Average Error: 6.3 → 0.7
Time: 2.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -1.4573431335557925 \cdot 10^{306} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 5.1138413582887425 \cdot 10^{302}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -1.4573431335557925 \cdot 10^{306} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 5.1138413582887425 \cdot 10^{302}\right):\\
\;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (x + (((y - x) * z) / t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((x + (((y - x) * z) / t)) <= -1.4573431335557925e+306) || !((x + (((y - x) * z) / t)) <= 5.1138413582887425e+302))) {
		VAR = fma((y - x), (z / t), x);
	} else {
		VAR = (x + (((y - x) * z) / t));
	}
	return VAR;
}

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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -1.4573431335557925e+306 or 5.1138413582887425e+302 < (+ x (/ (* (- y x) z) t))

    1. Initial program 59.2

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

    2. Simplified2.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef2.1

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

    6. Applied div-inv2.2

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

    7. Applied associate-*l*0.6

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

    8. Simplified0.5

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

    10. Applied fma-def0.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)}\]

    if -1.4573431335557925e+306 < (+ x (/ (* (- y x) z) t)) < 5.1138413582887425e+302

    1. Initial program 0.8

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -1.4573431335557925 \cdot 10^{306} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 5.1138413582887425 \cdot 10^{302}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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