Average Error: 2.0 → 2.5
Time: 4.5s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -33659643301491531166215560935505920 \lor \neg \left(t \le 1.625406329571911990929648461559105916592 \cdot 10^{-217}\right):\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -33659643301491531166215560935505920 \lor \neg \left(t \le 1.625406329571911990929648461559105916592 \cdot 10^{-217}\right):\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r540291 = x;
        double r540292 = y;
        double r540293 = r540292 - r540291;
        double r540294 = z;
        double r540295 = t;
        double r540296 = r540294 / r540295;
        double r540297 = r540293 * r540296;
        double r540298 = r540291 + r540297;
        return r540298;
}
↓
double f(double x, double y, double z, double t) {
        double r540299 = t;
        double r540300 = -3.365964330149153e+34;
        bool r540301 = r540299 <= r540300;
        double r540302 = 1.625406329571912e-217;
        bool r540303 = r540299 <= r540302;
        double r540304 = !r540303;
        bool r540305 = r540301 || r540304;
        double r540306 = x;
        double r540307 = y;
        double r540308 = r540307 - r540306;
        double r540309 = cbrt(r540299);
        double r540310 = r540309 * r540309;
        double r540311 = r540308 / r540310;
        double r540312 = z;
        double r540313 = r540312 / r540309;
        double r540314 = r540311 * r540313;
        double r540315 = r540306 + r540314;
        double r540316 = r540308 * r540312;
        double r540317 = 1.0;
        double r540318 = r540317 / r540299;
        double r540319 = r540316 * r540318;
        double r540320 = r540306 + r540319;
        double r540321 = r540305 ? r540315 : r540320;
        return r540321;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target2.1
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.365964330149153e+34 or 1.625406329571912e-217 < t

    1. Initial program 1.5

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt1.9

      \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\]

    4. Applied *-un-lft-identity1.9

      \[\leadsto x + \left(y - x\right) \cdot \frac{\color{blue}{1 \cdot z}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}\]

    5. Applied times-frac1.9

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)}\]

    6. Applied associate-*r*2.6

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{z}{\sqrt[3]{t}}}\]

    7. Simplified2.6

      \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\]

    if -3.365964330149153e+34 < t < 1.625406329571912e-217

    1. Initial program 3.4

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]
    2. Using strategy rm

    3. Applied div-inv3.5

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

    4. Applied associate-*r*2.0

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -33659643301491531166215560935505920 \lor \neg \left(t \le 1.625406329571911990929648461559105916592 \cdot 10^{-217}\right):\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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