Average Error: 25.0 → 11.0
Time: 5.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.9975742700347867 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;a \le -5.7590695335687623 \cdot 10^{-202}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{elif}\;a \le -2.51426370931477275 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{\frac{y - x}{a - t}}{\frac{1}{z - t}}\\ \mathbf{elif}\;a \le 1.82900585396431584 \cdot 10^{-137}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.9975742700347867 \cdot 10^{-153}:\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

\mathbf{elif}\;a \le -5.7590695335687623 \cdot 10^{-202}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{elif}\;a \le -2.51426370931477275 \cdot 10^{-256}:\\
\;\;\;\;x + \frac{\frac{y - x}{a - t}}{\frac{1}{z - t}}\\

\mathbf{elif}\;a \le 1.82900585396431584 \cdot 10^{-137}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + (((y - x) * (z - t)) / (a - t)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((a <= -1.9975742700347867e-153)) {
		VAR = (x + ((y - x) / ((a - t) * (1.0 / (z - t)))));
	} else {
		double VAR_1;
		if ((a <= -5.759069533568762e-202)) {
			VAR_1 = ((y + ((x * z) / t)) - ((z * y) / t));
		} else {
			double VAR_2;
			if ((a <= -2.5142637093147727e-256)) {
				VAR_2 = (x + (((y - x) / (a - t)) / (1.0 / (z - t))));
			} else {
				double VAR_3;
				if ((a <= 1.8290058539643158e-137)) {
					VAR_3 = ((y + ((x * z) / t)) - ((z * y) / t));
				} else {
					VAR_3 = (x + ((y - x) * ((z - t) / (a - t))));
				}
				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

Original25.0
Target9.6
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if a < -1.9975742700347867e-153

    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*9.6

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

    5. Applied div-inv9.6

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

    if -1.9975742700347867e-153 < a < -5.759069533568762e-202 or -2.5142637093147727e-256 < a < 1.8290058539643158e-137

    1. Initial program 28.7

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

    2. Taylor expanded around inf 13.6

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

    if -5.759069533568762e-202 < a < -2.5142637093147727e-256

    1. Initial program 29.4

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

    3. Applied associate-/l*20.3

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

    5. Applied div-inv20.4

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

    6. Applied associate-/r*27.0

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

    if 1.8290058539643158e-137 < a

    1. Initial program 23.9

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

    3. Applied *-un-lft-identity23.9

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

    4. Applied times-frac9.6

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

    5. Simplified9.6

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

  4. Final simplification11.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.9975742700347867 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;a \le -5.7590695335687623 \cdot 10^{-202}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{elif}\;a \le -2.51426370931477275 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{\frac{y - x}{a - t}}{\frac{1}{z - t}}\\ \mathbf{elif}\;a \le 1.82900585396431584 \cdot 10^{-137}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020106 
(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) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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