Average Error: 24.0 → 10.9
Time: 6.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.54383536088708091 \cdot 10^{233}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y - \frac{z \cdot y}{t}\right)\\ \mathbf{elif}\;t \le 4.80918778606114512 \cdot 10^{-143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}} - \left(\frac{t}{\frac{a - t}{y - x}} - x\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.54383536088708091 \cdot 10^{233}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y - \frac{z \cdot y}{t}\right)\\

\mathbf{elif}\;t \le 4.80918778606114512 \cdot 10^{-143}:\\
\;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{z}{\frac{a - t}{y - x}} - \left(\frac{t}{\frac{a - t}{y - x}} - 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 <= -2.543835360887081e+233)) {
		VAR = fma((x / t), z, (y - ((z * y) / t)));
	} else {
		double VAR_1;
		if ((t <= 4.809187786061145e-143)) {
			VAR_1 = fma(((z - t) / (a - t)), (y - x), x);
		} else {
			VAR_1 = ((z / ((a - t) / (y - x))) - ((t / ((a - t) / (y - x))) - x));
		}
		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

Original24.0
Target9.4
Herbie10.9
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -2.543835360887081e+233

    1. Initial program 51.4

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

    2. Simplified34.7

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

    4. Applied clear-num35.0

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

    6. Applied fma-udef35.1

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

    7. Simplified35.1

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

    8. Taylor expanded around inf 22.6

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

    9. Simplified18.0

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

    if -2.543835360887081e+233 < t < 4.809187786061145e-143

    1. Initial program 17.1

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

    2. Simplified10.8

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

    4. Applied clear-num11.1

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

    6. Applied fma-udef11.1

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

    7. Simplified10.8

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

    9. Applied associate-/r/7.7

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

    10. Applied fma-def7.7

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

    if 4.809187786061145e-143 < t

    1. Initial program 28.8

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

    2. Simplified16.9

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

    4. Applied clear-num17.2

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

    6. Applied fma-udef17.3

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

    7. Simplified17.1

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

    9. Applied div-sub17.1

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

    10. Applied associate-+l-14.1

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

  4. Final simplification10.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.54383536088708091 \cdot 10^{233}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y - \frac{z \cdot y}{t}\right)\\ \mathbf{elif}\;t \le 4.80918778606114512 \cdot 10^{-143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}} - \left(\frac{t}{\frac{a - t}{y - x}} - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 +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))))