Average Error: 24.1 → 7.5
Time: 28.6s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{y}{\frac{a - t}{z - t}} - \left(\frac{x}{\frac{a - t}{z - t}} - x\right)\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\frac{y}{\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 r22077544 = x;
        double r22077545 = y;
        double r22077546 = r22077545 - r22077544;
        double r22077547 = z;
        double r22077548 = t;
        double r22077549 = r22077547 - r22077548;
        double r22077550 = r22077546 * r22077549;
        double r22077551 = a;
        double r22077552 = r22077551 - r22077548;
        double r22077553 = r22077550 / r22077552;
        double r22077554 = r22077544 + r22077553;
        return r22077554;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r22077555 = y;
        double r22077556 = a;
        double r22077557 = t;
        double r22077558 = r22077556 - r22077557;
        double r22077559 = z;
        double r22077560 = r22077559 - r22077557;
        double r22077561 = r22077558 / r22077560;
        double r22077562 = r22077555 / r22077561;
        double r22077563 = x;
        double r22077564 = r22077563 / r22077561;
        double r22077565 = r22077564 - r22077563;
        double r22077566 = r22077562 - r22077565;
        return r22077566;
}

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

Original24.1
Target9.5
Herbie7.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 24.1

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

  2. Simplified11.8

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

  4. Applied clear-num11.9

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

  6. Applied fma-udef11.9

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

  7. Simplified11.8

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

  9. Applied div-sub11.8

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

  10. Applied associate-+l-7.5

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

  11. Final simplification7.5

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

Reproduce

herbie shell --seed 2019172 +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) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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