Average Error: 15.9 → 6.9
Time: 1.5s
Precision: binary64
\[\frac{a \cdot b - 2 \cdot \left(c \cdot d\right)}{2 \cdot \left(c \cdot d\right)}\]
↓
\[\frac{a \cdot b}{2 \cdot \left(c \cdot d\right)} + -1\]
\frac{a \cdot b - 2 \cdot \left(c \cdot d\right)}{2 \cdot \left(c \cdot d\right)}
↓
\frac{a \cdot b}{2 \cdot \left(c \cdot d\right)} + -1
double code(double a, double b, double c, double d) {
	return ((double) (((double) (((double) (a * b)) - ((double) (2.0 * ((double) (c * d)))))) / ((double) (2.0 * ((double) (c * d))))));
}
↓
double code(double a, double b, double c, double d) {
	return ((double) (((double) (((double) (a * b)) / ((double) (2.0 * ((double) (c * d)))))) + -1.0));
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.9

    \[\frac{a \cdot b - 2 \cdot \left(c \cdot d\right)}{2 \cdot \left(c \cdot d\right)}\]

  2. Simplified6.9

    \[\leadsto \color{blue}{\frac{a \cdot b}{2 \cdot \left(c \cdot d\right)} + -1}\]

  3. Final simplification6.9

    \[\leadsto \frac{a \cdot b}{2 \cdot \left(c \cdot d\right)} + -1\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b c d)
  :name "(/ (- (* a b) (* 2 (* c d))) (* 2 (* c d)))"
  :precision binary64
  (/ (- (* a b) (* 2.0 (* c d))) (* 2.0 (* c d))))