Average Error: 6.7 → 2.3
Time: 14.1s
Precision: binary64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;c \leq -2.484056664408104 \cdot 10^{+118}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.4408878131790536 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array}\]
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}\;c \leq -2.484056664408104 \cdot 10^{+118}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\

\mathbf{elif}\;c \leq 2.4408878131790536 \cdot 10^{+41}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\

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

\end{array}
(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.484056664408104e+118)
   (* 2.0 (- (+ (* x y) (* z t)) (* c (* i (+ a (* c b))))))
   (if (<= c 2.4408878131790536e+41)
     (* 2.0 (- (+ (* x y) (* z t)) (* i (* c (+ a (* c b))))))
     (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* c b)) (* c i)))))))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.484056664408104e+118) {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (i * (a + (c * b)))));
	} else if (c <= 2.4408878131790536e+41) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * (a + (c * b)))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - ((a + (c * b)) * (c * i)));
	}
	return tmp;
}

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

Original6.7
Target2.0
Herbie2.3
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 3 regimes

  2. if c < -2.48405666440810399e118

    1. Initial program 35.2

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

    2. Taylor expanded around 0 49.7

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

    3. Simplified4.8

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

    if -2.48405666440810399e118 < c < 2.44088781317905363e41

    1. Initial program 1.7

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

    if 2.44088781317905363e41 < c

    1. Initial program 24.0

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

    2. Taylor expanded around inf 5.0

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.484056664408104 \cdot 10^{+118}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.4408878131790536 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021014 
(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))))