Average Error: 6.4 → 1.7
Time: 6.5s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.7909949964603828 \cdot 10^{-105}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x \le 3.9693728580724161 \cdot 10^{-120}:\\ \;\;\;\;x + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \frac{y - x}{\frac{t}{\sqrt[3]{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.7909949964603828 \cdot 10^{-105}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;x \le 3.9693728580724161 \cdot 10^{-120}:\\
\;\;\;\;x + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \frac{y - x}{\frac{t}{\sqrt[3]{z}}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * z)) / t))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((x <= -3.790994996460383e-105)) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
	} else {
		double VAR_1;
		if ((x <= 3.969372858072416e-120)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) cbrt(z)) * ((double) cbrt(z)))) * ((double) (((double) (y - x)) / ((double) (t / ((double) cbrt(z))))))))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (y - x)) / ((double) (t / z))))));
		}
		VAR = VAR_1;
	}
	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

Original6.4
Target2.2
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -3.7909949964603828e-105

    1. Initial program 6.9

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

    3. Applied *-un-lft-identity6.9

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -3.7909949964603828e-105 < x < 3.9693728580724161e-120

    1. Initial program 5.2

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

    3. Applied associate-/l*5.3

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

    5. Applied add-cube-cbrt6.0

      \[\leadsto x + \frac{y - x}{\frac{t}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}}\]

    6. Applied *-un-lft-identity6.0

      \[\leadsto x + \frac{y - x}{\frac{\color{blue}{1 \cdot t}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    7. Applied times-frac6.0

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{t}{\sqrt[3]{z}}}}\]

    8. Applied *-un-lft-identity6.0

      \[\leadsto x + \frac{\color{blue}{1 \cdot \left(y - x\right)}}{\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{t}{\sqrt[3]{z}}}\]

    9. Applied times-frac3.7

      \[\leadsto x + \color{blue}{\frac{1}{\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \frac{y - x}{\frac{t}{\sqrt[3]{z}}}}\]

    10. Simplified3.6

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \frac{y - x}{\frac{t}{\sqrt[3]{z}}}\]

    if 3.9693728580724161e-120 < x

    1. Initial program 7.4

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

    3. Applied associate-/l*0.6

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.7909949964603828 \cdot 10^{-105}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x \le 3.9693728580724161 \cdot 10^{-120}:\\ \;\;\;\;x + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \frac{y - x}{\frac{t}{\sqrt[3]{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020164 
(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)))