Average Error: 1.4 → 1.4
Time: 10.4s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{t}{a - t}\right)\right)\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{t}{a - t}\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r526362 = x;
        double r526363 = y;
        double r526364 = z;
        double r526365 = t;
        double r526366 = r526364 - r526365;
        double r526367 = a;
        double r526368 = r526367 - r526365;
        double r526369 = r526366 / r526368;
        double r526370 = r526363 * r526369;
        double r526371 = r526362 + r526370;
        return r526371;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r526372 = x;
        double r526373 = y;
        double r526374 = z;
        double r526375 = a;
        double r526376 = t;
        double r526377 = r526375 - r526376;
        double r526378 = r526374 / r526377;
        double r526379 = r526376 / r526377;
        double r526380 = expm1(r526379);
        double r526381 = log1p(r526380);
        double r526382 = r526378 - r526381;
        double r526383 = r526373 * r526382;
        double r526384 = r526372 + r526383;
        return r526384;
}

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

Original1.4
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.4

    \[x + y \cdot \frac{z - t}{a - t}\]
  2. Using strategy rm

  3. Applied div-sub1.4

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

  5. Applied log1p-expm1-u1.4

    \[\leadsto x + y \cdot \left(\frac{z}{a - t} - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{t}{a - t}\right)\right)}\right)\]

  6. Final simplification1.4

    \[\leadsto x + y \cdot \left(\frac{z}{a - t} - \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{t}{a - t}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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