Average Error: 24.1 → 10.9
Time: 5.0s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.2351020962998769 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;a \le 2.21132819556242 \cdot 10^{-67}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \frac{y - x}{\frac{a - t}{\sqrt[3]{z - t}}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.2351020962998769 \cdot 10^{-171}:\\
\;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\

\mathbf{elif}\;a \le 2.21132819556242 \cdot 10^{-67}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((a <= -7.235102096299877e-171)) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (((double) (z - t)) * ((double) (1.0 / ((double) (a - t))))))))));
	} else {
		double VAR_1;
		if ((a <= 2.21132819556242e-67)) {
			VAR_1 = ((double) (((double) (y + ((double) (((double) (x * z)) / t)))) - ((double) (((double) (z * y)) / t))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (((double) cbrt(((double) (z - t)))) * ((double) cbrt(((double) (z - t)))))) * ((double) (((double) (y - x)) / ((double) (((double) (a - t)) / ((double) cbrt(((double) (z - t))))))))))));
		}
		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

Original24.1
Target9.0
Herbie10.9
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -7.2351020962998769e-171

    1. Initial program 23.3

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

    3. Applied *-un-lft-identity23.3

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

    4. Applied times-frac9.6

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

    5. Simplified9.6

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

    7. Applied div-inv9.6

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

    if -7.2351020962998769e-171 < a < 2.21132819556242e-67

    1. Initial program 28.1

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

    2. Taylor expanded around inf 15.8

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

    if 2.21132819556242e-67 < a

    1. Initial program 21.8

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

    3. Applied associate-/l*7.4

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

    5. Applied add-cube-cbrt7.9

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

    6. Applied *-un-lft-identity7.9

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

    7. Applied times-frac7.9

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

    8. Applied *-un-lft-identity7.9

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

    9. Applied times-frac8.4

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

    10. Simplified8.4

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

  4. Final simplification10.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.2351020962998769 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;a \le 2.21132819556242 \cdot 10^{-67}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \frac{y - x}{\frac{a - t}{\sqrt[3]{z - t}}}\\ \end{array}\]

Reproduce

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

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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