Average Error: 24.0 → 11.3
Time: 5.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\left(y - x\right) \cdot \frac{z - t}{a - t} + x\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\left(y - x\right) \cdot \frac{z - t}{a - t} + x
double f(double x, double y, double z, double t, double a) {
        double r573816 = x;
        double r573817 = y;
        double r573818 = r573817 - r573816;
        double r573819 = z;
        double r573820 = t;
        double r573821 = r573819 - r573820;
        double r573822 = r573818 * r573821;
        double r573823 = a;
        double r573824 = r573823 - r573820;
        double r573825 = r573822 / r573824;
        double r573826 = r573816 + r573825;
        return r573826;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r573827 = y;
        double r573828 = x;
        double r573829 = r573827 - r573828;
        double r573830 = z;
        double r573831 = t;
        double r573832 = r573830 - r573831;
        double r573833 = a;
        double r573834 = r573833 - r573831;
        double r573835 = r573832 / r573834;
        double r573836 = r573829 * r573835;
        double r573837 = r573836 + r573828;
        return r573837;
}

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

Original24.0
Target9.0
Herbie11.3
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 24.0

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

  2. Simplified14.3

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

  4. Applied fma-udef14.4

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

  6. Applied div-inv14.4

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

  8. Applied associate-*l*11.4

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

  9. Simplified11.3

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

  10. Final simplification11.3

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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