Average Error: 6.3 → 1.7
Time: 14.4s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.363664958439672667278554160764100153889 \cdot 10^{69}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t \le 7.486542709900388243398285213925344255536 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.363664958439672667278554160764100153889 \cdot 10^{69}:\\
\;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\

\mathbf{elif}\;t \le 7.486542709900388243398285213925344255536 \cdot 10^{-169}:\\
\;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r19902748 = x;
        double r19902749 = y;
        double r19902750 = z;
        double r19902751 = r19902750 - r19902748;
        double r19902752 = r19902749 * r19902751;
        double r19902753 = t;
        double r19902754 = r19902752 / r19902753;
        double r19902755 = r19902748 + r19902754;
        return r19902755;
}
↓
double f(double x, double y, double z, double t) {
        double r19902756 = t;
        double r19902757 = -8.363664958439673e+69;
        bool r19902758 = r19902756 <= r19902757;
        double r19902759 = x;
        double r19902760 = z;
        double r19902761 = r19902760 - r19902759;
        double r19902762 = y;
        double r19902763 = r19902762 / r19902756;
        double r19902764 = r19902761 * r19902763;
        double r19902765 = r19902759 + r19902764;
        double r19902766 = 7.486542709900388e-169;
        bool r19902767 = r19902756 <= r19902766;
        double r19902768 = r19902761 * r19902762;
        double r19902769 = r19902768 / r19902756;
        double r19902770 = r19902759 + r19902769;
        double r19902771 = r19902767 ? r19902770 : r19902765;
        double r19902772 = r19902758 ? r19902765 : r19902771;
        return r19902772;
}

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

Original6.3
Target2.0
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -8.363664958439673e+69 or 7.486542709900388e-169 < t

    1. Initial program 8.1

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

    3. Applied associate-/l*2.4

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]
    4. Using strategy rm

    5. Applied associate-/r/1.3

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

    if -8.363664958439673e+69 < t < 7.486542709900388e-169

    1. Initial program 2.7

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.363664958439672667278554160764100153889 \cdot 10^{69}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t \le 7.486542709900388243398285213925344255536 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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