Average Error: 2.1 → 1.3
Time: 3.8s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -52557646.20646281:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.0218493211776868 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt{t}} \cdot \frac{z}{\sqrt{t}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -52557646.20646281:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;t \leq 2.0218493211776868 \cdot 10^{+54}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\sqrt{t}} \cdot \frac{z}{\sqrt{t}}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= t -52557646.20646281)
   (+ x (* (- y x) (/ z t)))
   (if (<= t 2.0218493211776868e+54)
     (+ x (/ (* (- y x) z) t))
     (+ x (* (/ (- y x) (sqrt t)) (/ z (sqrt t)))))))
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -52557646.20646281)) {
		tmp = ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
	} else {
		double tmp_1;
		if ((t <= 2.0218493211776868e+54)) {
			tmp_1 = ((double) (x + (((double) (((double) (y - x)) * z)) / t)));
		} else {
			tmp_1 = ((double) (x + ((double) ((((double) (y - x)) / ((double) sqrt(t))) * (z / ((double) sqrt(t)))))));
		}
		tmp = tmp_1;
	}
	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

Original2.1
Target2.3
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < -0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -52557646.206462808

    1. Initial program 1.1

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

    if -52557646.206462808 < t < 2.02184932117768678e54

    1. Initial program 3.3

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

    3. Applied associate-*r/_binary641.7

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

    if 2.02184932117768678e54 < t

    1. Initial program 1.1

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

    3. Applied add-sqr-sqrt_binary641.2

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

    4. Applied *-un-lft-identity_binary641.2

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

    5. Applied times-frac_binary641.2

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

    6. Applied associate-*r*_binary640.7

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

    7. Simplified0.7

      \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt{t}}} \cdot \frac{z}{\sqrt{t}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -52557646.20646281:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.0218493211776868 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt{t}} \cdot \frac{z}{\sqrt{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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))))