Average Error: 6.3 → 1.4
Time: 3.3s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -4.677111126960139 \cdot 10^{+291} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 5.076033290164541 \cdot 10^{+285}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -4.677111126960139 \cdot 10^{+291} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 5.076033290164541 \cdot 10^{+285}\right):\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ x (/ (* (- y x) z) t)) -4.677111126960139e+291)
         (not (<= (+ x (/ (* (- y x) z) t)) 5.076033290164541e+285)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ (* (- y x) z) t))))
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (((double) (y - x)) * z)) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (((((double) (x + (((double) (((double) (y - x)) * z)) / t))) <= -4.677111126960139e+291) || !(((double) (x + (((double) (((double) (y - x)) * z)) / t))) <= 5.076033290164541e+285))) {
		tmp = ((double) (x + ((double) (z * (((double) (y - x)) / t)))));
	} else {
		tmp = ((double) (x + (((double) (((double) (y - x)) * z)) / t)));
	}
	return tmp;
}

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
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -4.6771111269601391e291 or 5.07603329016454078e285 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

    1. Initial program 45.6

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

    3. Applied associate-/l*_binary642.3

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

    5. Applied associate-/r/_binary646.4

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

    if -4.6771111269601391e291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 5.07603329016454078e285

    1. Initial program 0.7

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -4.677111126960139 \cdot 10^{+291} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 5.076033290164541 \cdot 10^{+285}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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)))