seed 2019164 
(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))))