Average Error: 24.4 → 12.0
Time: 12.1s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.81935027695448 \cdot 10^{-119}:\\ \;\;\;\;x + \left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{elif}\;a \le 8.27934573687776677 \cdot 10^{-263}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;a \le 3.2061056078539232 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y - z}{\sqrt{a - z}} \cdot \frac{t - x}{\sqrt{a - z}}\\ \mathbf{elif}\;a \le 1.30015053040573357 \cdot 10^{-97}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.81935027695448 \cdot 10^{-119}:\\
\;\;\;\;x + \left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\

\mathbf{elif}\;a \le 8.27934573687776677 \cdot 10^{-263}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\mathbf{elif}\;a \le 3.2061056078539232 \cdot 10^{-215}:\\
\;\;\;\;x + \frac{y - z}{\sqrt{a - z}} \cdot \frac{t - x}{\sqrt{a - z}}\\

\mathbf{elif}\;a \le 1.30015053040573357 \cdot 10^{-97}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) (y - z)) * ((double) (t - x)))) / ((double) (a - z))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((a <= -4.81935027695448e-119)) {
		VAR = ((double) (x + ((double) (((double) (((double) (((double) (y - z)) / ((double) (((double) cbrt(((double) (a - z)))) * ((double) cbrt(((double) (a - z)))))))) * ((double) (((double) (((double) cbrt(((double) (t - x)))) * ((double) cbrt(((double) (t - x)))))) / ((double) cbrt(((double) (((double) cbrt(((double) (a - z)))) * ((double) cbrt(((double) (a - z)))))))))))) * ((double) (((double) cbrt(((double) (t - x)))) / ((double) cbrt(((double) cbrt(((double) (a - z))))))))))));
	} else {
		double VAR_1;
		if ((a <= 8.279345736877767e-263)) {
			VAR_1 = ((double) (((double) (((double) (((double) (x * y)) / z)) + t)) - ((double) (((double) (t * y)) / z))));
		} else {
			double VAR_2;
			if ((a <= 3.206105607853923e-215)) {
				VAR_2 = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) sqrt(((double) (a - z)))))) * ((double) (((double) (t - x)) / ((double) sqrt(((double) (a - z))))))))));
			} else {
				double VAR_3;
				if ((a <= 1.3001505304057336e-97)) {
					VAR_3 = ((double) (((double) (((double) (((double) (x * y)) / z)) + t)) - ((double) (((double) (t * y)) / z))));
				} else {
					VAR_3 = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) (((double) cbrt(((double) (a - z)))) * ((double) cbrt(((double) (a - z)))))))) * ((double) (((double) (t - x)) / ((double) cbrt(((double) (a - z))))))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original24.4
Target12.4
Herbie12.0
\[\begin{array}{l} \mathbf{if}\;z \lt -1.25361310560950359 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if a < -4.81935027695448e-119

    1. Initial program 23.2

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

    3. Applied add-cube-cbrt23.5

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

    4. Applied times-frac9.8

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt9.8

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

    7. Applied cbrt-prod9.8

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

    8. Applied add-cube-cbrt10.0

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

    9. Applied times-frac10.0

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

    10. Applied associate-*r*9.5

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

    if -4.81935027695448e-119 < a < 8.27934573687776677e-263 or 3.2061056078539232e-215 < a < 1.30015053040573357e-97

    1. Initial program 29.3

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

    2. Taylor expanded around inf 16.0

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

    if 8.27934573687776677e-263 < a < 3.2061056078539232e-215

    1. Initial program 30.3

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

    3. Applied add-sqr-sqrt43.1

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

    4. Applied times-frac41.7

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

    if 1.30015053040573357e-97 < a

    1. Initial program 21.6

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

    3. Applied add-cube-cbrt22.0

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

    4. Applied times-frac8.6

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.81935027695448 \cdot 10^{-119}:\\ \;\;\;\;x + \left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{elif}\;a \le 8.27934573687776677 \cdot 10^{-263}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;a \le 3.2061056078539232 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y - z}{\sqrt{a - z}} \cdot \frac{t - x}{\sqrt{a - z}}\\ \mathbf{elif}\;a \le 1.30015053040573357 \cdot 10^{-97}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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