Average Error: 24.0 → 7.8
Time: 27.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[y \cdot \frac{1}{\frac{a - t}{z - t}} - \left(\frac{x}{\frac{a - t}{z - t}} - x\right)\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
y \cdot \frac{1}{\frac{a - t}{z - t}} - \left(\frac{x}{\frac{a - t}{z - t}} - x\right)
double f(double x, double y, double z, double t, double a) {
        double r26648806 = x;
        double r26648807 = y;
        double r26648808 = r26648807 - r26648806;
        double r26648809 = z;
        double r26648810 = t;
        double r26648811 = r26648809 - r26648810;
        double r26648812 = r26648808 * r26648811;
        double r26648813 = a;
        double r26648814 = r26648813 - r26648810;
        double r26648815 = r26648812 / r26648814;
        double r26648816 = r26648806 + r26648815;
        return r26648816;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26648817 = y;
        double r26648818 = 1.0;
        double r26648819 = a;
        double r26648820 = t;
        double r26648821 = r26648819 - r26648820;
        double r26648822 = z;
        double r26648823 = r26648822 - r26648820;
        double r26648824 = r26648821 / r26648823;
        double r26648825 = r26648818 / r26648824;
        double r26648826 = r26648817 * r26648825;
        double r26648827 = x;
        double r26648828 = r26648827 / r26648824;
        double r26648829 = r26648828 - r26648827;
        double r26648830 = r26648826 - r26648829;
        return r26648830;
}

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
Target9.5
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 24.0

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

  2. Simplified12.0

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

  4. Applied clear-num12.1

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{z - t}}}, y - x, x\right)\]
  5. Using strategy rm

  6. Applied fma-udef12.1

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

  7. Simplified12.0

    \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x\]
  8. Using strategy rm

  9. Applied div-sub12.0

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

  10. Applied associate-+l-7.7

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

  12. Applied div-inv7.8

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

  13. Final simplification7.8

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"

  :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))))