Average Error: 6.0 → 3.1
Time: 19.4s
Precision: binary64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.68010719244830644 \cdot 10^{-120} \lor \neg \left(b \le 2.51425795026807799 \cdot 10^{-228}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) \cdot \sqrt[3]{x \cdot y + z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
\begin{array}{l}
\mathbf{if}\;b \le -1.68010719244830644 \cdot 10^{-120} \lor \neg \left(b \le 2.51425795026807799 \cdot 10^{-228}\right):\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \left(\left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) \cdot \sqrt[3]{x \cdot y + z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (((double) (((double) (a + ((double) (b * c)))) * c)) * i))))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double VAR;
	if (((b <= -1.6801071924483064e-120) || !(b <= 2.514257950268078e-228))) {
		VAR = ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (((double) cbrt(((double) (a + ((double) (b * c)))))) * ((double) (((double) cbrt(((double) (a + ((double) (b * c)))))) * ((double) (((double) cbrt(((double) (a + ((double) (b * c)))))) * ((double) (c * i))))))))))));
	} else {
		VAR = ((double) (2.0 * ((double) (((double) (((double) (((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))) * ((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))))) * ((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))))) - ((double) (((double) (((double) (a + ((double) (b * c)))) * c)) * i))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.0
Target2.0
Herbie3.1
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if b < -1.68010719244830644e-120 or 2.51425795026807799e-228 < b

    1. Initial program 6.6

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
    2. Using strategy rm

    3. Applied associate-*l*2.1

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
    4. Using strategy rm

    5. Applied add-cube-cbrt2.5

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(c \cdot i\right)\right)\]

    6. Applied associate-*l*2.5

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)}\right)\]
    7. Using strategy rm

    8. Applied associate-*l*2.5

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)}\right)\]

    if -1.68010719244830644e-120 < b < 2.51425795026807799e-228

    1. Initial program 4.1

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt5.0

      \[\leadsto 2 \cdot \left(\color{blue}{\left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) \cdot \sqrt[3]{x \cdot y + z \cdot t}} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.68010719244830644 \cdot 10^{-120} \lor \neg \left(b \le 2.51425795026807799 \cdot 10^{-228}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) \cdot \sqrt[3]{x \cdot y + z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))