Average Error: 14.8 → 1.5
Time: 3.9s
Precision: binary64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq -1.8435525049519473 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq -\infty:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq -1.8435525049519473 \cdot 10^{-299}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\

\end{array}
(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (* x (/ (* (/ y z) t) t)) (- INFINITY))
   (/ 1.0 (/ (/ z x) y))
   (if (<= (* x (/ (* (/ y z) t) t)) -1.8435525049519473e-299)
     (* x (/ y z))
     (*
      (* x (/ (* (cbrt y) (cbrt y)) (* (cbrt z) (cbrt z))))
      (/ (cbrt y) (cbrt z))))))
double code(double x, double y, double z, double t) {
	return x * (((y / z) * t) / t);
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * (((y / z) * t) / t)) <= -((double) INFINITY)) {
		tmp = 1.0 / ((z / x) / y);
	} else if ((x * (((y / z) * t) / t)) <= -1.8435525049519473e-299) {
		tmp = x * (y / z);
	} else {
		tmp = (x * ((cbrt(y) * cbrt(y)) / (cbrt(z) * cbrt(z)))) * (cbrt(y) / cbrt(z));
	}
	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

Original14.8
Target1.5
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t)) < -inf.0

    1. Initial program 64.0

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified28.0

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied associate-*r/_binary64_165341.6

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
    5. Using strategy rm

    6. Applied clear-num_binary64_165891.7

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    7. Using strategy rm

    8. Applied associate-/r*_binary64_165362.8

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]

    if -inf.0 < (*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t)) < -1.8435525049519473e-299

    1. Initial program 0.7

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified0.4

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]

    if -1.8435525049519473e-299 < (*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t))

    1. Initial program 16.5

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified6.8

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied add-cube-cbrt_binary64_166227.5

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

    5. Applied add-cube-cbrt_binary64_166227.7

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

    6. Applied times-frac_binary64_165967.7

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

    7. Applied associate-*r*_binary64_165321.9

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq -1.8435525049519473 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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