Average Error: 24.4 → 11.6
Time: 3.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.62818059942686653 \cdot 10^{235}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{1}{a - t} \cdot \left(z - t\right), x\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.62818059942686653 \cdot 10^{235}:\\
\;\;\;\;y\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y - x, \frac{1}{a - t} \cdot \left(z - t\right), x\right)\\

\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 ((t <= -3.6281805994268665e+235)) {
		VAR = y;
	} else {
		VAR = fma((y - x), ((1.0 / (a - t)) * (z - t)), x);
	}
	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

Original24.4
Target9.4
Herbie11.6
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.6281805994268665e+235

    1. Initial program 52.6

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

    2. Simplified30.8

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

    3. Taylor expanded around 0 21.8

      \[\leadsto \color{blue}{y}\]

    if -3.6281805994268665e+235 < t

    1. Initial program 22.4

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

    2. Simplified13.5

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

    4. Applied fma-udef13.5

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

    6. Applied div-inv13.5

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

    7. Applied associate-*l*10.9

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

    8. Applied fma-def10.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{a - t} \cdot \left(z - t\right), x\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.62818059942686653 \cdot 10^{235}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{1}{a - t} \cdot \left(z - t\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020071 +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))))