Average Error: 23.9 → 10.4
Time: 6.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -2.6650803551403255 \cdot 10^{-282} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 1.36358456559634 \cdot 10^{-259}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}, \frac{\left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x}}\right) \cdot \sqrt[3]{\sqrt[3]{y - x}}}{\sqrt[3]{a - t}} \cdot \left(z - t\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]
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 -2.6650803551403255 \cdot 10^{-282} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 1.36358456559634 \cdot 10^{-259}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}, \frac{\left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x}}\right) \cdot \sqrt[3]{\sqrt[3]{y - x}}}{\sqrt[3]{a - t}} \cdot \left(z - t\right), x\right)\\

\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))) <= -2.6650803551403255e-282) || !((x + (((y - x) * (z - t)) / (a - t))) <= 1.3635845655963375e-259))) {
		VAR = fma(((cbrt((y - x)) * cbrt((y - x))) / (cbrt((a - t)) * cbrt((a - t)))), ((((cbrt(cbrt((y - x))) * cbrt(cbrt((y - x)))) * cbrt(cbrt((y - x)))) / cbrt((a - t))) * (z - t)), 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

Original23.9
Target9.3
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -2.6650803551403255e-282 or 1.3635845655963375e-259 < (+ 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. Simplified10.4

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

    4. Applied fma-udef10.4

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

    6. Applied add-cube-cbrt11.0

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

    7. Applied add-cube-cbrt11.2

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

    8. Applied times-frac11.2

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

    9. Applied associate-*l*7.5

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

    11. Applied fma-def7.5

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

    13. Applied add-cube-cbrt7.6

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

    if -2.6650803551403255e-282 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 1.3635845655963375e-259

    1. Initial program 55.2

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

    2. Simplified55.9

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

    3. Taylor expanded around 0 37.0

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -2.6650803551403255 \cdot 10^{-282} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 1.36358456559634 \cdot 10^{-259}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}, \frac{\left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x}}\right) \cdot \sqrt[3]{\sqrt[3]{y - x}}}{\sqrt[3]{a - t}} \cdot \left(z - t\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 +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))))