Rosa's DopplerBench

Percentage Accurate: 72.8% → 98.0%

Time: 9.7s

Alternatives: 11

Speedup: 1.0×

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: 72.8% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.4%

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

   1. times-frac 98.0%

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

3. Simplified 98.0%

   \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
4. Add Preprocessing

5. Final simplification 98.0%

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

Alternative 2: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -4.8 \cdot 10^{+24} \lor \neg \left(t1 \leq -2.5 \cdot 10^{-19}\right) \land \left(t1 \leq -2.5 \cdot 10^{-45} \lor \neg \left(t1 \leq 6.2 \cdot 10^{-73}\right)\right):\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{u} \cdot \frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -4.8e+24)
         (and (not (<= t1 -2.5e-19))
              (or (<= t1 -2.5e-45) (not (<= t1 6.2e-73)))))
   (/ (- v) (+ t1 u))
   (* (/ (- t1) u) (/ v u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -4.8e+24) || (!(t1 <= -2.5e-19) && ((t1 <= -2.5e-45) || !(t1 <= 6.2e-73)))) {
		tmp = -v / (t1 + u);
	} else {
		tmp = (-t1 / u) * (v / u);
	}
	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) :: tmp
    if ((t1 <= (-4.8d+24)) .or. (.not. (t1 <= (-2.5d-19))) .and. (t1 <= (-2.5d-45)) .or. (.not. (t1 <= 6.2d-73))) then
        tmp = -v / (t1 + u)
    else
        tmp = (-t1 / u) * (v / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -4.8e+24) || (!(t1 <= -2.5e-19) && ((t1 <= -2.5e-45) || !(t1 <= 6.2e-73)))) {
		tmp = -v / (t1 + u);
	} else {
		tmp = (-t1 / u) * (v / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -4.8e+24) or (not (t1 <= -2.5e-19) and ((t1 <= -2.5e-45) or not (t1 <= 6.2e-73))):
		tmp = -v / (t1 + u)
	else:
		tmp = (-t1 / u) * (v / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -4.8e+24) || (!(t1 <= -2.5e-19) && ((t1 <= -2.5e-45) || !(t1 <= 6.2e-73))))
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	else
		tmp = Float64(Float64(Float64(-t1) / u) * Float64(v / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -4.8e+24) || (~((t1 <= -2.5e-19)) && ((t1 <= -2.5e-45) || ~((t1 <= 6.2e-73)))))
		tmp = -v / (t1 + u);
	else
		tmp = (-t1 / u) * (v / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -4.8e+24], And[N[Not[LessEqual[t1, -2.5e-19]], $MachinePrecision], Or[LessEqual[t1, -2.5e-45], N[Not[LessEqual[t1, 6.2e-73]], $MachinePrecision]]]], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision], N[(N[((-t1) / u), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -4.8000000000000001e24 or -2.5000000000000002e-19 < t1 < -2.49999999999999988e-45 or 6.19999999999999938e-73 < t1

   1. Initial program 67.2%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around inf 83.7%

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

   if -4.8000000000000001e24 < t1 < -2.5000000000000002e-19 or -2.49999999999999988e-45 < t1 < 6.19999999999999938e-73

   1. Initial program 78.9%

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

      1. times-frac 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in t1 around 0 82.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -4.8 \cdot 10^{+24} \lor \neg \left(t1 \leq -2.5 \cdot 10^{-19}\right) \land \left(t1 \leq -2.5 \cdot 10^{-45} \lor \neg \left(t1 \leq 6.2 \cdot 10^{-73}\right)\right):\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{u} \cdot \frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-v}{t1 + u}\\ t_2 := \frac{-t1}{u} \cdot \frac{v}{u}\\ \mathbf{if}\;t1 \leq -4.3 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq -3.6 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t1 \leq -8.8 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq 3.65 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t1 + u}{v}}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ (- v) (+ t1 u))) (t_2 (* (/ (- t1) u) (/ v u))))
   (if (<= t1 -4.3e+27)
     t_1
     (if (<= t1 -3.6e-19)
       t_2
       (if (<= t1 -8.8e-45)
         t_1
         (if (<= t1 3.65e-72) t_2 (/ -1.0 (/ (+ t1 u) v))))))))

