Average Error: 24.0 → 7.8
Time: 26.0s
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 r27325664 = x;
        double r27325665 = y;
        double r27325666 = r27325665 - r27325664;
        double r27325667 = z;
        double r27325668 = t;
        double r27325669 = r27325667 - r27325668;
        double r27325670 = r27325666 * r27325669;
        double r27325671 = a;
        double r27325672 = r27325671 - r27325668;
        double r27325673 = r27325670 / r27325672;
        double r27325674 = r27325664 + r27325673;
        return r27325674;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27325675 = y;
        double r27325676 = 1.0;
        double r27325677 = a;
        double r27325678 = t;
        double r27325679 = r27325677 - r27325678;
        double r27325680 = z;
        double r27325681 = r27325680 - r27325678;
        double r27325682 = r27325679 / r27325681;
        double r27325683 = r27325676 / r27325682;
        double r27325684 = r27325675 * r27325683;
        double r27325685 = x;
        double r27325686 = r27325685 / r27325682;
        double r27325687 = r27325686 - r27325685;
        double r27325688 = r27325684 - r27325687;
        return r27325688;
}

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))))