Average Error: 15.0 → 11.9
Time: 23.1s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\left(t - x\right) \cdot \frac{y - z}{a - z} + x\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\left(t - x\right) \cdot \frac{y - z}{a - z} + x
double f(double x, double y, double z, double t, double a) {
        double r90715 = x;
        double r90716 = y;
        double r90717 = z;
        double r90718 = r90716 - r90717;
        double r90719 = t;
        double r90720 = r90719 - r90715;
        double r90721 = a;
        double r90722 = r90721 - r90717;
        double r90723 = r90720 / r90722;
        double r90724 = r90718 * r90723;
        double r90725 = r90715 + r90724;
        return r90725;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r90726 = t;
        double r90727 = x;
        double r90728 = r90726 - r90727;
        double r90729 = y;
        double r90730 = z;
        double r90731 = r90729 - r90730;
        double r90732 = a;
        double r90733 = r90732 - r90730;
        double r90734 = r90731 / r90733;
        double r90735 = r90728 * r90734;
        double r90736 = r90735 + r90727;
        return r90736;
}

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

Derivation

  1. Initial program 15.0

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

  2. Simplified14.9

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef15.0

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

  6. Applied div-inv15.1

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

  7. Applied associate-*l*11.9

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

  8. Simplified11.9

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

  9. Final simplification11.9

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))