Average Error: 37.0 → 37.0
Time: 2.1s
Precision: binary64
\[\frac{\left(c \cdot d\right) \cdot u}{\sqrt{\left(\left(\left(c \cdot c\right) \cdot u\right) \cdot u + v \cdot v\right) - \left(\left(\left(2 \cdot c\right) \cdot u\right) \cdot v\right) \cdot \cos \left(\pi - \gamma\right)}}\]
↓
\[\frac{\left(c \cdot d\right) \cdot u}{\sqrt{\left(\left(\left(c \cdot c\right) \cdot u\right) \cdot u + v \cdot v\right) - \left(\left(\left(2 \cdot c\right) \cdot u\right) \cdot v\right) \cdot \cos \left(\pi - \gamma\right)}}\]
\frac{\left(c \cdot d\right) \cdot u}{\sqrt{\left(\left(\left(c \cdot c\right) \cdot u\right) \cdot u + v \cdot v\right) - \left(\left(\left(2 \cdot c\right) \cdot u\right) \cdot v\right) \cdot \cos \left(\pi - \gamma\right)}}
↓
\frac{\left(c \cdot d\right) \cdot u}{\sqrt{\left(\left(\left(c \cdot c\right) \cdot u\right) \cdot u + v \cdot v\right) - \left(\left(\left(2 \cdot c\right) \cdot u\right) \cdot v\right) \cdot \cos \left(\pi - \gamma\right)}}
double code(double c, double d, double u, double v, double gamma) {
	return ((double) (((double) (((double) (c * d)) * u)) / ((double) sqrt(((double) (((double) (((double) (((double) (((double) (c * c)) * u)) * u)) + ((double) (v * v)))) - ((double) (((double) (((double) (((double) (2.0 * c)) * u)) * v)) * ((double) cos(((double) (((double) M_PI) - gamma))))))))))));
}
↓
double code(double c, double d, double u, double v, double gamma) {
	return ((double) (((double) (((double) (c * d)) * u)) / ((double) sqrt(((double) (((double) (((double) (((double) (((double) (c * c)) * u)) * u)) + ((double) (v * v)))) - ((double) (((double) (((double) (((double) (2.0 * c)) * u)) * v)) * ((double) cos(((double) (((double) M_PI) - gamma))))))))))));
}

Error

Bits error versus c

Bits error versus d

Bits error versus u

Bits error versus v

Bits error versus gamma

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 37.0

    \[\frac{\left(c \cdot d\right) \cdot u}{\sqrt{\left(\left(\left(c \cdot c\right) \cdot u\right) \cdot u + v \cdot v\right) - \left(\left(\left(2 \cdot c\right) \cdot u\right) \cdot v\right) \cdot \cos \left(\pi - \gamma\right)}}\]

  2. Final simplification37.0

    \[\leadsto \frac{\left(c \cdot d\right) \cdot u}{\sqrt{\left(\left(\left(c \cdot c\right) \cdot u\right) \cdot u + v \cdot v\right) - \left(\left(\left(2 \cdot c\right) \cdot u\right) \cdot v\right) \cdot \cos \left(\pi - \gamma\right)}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (c d u v gamma)
  :name "(/ (* (* c d) u) (sqrt (- (+ (* (* (* c c) u) u) (* v v)) (* (* (* (* 2 c) u) v) (cos (- PI gamma))))))"
  :precision binary64
  (/ (* (* c d) u) (sqrt (- (+ (* (* (* c c) u) u) (* v v)) (* (* (* (* 2.0 c) u) v) (cos (- PI gamma)))))))