C

double code(double u, double v, double t1) {
	double t_1 = -v / (t1 + u);
	double t_2 = (-t1 / u) * (v / u);
	double tmp;
	if (t1 <= -4.3e+27) {
		tmp = t_1;
	} else if (t1 <= -3.6e-19) {
		tmp = t_2;
	} else if (t1 <= -8.8e-45) {
		tmp = t_1;
	} else if (t1 <= 3.65e-72) {
		tmp = t_2;
	} else {
		tmp = -1.0 / ((t1 + u) / v);
	}
	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 = -v / (t1 + u)
    t_2 = (-t1 / u) * (v / u)
    if (t1 <= (-4.3d+27)) then
        tmp = t_1
    else if (t1 <= (-3.6d-19)) then
        tmp = t_2
    else if (t1 <= (-8.8d-45)) then
        tmp = t_1
    else if (t1 <= 3.65d-72) then
        tmp = t_2
    else
        tmp = (-1.0d0) / ((t1 + u) / v)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = -v / (t1 + u);
	double t_2 = (-t1 / u) * (v / u);
	double tmp;
	if (t1 <= -4.3e+27) {
		tmp = t_1;
	} else if (t1 <= -3.6e-19) {
		tmp = t_2;
	} else if (t1 <= -8.8e-45) {
		tmp = t_1;
	} else if (t1 <= 3.65e-72) {
		tmp = t_2;
	} else {
		tmp = -1.0 / ((t1 + u) / v);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = -v / (t1 + u)
	t_2 = (-t1 / u) * (v / u)
	tmp = 0
	if t1 <= -4.3e+27:
		tmp = t_1
	elif t1 <= -3.6e-19:
		tmp = t_2
	elif t1 <= -8.8e-45:
		tmp = t_1
	elif t1 <= 3.65e-72:
		tmp = t_2
	else:
		tmp = -1.0 / ((t1 + u) / v)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(-v) / Float64(t1 + u))
	t_2 = Float64(Float64(Float64(-t1) / u) * Float64(v / u))
	tmp = 0.0
	if (t1 <= -4.3e+27)
		tmp = t_1;
	elseif (t1 <= -3.6e-19)
		tmp = t_2;
	elseif (t1 <= -8.8e-45)
		tmp = t_1;
	elseif (t1 <= 3.65e-72)
		tmp = t_2;
	else
		tmp = Float64(-1.0 / Float64(Float64(t1 + u) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = -v / (t1 + u);
	t_2 = (-t1 / u) * (v / u);
	tmp = 0.0;
	if (t1 <= -4.3e+27)
		tmp = t_1;
	elseif (t1 <= -3.6e-19)
		tmp = t_2;
	elseif (t1 <= -8.8e-45)
		tmp = t_1;
	elseif (t1 <= 3.65e-72)
		tmp = t_2;
	else
		tmp = -1.0 / ((t1 + u) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-t1) / u), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -4.3e+27], t$95$1, If[LessEqual[t1, -3.6e-19], t$95$2, If[LessEqual[t1, -8.8e-45], t$95$1, If[LessEqual[t1, 3.65e-72], t$95$2, N[(-1.0 / N[(N[(t1 + u), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -4.30000000000000008e27 or -3.6000000000000001e-19 < t1 < -8.79999999999999974e-45

   1. Initial program 59.7%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around inf 86.7%

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

   if -4.30000000000000008e27 < t1 < -3.6000000000000001e-19 or -8.79999999999999974e-45 < t1 < 3.65000000000000001e-72

   1. Initial program 78.9%

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

      1. times-frac 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in t1 around 0 82.0%

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

   if 3.65000000000000001e-72 < t1

   1. Initial program 74.8%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.1%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t1 around inf 80.5%

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

      1. associate-/r/ 80.9%

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

   9. Applied egg-rr 80.9%

      \[\leadsto -1 \cdot \color{blue}{\frac{1}{\frac{t1 + u}{v}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -4.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq -3.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{-t1}{u} \cdot \frac{v}{u}\\ \mathbf{elif}\;t1 \leq -8.8 \cdot 10^{-45}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq 3.65 \cdot 10^{-72}:\\ \;\;\;\;\frac{-t1}{u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t1 + u}{v}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-v}{t1 + u}\\ \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq -3.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{\frac{t1 \cdot v}{u}}{t1 - u}\\ \mathbf{elif}\;t1 \leq -8 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq 6.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{-t1}{u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t1 + u}{v}}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ (- v) (+ t1 u))))
   (if (<= t1 -1.3e+25)
     t_1
     (if (<= t1 -3.9e-20)
       (/ (/ (* t1 v) u) (- t1 u))
       (if (<= t1 -8e-45)
         t_1
         (if (<= t1 6.2e-73)
           (* (/ (- t1) u) (/ v u))
           (/ -1.0 (/ (+ t1 u) v))))))))

