Average Error: 14.8 → 1.9
Time: 8.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.1216973775124759 \cdot 10^{253}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.58981900482305871 \cdot 10^{-298} \lor \neg \left(\frac{y}{z} \le 1.0873747502010816 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.1216973775124759 \cdot 10^{253}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le -1.58981900482305871 \cdot 10^{-298} \lor \neg \left(\frac{y}{z} \le 1.0873747502010816 \cdot 10^{-201}\right):\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r388564 = x;
        double r388565 = y;
        double r388566 = z;
        double r388567 = r388565 / r388566;
        double r388568 = t;
        double r388569 = r388567 * r388568;
        double r388570 = r388569 / r388568;
        double r388571 = r388564 * r388570;
        return r388571;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r388572 = y;
        double r388573 = z;
        double r388574 = r388572 / r388573;
        double r388575 = -2.121697377512476e+253;
        bool r388576 = r388574 <= r388575;
        double r388577 = x;
        double r388578 = r388573 / r388577;
        double r388579 = r388572 / r388578;
        double r388580 = -1.5898190048230587e-298;
        bool r388581 = r388574 <= r388580;
        double r388582 = 1.0873747502010816e-201;
        bool r388583 = r388574 <= r388582;
        double r388584 = !r388583;
        bool r388585 = r388581 || r388584;
        double r388586 = r388574 * r388577;
        double r388587 = 1.0;
        double r388588 = r388587 / r388573;
        double r388589 = r388572 * r388577;
        double r388590 = r388588 * r388589;
        double r388591 = r388585 ? r388586 : r388590;
        double r388592 = r388576 ? r388579 : r388591;
        return r388592;
}

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

Original14.8
Target1.7
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -2.121697377512476e+253

    1. Initial program 50.4

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified0.6

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
    3. Using strategy rm

    4. Applied associate-/l*0.3

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]

    if -2.121697377512476e+253 < (/ y z) < -1.5898190048230587e-298 or 1.0873747502010816e-201 < (/ y z)

    1. Initial program 12.1

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified8.4

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
    3. Using strategy rm

    4. Applied associate-/l*8.0

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
    5. Using strategy rm

    6. Applied associate-/r/2.5

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]

    if -1.5898190048230587e-298 < (/ y z) < 1.0873747502010816e-201

    1. Initial program 17.8

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified0.3

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
    3. Using strategy rm

    4. Applied associate-/l*0.3

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
    5. Using strategy rm

    6. Applied div-inv0.4

      \[\leadsto \frac{y}{\color{blue}{z \cdot \frac{1}{x}}}\]

    7. Applied *-un-lft-identity0.4

      \[\leadsto \frac{\color{blue}{1 \cdot y}}{z \cdot \frac{1}{x}}\]

    8. Applied times-frac0.4

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{y}{\frac{1}{x}}}\]

    9. Simplified0.4

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.1216973775124759 \cdot 10^{253}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.58981900482305871 \cdot 10^{-298} \lor \neg \left(\frac{y}{z} \le 1.0873747502010816 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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