Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B

Average Error: 14.3 → 0.4

Time: 13.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.49778287371169 \cdot 10^{+261}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -7.858505420200056 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.366075407571311 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.0902183033222777 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r28689817 = x;
        double r28689818 = y;
        double r28689819 = z;
        double r28689820 = r28689818 / r28689819;
        double r28689821 = t;
        double r28689822 = r28689820 * r28689821;
        double r28689823 = r28689822 / r28689821;
        double r28689824 = r28689817 * r28689823;
        return r28689824;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r28689825 = y;
        double r28689826 = z;
        double r28689827 = r28689825 / r28689826;
        double r28689828 = -5.49778287371169e+261;
        bool r28689829 = r28689827 <= r28689828;
        double r28689830 = x;
        double r28689831 = r28689830 / r28689826;
        double r28689832 = r28689825 * r28689831;
        double r28689833 = -7.858505420200056e-207;
        bool r28689834 = r28689827 <= r28689833;
        double r28689835 = r28689827 * r28689830;
        double r28689836 = 9.366075407571311e-161;
        bool r28689837 = r28689827 <= r28689836;
        double r28689838 = r28689830 * r28689825;
        double r28689839 = r28689838 / r28689826;
        double r28689840 = 4.0902183033222777e+188;
        bool r28689841 = r28689827 <= r28689840;
        double r28689842 = r28689841 ? r28689835 : r28689832;
        double r28689843 = r28689837 ? r28689839 : r28689842;
        double r28689844 = r28689834 ? r28689835 : r28689843;
        double r28689845 = r28689829 ? r28689832 : r28689844;
        return r28689845;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.3
Target	1.7
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -5.49778287371169e+261 or 4.0902183033222777e+188 < (/ y z)

   1. Initial program 43.2

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

   2. Simplified 0.8

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

   if -5.49778287371169e+261 < (/ y z) < -7.858505420200056e-207 or 9.366075407571311e-161 < (/ y z) < 4.0902183033222777e+188

   1. Initial program 8.2

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

   2. Simplified 9.7

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

   4. Applied associate-*r/ 9.4

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

   6. Applied associate-/l* 9.7

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

   8. Applied associate-/r/ 0.2

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

   if -7.858505420200056e-207 < (/ y z) < 9.366075407571311e-161

   1. Initial program 17.0

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

   2. Simplified 0.8

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

   4. Applied associate-*r/ 0.7

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.49778287371169 \cdot 10^{+261}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -7.858505420200056 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.366075407571311 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.0902183033222777 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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)))