Average Error: 17.6 → 1.4
Time: 3.1s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
↓
\[\frac{1}{t1 + u} \cdot \frac{v}{-1 - \frac{u}{t1}} \]
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1)
 :precision binary64
 (* (/ 1.0 (+ t1 u)) (/ v (- -1.0 (/ 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 (1.0 / (t1 + u)) * (v / (-1.0 - (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 = (1.0d0 / (t1 + u)) * (v / ((-1.0d0) - (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 (1.0 / (t1 + u)) * (v / (-1.0 - (u / t1)));
}

def code(u, v, t1):
	return (-t1 * v) / ((t1 + u) * (t1 + u))
↓
def code(u, v, t1):
	return (1.0 / (t1 + u)) * (v / (-1.0 - (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(1.0 / Float64(t1 + u)) * Float64(v / Float64(-1.0 - 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 = (1.0 / (t1 + u)) * (v / (-1.0 - (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[(1.0 / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(v / N[(-1.0 - N[(u / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.6

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

  2. Simplified1.4

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

  3. Applied egg-rr1.8

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

  4. Applied egg-rr1.6

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

  5. Applied egg-rr1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2022190 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))