Average Error: 6.4 → 1.7
Time: 9.8s
Precision: binary64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;c \leq -3.7048220371515083 \cdot 10^{-34} \lor \neg \left(c \leq 7.834458098323896 \cdot 10^{-93}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \end{array}\]
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}\;c \leq -3.7048220371515083 \cdot 10^{-34} \lor \neg \left(c \leq 7.834458098323896 \cdot 10^{-93}\right):\\
\;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\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 (or (<= c -3.7048220371515083e-34) (not (<= c 7.834458098323896e-93)))
   (* 2.0 (+ (* x y) (- (* z t) (* c (* (+ a (* c b)) i)))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* c (+ a (* c b))))))))
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 tmp;
	if (((c <= -3.7048220371515083e-34) || !(c <= 7.834458098323896e-93))) {
		tmp = ((double) (2.0 * ((double) (((double) (x * y)) + ((double) (((double) (z * t)) - ((double) (c * ((double) (((double) (a + ((double) (c * b)))) * i))))))))));
	} else {
		tmp = ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (i * ((double) (c * ((double) (a + ((double) (c * b))))))))))));
	}
	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

Original6.4
Target1.9
Herbie1.7
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if c < -3.7048220371515083e-34 or 7.8344580983238958e-93 < c

    1. Initial program Error: 13.8 bits

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

    2. SimplifiedError: 3.3 bits

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

    if -3.7048220371515083e-34 < c < 7.8344580983238958e-93

    1. Initial program Error: 0.5 bits

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

  4. Final simplificationError: 1.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7048220371515083 \cdot 10^{-34} \lor \neg \left(c \leq 7.834458098323896 \cdot 10^{-93}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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))))