Average Error: 2.3 → 1.8
Time: 5.3s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -6.313002064818998 \cdot 10^{+86}:\\ \;\;\;\;x + \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(z \cdot \frac{\sqrt[3]{y - x}}{t}\right)\\ \mathbf{elif}\;t \leq 4.633125479398495 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -6.313002064818998 \cdot 10^{+86}:\\
\;\;\;\;x + \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(z \cdot \frac{\sqrt[3]{y - x}}{t}\right)\\

\mathbf{elif}\;t \leq 4.633125479398495 \cdot 10^{+59}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{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 -6.313002064818998e+86)
   (+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* z (/ (cbrt (- y x)) t))))
   (if (<= t 4.633125479398495e+59)
     (+ x (/ (* (- y x) z) 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 <= -6.313002064818998e+86) {
		tmp = x + ((cbrt(y - x) * cbrt(y - x)) * (z * (cbrt(y - x) / t)));
	} else if (t <= 4.633125479398495e+59) {
		tmp = x + (((y - x) * z) / 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
Target2.5
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -6.3130020648189983e86

    1. Initial program 1.6

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

    3. Applied add-cube-cbrt_binary641.9

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

    4. Applied associate-*l*_binary641.9

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

    5. Simplified1.9

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

    7. Applied div-inv_binary641.9

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

    8. Applied associate-*l*_binary641.1

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

    9. Simplified1.1

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

    if -6.3130020648189983e86 < t < 4.6331254793984947e59

    1. Initial program 3.2

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

    3. Applied associate-*r/_binary642.4

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

    if 4.6331254793984947e59 < t

    1. Initial program 1.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.313002064818998 \cdot 10^{+86}:\\ \;\;\;\;x + \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(z \cdot \frac{\sqrt[3]{y - x}}{t}\right)\\ \mathbf{elif}\;t \leq 4.633125479398495 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(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))))