Rosa's DopplerBench

Percentage Accurate: 71.9% → 98.0%

Time: 10.1s

Alternatives: 8

Speedup: 0.8×

Specification

Math

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

FPCore

(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 71.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (u v t1) :precision binary64 (/ (* t1 (/ v (+ t1 u))) (- (- t1) u)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.4%

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. times-frac N/A

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

   6. lift-neg.f64 N/A

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

   7. distribute-frac-neg N/A

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

   8. distribute-frac-neg2 N/A

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

   9. associate-*r/ N/A

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

   10. lower-/.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lower-neg.f64 98.4

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

4. Applied rewrites 98.4%

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

5. Final simplification 98.4%

   \[\leadsto \frac{t1 \cdot \frac{v}{t1 + u}}{\left(-t1\right) - u} \]
6. Add Preprocessing

Alternative 2: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t1\right) - u\\ t_2 := \frac{v \cdot 1}{t\_1}\\ \mathbf{if}\;t1 \leq -1.34 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t1 \leq 1.7 \cdot 10^{+113}:\\ \;\;\;\;v \cdot \frac{t1}{\left(t1 + u\right) \cdot t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (- (- t1) u)) (t_2 (/ (* v 1.0) t_1)))
   (if (<= t1 -1.34e+154)
     t_2
     (if (<= t1 1.7e+113) (* v (/ t1 (* (+ t1 u) t_1))) t_2))))

C

double code(double u, double v, double t1) {
	double t_1 = -t1 - u;
	double t_2 = (v * 1.0) / t_1;
	double tmp;
	if (t1 <= -1.34e+154) {
		tmp = t_2;
	} else if (t1 <= 1.7e+113) {
		tmp = v * (t1 / ((t1 + u) * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -t1 - u
    t_2 = (v * 1.0d0) / t_1
    if (t1 <= (-1.34d+154)) then
        tmp = t_2
    else if (t1 <= 1.7d+113) then
        tmp = v * (t1 / ((t1 + u) * t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = -t1 - u;
	double t_2 = (v * 1.0) / t_1;
	double tmp;
	if (t1 <= -1.34e+154) {
		tmp = t_2;
	} else if (t1 <= 1.7e+113) {
		tmp = v * (t1 / ((t1 + u) * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = -t1 - u
	t_2 = (v * 1.0) / t_1
	tmp = 0
	if t1 <= -1.34e+154:
		tmp = t_2
	elif t1 <= 1.7e+113:
		tmp = v * (t1 / ((t1 + u) * t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(-t1) - u)
	t_2 = Float64(Float64(v * 1.0) / t_1)
	tmp = 0.0
	if (t1 <= -1.34e+154)
		tmp = t_2;
	elseif (t1 <= 1.7e+113)
		tmp = Float64(v * Float64(t1 / Float64(Float64(t1 + u) * t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = -t1 - u;
	t_2 = (v * 1.0) / t_1;
	tmp = 0.0;
	if (t1 <= -1.34e+154)
		tmp = t_2;
	elseif (t1 <= 1.7e+113)
		tmp = v * (t1 / ((t1 + u) * t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[((-t1) - u), $MachinePrecision]}, Block[{t$95$2 = N[(N[(v * 1.0), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t1, -1.34e+154], t$95$2, If[LessEqual[t1, 1.7e+113], N[(v * N[(t1 / N[(N[(t1 + u), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if t1 < -1.34000000000000001e154 or 1.70000000000000009e113 < t1

   1. Initial program 42.7%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. distribute-lft-neg-out N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-neg.f64 46.3

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

   4. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\left(\frac{1}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \cdot t1\right) \cdot \left(-v\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 96.5

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

   6. Applied rewrites 96.5%

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

   7. Taylor expanded in t1 around inf

      \[\leadsto \frac{\color{blue}{1}}{t1 + u} \cdot \left(\mathsf{neg}\left(v\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 90.6%

      \[\leadsto \frac{\color{blue}{1}}{t1 + u} \cdot \left(-v\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-*l/ N/A

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

       5. frac-2neg N/A

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

       6. lift-+.f64 N/A

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

       7. lift-neg.f64 N/A

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

       8. lower-/.f64 N/A

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

       9. *-commutative N/A

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

       10. distribute-lft-neg-in N/A

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

       11. lift-neg.f64 N/A

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

       12. remove-double-neg N/A

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

       13. lower-*.f64 90.8

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

       14. lift-neg.f64 N/A

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

       15. lift-+.f64 N/A

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

       16. distribute-neg-in N/A

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

       17. unsub-neg N/A

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

       18. lower--.f64 N/A

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

       19. lower-neg.f64 90.8

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

   11. Applied rewrites 90.8%

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

   if -1.34000000000000001e154 < t1 < 1.70000000000000009e113

   1. Initial program 83.7%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 87.0

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

   4. Applied rewrites 87.0%

      \[\leadsto \color{blue}{\frac{-t1}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \cdot v} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.34 \cdot 10^{+154}:\\ \;\;\;\;\frac{v \cdot 1}{\left(-t1\right) - u}\\ \mathbf{elif}\;t1 \leq 1.7 \cdot 10^{+113}:\\ \;\;\;\;v \cdot \frac{t1}{\left(t1 + u\right) \cdot \left(\left(-t1\right) - u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot 1}{\left(-t1\right) - u}\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))