Average Error: 2.3 → 1.5
Time: 3.7s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t} \]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -1.1041604840852519 \cdot 10^{+92}:\\ \;\;\;\;x + z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 21595849726.253307:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -1.1041604840852519 \cdot 10^{+92}:\\
\;\;\;\;x + z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\

\mathbf{elif}\;t \leq 21595849726.253307:\\
\;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\

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


\end{array}

(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.1041604840852519e+92)
   (+ x (* z (- (/ y t) (/ x t))))
   (if (<= t 21595849726.253307)
     (+ x (/ (* z (- y x)) t))
     (+ x (* (- y x) (/ z t))))))
double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.1041604840852519e+92) {
		tmp = x + (z * ((y / t) - (x / t)));
	} else if (t <= 21595849726.253307) {
		tmp = x + ((z * (y - x)) / t);
	} else {
		tmp = x + ((y - x) * (z / t));
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.3
Target2.4
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.1041604840852519e92

    1. Initial program 1.4

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

    2. Taylor expanded around 0 12.1

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

    3. Simplified1.3

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

    5. Applied div-sub_binary641.3

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

    if -1.1041604840852519e92 < t < 21595849726.2533073

    1. Initial program 3.4

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

    2. Taylor expanded around 0 1.9

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

    if 21595849726.2533073 < t

    1. Initial program 1.2

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

    3. Applied add-cube-cbrt_binary641.5

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

    4. Applied *-un-lft-identity_binary641.5

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

    5. Applied times-frac_binary641.5

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

    6. Applied associate-*r*_binary640.9

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

    7. Simplified0.9

      \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}} \]
    8. Using strategy rm

    9. Applied *-un-lft-identity_binary640.9

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

    10. Applied associate-*l*_binary640.9

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

    11. Simplified1.2

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1041604840852519 \cdot 10^{+92}:\\ \;\;\;\;x + z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 21595849726.253307:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Reproduce

herbie shell --seed 2021204 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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