Average Error: 1.9 → 2.1
Time: 11.4s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\left(\frac{1}{\frac{z - y}{x}} - \frac{y}{z - y}\right) \cdot t\]
\frac{x - y}{z - y} \cdot t
↓
\left(\frac{1}{\frac{z - y}{x}} - \frac{y}{z - y}\right) \cdot t
double f(double x, double y, double z, double t) {
        double r306484 = x;
        double r306485 = y;
        double r306486 = r306484 - r306485;
        double r306487 = z;
        double r306488 = r306487 - r306485;
        double r306489 = r306486 / r306488;
        double r306490 = t;
        double r306491 = r306489 * r306490;
        return r306491;
}
↓
double f(double x, double y, double z, double t) {
        double r306492 = 1.0;
        double r306493 = z;
        double r306494 = y;
        double r306495 = r306493 - r306494;
        double r306496 = x;
        double r306497 = r306495 / r306496;
        double r306498 = r306492 / r306497;
        double r306499 = r306494 / r306495;
        double r306500 = r306498 - r306499;
        double r306501 = t;
        double r306502 = r306500 * r306501;
        return r306502;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.9
Target2.0
Herbie2.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 1.9

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

  3. Applied div-sub1.9

    \[\leadsto \color{blue}{\left(\frac{x}{z - y} - \frac{y}{z - y}\right)} \cdot t\]
  4. Using strategy rm

  5. Applied clear-num2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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