Average Error: 6.3 → 1.6
Time: 8.4s
Precision: binary64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -4.390460365680553 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \le 1.176419138377631 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{elif}\;i \le 7.387088960346427 \cdot 10^{+199}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(c \cdot \left(i \cdot \sqrt[3]{a + b \cdot c}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array}\]
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}\;i \le -4.390460365680553 \cdot 10^{+23}:\\
\;\;\;\;2 \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\

\mathbf{elif}\;i \le 1.176419138377631 \cdot 10^{+16}:\\
\;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\\

\mathbf{elif}\;i \le 7.387088960346427 \cdot 10^{+199}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(c \cdot \left(i \cdot \sqrt[3]{a + b \cdot c}\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\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 ((i <= -4.390460365680553e+23)) {
		VAR = ((double) (2.0 * ((double) (((double) (((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))) * ((double) (((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))) * ((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))))))) - ((double) (i * ((double) (c * ((double) (a + ((double) (b * c))))))))))));
	} else {
		double VAR_1;
		if ((i <= 1.176419138377631e+16)) {
			VAR_1 = ((double) (2.0 * ((double) (((double) (x * y)) + ((double) (((double) (z * t)) - ((double) (c * ((double) (i * ((double) (a + ((double) (b * c))))))))))))));
		} else {
			double VAR_2;
			if ((i <= 7.387088960346427e+199)) {
				VAR_2 = ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (((double) (((double) cbrt(((double) (a + ((double) (b * c)))))) * ((double) cbrt(((double) (a + ((double) (b * c)))))))) * ((double) (c * ((double) (i * ((double) cbrt(((double) (a + ((double) (b * c))))))))))))))));
			} else {
				VAR_2 = ((double) (2.0 * ((double) (((double) (((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))) * ((double) (((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))) * ((double) cbrt(((double) (((double) (x * y)) + ((double) (z * t)))))))))) - ((double) (i * ((double) (c * ((double) (a + ((double) (b * c))))))))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	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

Original6.3
Target2.1
Herbie1.6
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 3 regimes

  2. if i < -4.39046036568055323e23 or 7.38708896034642738e199 < i

    1. Initial program 0.8

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

    3. Applied add-cube-cbrt1.4

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

    if -4.39046036568055323e23 < i < 11764191383776310

    1. Initial program 9.5

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

    2. Simplified1.9

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

    if 11764191383776310 < i < 7.38708896034642738e199

    1. Initial program 0.4

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

    3. Applied associate-*l*0.6

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

    5. Applied add-cube-cbrt1.1

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

    6. Applied associate-*l*1.1

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

    7. Simplified0.8

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -4.390460365680553 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \le 1.176419138377631 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{elif}\;i \le 7.387088960346427 \cdot 10^{+199}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(c \cdot \left(i \cdot \sqrt[3]{a + b \cdot c}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \left(\sqrt[3]{x \cdot y + z \cdot t} \cdot \sqrt[3]{x \cdot y + z \cdot t}\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))))