Average Error: 17.4 → 1.3
Time: 2.7s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
↓
\[\frac{\frac{v}{-1 - \frac{u}{t1}}}{u + t1} \]
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1) :precision binary64 (/ (/ v (- -1.0 (/ u t1))) (+ u t1)))
double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}
↓
double code(double u, double v, double t1) {
	return (v / (-1.0 - (u / t1))) / (u + t1);
}

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = (-t1 * v) / ((t1 + u) * (t1 + u))
end function
↓
real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = (v / ((-1.0d0) - (u / t1))) / (u + t1)
end function

public static double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}
↓
public static double code(double u, double v, double t1) {
	return (v / (-1.0 - (u / t1))) / (u + t1);
}

def code(u, v, t1):
	return (-t1 * v) / ((t1 + u) * (t1 + u))
↓
def code(u, v, t1):
	return (v / (-1.0 - (u / t1))) / (u + t1)

function code(u, v, t1)
	return Float64(Float64(Float64(-t1) * v) / Float64(Float64(t1 + u) * Float64(t1 + u)))
end
↓
function code(u, v, t1)
	return Float64(Float64(v / Float64(-1.0 - Float64(u / t1))) / Float64(u + t1))
end

function tmp = code(u, v, t1)
	tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
end
↓
function tmp = code(u, v, t1)
	tmp = (v / (-1.0 - (u / t1))) / (u + t1);
end

code[u_, v_, t1_] := N[(N[((-t1) * v), $MachinePrecision] / N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[u_, v_, t1_] := N[(N[(v / N[(-1.0 - N[(u / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(u + t1), $MachinePrecision]), $MachinePrecision]

\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{-1 - \frac{u}{t1}}}{u + t1}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]

  2. Simplified1.5

    \[\leadsto \color{blue}{\frac{\frac{v}{t1 + u}}{-1 - \frac{u}{t1}}} \]

  3. Applied egg-rr3.7

    \[\leadsto \color{blue}{v \cdot \frac{1}{\left(t1 + u\right) \cdot \left(-1 - \frac{u}{t1}\right)}} \]

  4. Applied egg-rr1.3

    \[\leadsto \color{blue}{\frac{\frac{v}{-1 - \frac{u}{t1}}}{t1 + u}} \]

  5. Final simplification1.3

    \[\leadsto \frac{\frac{v}{-1 - \frac{u}{t1}}}{u + t1} \]

Reproduce

herbie shell --seed 2022150 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))