Average Error: 24.1 → 10.3
Time: 5.9s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -1.5436284696018093 \cdot 10^{-203}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;a \leq 9.208735455584218 \cdot 10^{-245}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{a - t}}{z - t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \leq -1.5436284696018093 \cdot 10^{-203}:\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

\mathbf{elif}\;a \leq 9.208735455584218 \cdot 10^{-245}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5436284696018093e-203)
   (+ x (/ (- y x) (* (- a t) (/ 1.0 (- z t)))))
   (if (<= a 9.208735455584218e-245)
     (- (+ y (/ (* x z) t)) (/ (* y z) t))
     (+
      x
      (*
       (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))
       (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t))))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5436284696018093e-203)) {
		tmp = ((double) (x + (((double) (y - x)) / ((double) (((double) (a - t)) * (1.0 / ((double) (z - t))))))));
	} else {
		double tmp_1;
		if ((a <= 9.208735455584218e-245)) {
			tmp_1 = ((double) (((double) (y + (((double) (x * z)) / t))) - (((double) (y * z)) / t)));
		} else {
			tmp_1 = ((double) (x + ((double) ((((double) (((double) cbrt(((double) (y - x)))) * ((double) cbrt(((double) (y - x)))))) / ((double) (((double) cbrt(((double) (a - t)))) * ((double) cbrt(((double) (a - t))))))) * (((double) cbrt(((double) (y - x)))) / (((double) cbrt(((double) (a - t)))) / ((double) (z - t))))))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

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
Target9.5
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.54362846960180928e-203

    1. Initial program 23.7

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

    3. Applied associate-/l*_binary6410.6

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

    5. Applied div-inv_binary6410.7

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

    if -1.54362846960180928e-203 < a < 9.2087354555842178e-245

    1. Initial program 30.1

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

    2. Taylor expanded around inf 8.5

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

    3. Simplified8.5

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

    if 9.2087354555842178e-245 < a

    1. Initial program 22.8

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

    3. Applied associate-/l*_binary6410.0

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

    5. Applied *-un-lft-identity_binary6410.0

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

    6. Applied add-cube-cbrt_binary6410.6

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

    7. Applied times-frac_binary6410.6

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

    8. Applied add-cube-cbrt_binary6410.8

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

    9. Applied times-frac_binary6410.5

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

    10. Simplified10.5

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5436284696018093 \cdot 10^{-203}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;a \leq 9.208735455584218 \cdot 10^{-245}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{a - t}}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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))))