Average Error: 2.1 → 2.1
Time: 6.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{z - t}{\frac{y}{x}} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{z - t}{\frac{y}{x}} + t
double f(double x, double y, double z, double t) {
        double r312492 = x;
        double r312493 = y;
        double r312494 = r312492 / r312493;
        double r312495 = z;
        double r312496 = t;
        double r312497 = r312495 - r312496;
        double r312498 = r312494 * r312497;
        double r312499 = r312498 + r312496;
        return r312499;
}
↓
double f(double x, double y, double z, double t) {
        double r312500 = z;
        double r312501 = t;
        double r312502 = r312500 - r312501;
        double r312503 = y;
        double r312504 = x;
        double r312505 = r312503 / r312504;
        double r312506 = r312502 / r312505;
        double r312507 = r312506 + r312501;
        return r312507;
}

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

Original2.1
Target2.4
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.1

    \[\frac{x}{y} \cdot \left(z - t\right) + t\]
  2. Using strategy rm

  3. Applied associate-*l/6.3

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

  5. Applied clear-num6.3

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x \cdot \left(z - t\right)}}} + t\]
  6. Using strategy rm

  7. Applied associate-/r*2.1

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

  8. Taylor expanded around 0 6.3

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

  9. Simplified2.1

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

  10. Final simplification2.1

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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