Average Error: 9.7 → 0.3
Time: 18.8s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right) + x\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 6.435234859789346 \cdot 10^{+285}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right) + x\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\
\;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right) + x\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 6.435234859789346 \cdot 10^{+285}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r16697106 = x;
        double r16697107 = y;
        double r16697108 = z;
        double r16697109 = r16697107 - r16697108;
        double r16697110 = t;
        double r16697111 = r16697109 * r16697110;
        double r16697112 = a;
        double r16697113 = r16697112 - r16697108;
        double r16697114 = r16697111 / r16697113;
        double r16697115 = r16697106 + r16697114;
        return r16697115;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r16697116 = y;
        double r16697117 = z;
        double r16697118 = r16697116 - r16697117;
        double r16697119 = t;
        double r16697120 = r16697118 * r16697119;
        double r16697121 = a;
        double r16697122 = r16697121 - r16697117;
        double r16697123 = r16697120 / r16697122;
        double r16697124 = -inf.0;
        bool r16697125 = r16697123 <= r16697124;
        double r16697126 = r16697119 / r16697122;
        double r16697127 = r16697126 * r16697118;
        double r16697128 = x;
        double r16697129 = r16697127 + r16697128;
        double r16697130 = 6.435234859789346e+285;
        bool r16697131 = r16697123 <= r16697130;
        double r16697132 = r16697123 + r16697128;
        double r16697133 = r16697131 ? r16697132 : r16697129;
        double r16697134 = r16697125 ? r16697129 : r16697133;
        return r16697134;
}

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

Original9.7
Target0.6
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 6.435234859789346e+285 < (/ (* (- y z) t) (- a z))

    1. Initial program 58.6

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

    3. Applied *-un-lft-identity58.6

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 6.435234859789346e+285

    1. Initial program 0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right) + x\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 6.435234859789346 \cdot 10^{+285}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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