Average Error: 24.5 → 8.7
Time: 8.5s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -3.053102413771768 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -3.053102413771768 \cdot 10^{-225}:\\
\;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* (- y x) (- z t)) (- a t))) -3.053102413771768e-225)
   (+ x (/ (- y x) (/ (- a t) (- z t))))
   (if (<= (+ x (/ (* (- y x) (- z t)) (- a t))) 0.0)
     (- (+ y (/ (* x z) t)) (/ (* y z) t))
     (+ x (* (- y x) (/ (- z t) (- a t)))))))
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 tmp;
	if ((x + (((y - x) * (z - t)) / (a - t))) <= -3.053102413771768e-225) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if ((x + (((y - x) * (z - t)) / (a - t))) <= 0.0) {
		tmp = (y + ((x * z) / t)) - ((y * z) / t);
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

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

Original24.5
Target9.4
Herbie8.7
\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.05310241377176773e-225

    1. Initial program 21.6

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

    3. Applied associate-/l*_binary64_157097.1

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

    if -3.05310241377176773e-225 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

    1. Initial program 55.0

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

    2. Taylor expanded around inf 21.7

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

    3. Simplified21.7

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

    if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

    1. Initial program 21.1

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

    3. Applied *-un-lft-identity_binary64_1576421.1

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

    4. Applied times-frac_binary64_157707.6

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

    5. Simplified7.6

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

  4. Final simplification8.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -3.053102413771768 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020342 
(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) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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