Average Error: 24.2 → 9.7
Time: 4.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -5.11466826064621464 \cdot 10^{-284} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0\right):\\ \;\;\;\;\left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -5.11466826064621464 \cdot 10^{-284} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0\right):\\
\;\;\;\;\left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) + x\\

\mathbf{else}:\\
\;\;\;\;y\\

\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 ((((x + (((y - x) * (z - t)) / (a - t))) <= -5.1146682606462146e-284) || !((x + (((y - x) * (z - t)) / (a - t))) <= 0.0))) {
		VAR = ((((z - t) * (1.0 / (a - t))) * (y - x)) + x);
	} else {
		VAR = y;
	}
	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

Original24.2
Target9.5
Herbie9.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -5.1146682606462146e-284 or 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

    1. Initial program 20.7

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

    2. Simplified10.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied div-inv10.6

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y - x\right) \cdot \frac{1}{a - t}}, z - t, x\right)\]
    5. Using strategy rm

    6. Applied add-cube-cbrt11.3

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

    7. Applied associate-*r*11.3

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(y - x\right) \cdot \left(\sqrt[3]{\frac{1}{a - t}} \cdot \sqrt[3]{\frac{1}{a - t}}\right)\right) \cdot \sqrt[3]{\frac{1}{a - t}}}, z - t, x\right)\]
    8. Using strategy rm

    9. Applied fma-udef11.3

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

    10. Simplified7.1

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

    if -5.1146682606462146e-284 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

    1. Initial program 59.5

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

    2. Simplified59.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)}\]

    3. Taylor expanded around 0 36.5

      \[\leadsto \color{blue}{y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -5.11466826064621464 \cdot 10^{-284} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0\right):\\ \;\;\;\;\left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(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))))