C

double code(double u, double v, double t1) {
	double t_1 = -v / (t1 + u);
	double tmp;
	if (t1 <= -1.3e+25) {
		tmp = t_1;
	} else if (t1 <= -3.9e-20) {
		tmp = ((t1 * v) / u) / (t1 - u);
	} else if (t1 <= -8e-45) {
		tmp = t_1;
	} else if (t1 <= 6.2e-73) {
		tmp = (-t1 / u) * (v / u);
	} else {
		tmp = -1.0 / ((t1 + u) / v);
	}
	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) :: tmp
    t_1 = -v / (t1 + u)
    if (t1 <= (-1.3d+25)) then
        tmp = t_1
    else if (t1 <= (-3.9d-20)) then
        tmp = ((t1 * v) / u) / (t1 - u)
    else if (t1 <= (-8d-45)) then
        tmp = t_1
    else if (t1 <= 6.2d-73) then
        tmp = (-t1 / u) * (v / u)
    else
        tmp = (-1.0d0) / ((t1 + u) / v)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = -v / (t1 + u);
	double tmp;
	if (t1 <= -1.3e+25) {
		tmp = t_1;
	} else if (t1 <= -3.9e-20) {
		tmp = ((t1 * v) / u) / (t1 - u);
	} else if (t1 <= -8e-45) {
		tmp = t_1;
	} else if (t1 <= 6.2e-73) {
		tmp = (-t1 / u) * (v / u);
	} else {
		tmp = -1.0 / ((t1 + u) / v);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = -v / (t1 + u)
	tmp = 0
	if t1 <= -1.3e+25:
		tmp = t_1
	elif t1 <= -3.9e-20:
		tmp = ((t1 * v) / u) / (t1 - u)
	elif t1 <= -8e-45:
		tmp = t_1
	elif t1 <= 6.2e-73:
		tmp = (-t1 / u) * (v / u)
	else:
		tmp = -1.0 / ((t1 + u) / v)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(-v) / Float64(t1 + u))
	tmp = 0.0
	if (t1 <= -1.3e+25)
		tmp = t_1;
	elseif (t1 <= -3.9e-20)
		tmp = Float64(Float64(Float64(t1 * v) / u) / Float64(t1 - u));
	elseif (t1 <= -8e-45)
		tmp = t_1;
	elseif (t1 <= 6.2e-73)
		tmp = Float64(Float64(Float64(-t1) / u) * Float64(v / u));
	else
		tmp = Float64(-1.0 / Float64(Float64(t1 + u) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = -v / (t1 + u);
	tmp = 0.0;
	if (t1 <= -1.3e+25)
		tmp = t_1;
	elseif (t1 <= -3.9e-20)
		tmp = ((t1 * v) / u) / (t1 - u);
	elseif (t1 <= -8e-45)
		tmp = t_1;
	elseif (t1 <= 6.2e-73)
		tmp = (-t1 / u) * (v / u);
	else
		tmp = -1.0 / ((t1 + u) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -1.3e+25], t$95$1, If[LessEqual[t1, -3.9e-20], N[(N[(N[(t1 * v), $MachinePrecision] / u), $MachinePrecision] / N[(t1 - u), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -8e-45], t$95$1, If[LessEqual[t1, 6.2e-73], N[(N[((-t1) / u), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(t1 + u), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -1.2999999999999999e25 or -3.90000000000000007e-20 < t1 < -7.99999999999999987e-45

   1. Initial program 59.7%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around inf 86.7%

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

   if -1.2999999999999999e25 < t1 < -3.90000000000000007e-20

   1. Initial program 58.4%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

      1. associate-*r/ 58.4%

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

      2. frac-times 99.8%

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

      3. frac-2neg 99.8%

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

      4. remove-double-neg 99.8%

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

      5. associate-*l/ 99.7%

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

      6. distribute-neg-in 99.7%

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

      7. add-sqr-sqrt 99.5%

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

      8. sqrt-unprod 99.7%

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

      9. sqr-neg 99.7%

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

      10. sqrt-unprod 0.0%

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

      11. add-sqr-sqrt 88.8%

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

      12. sub-neg 88.8%

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

   6. Applied egg-rr 88.8%

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

   7. Taylor expanded in t1 around 0 89.1%

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

   if -7.99999999999999987e-45 < t1 < 6.19999999999999938e-73

   1. Initial program 80.6%

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

      1. times-frac 95.3%

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

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around 0 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in t1 around 0 81.4%

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

   if 6.19999999999999938e-73 < t1

   1. Initial program 74.8%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.1%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t1 around inf 80.5%

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

      1. associate-/r/ 80.9%

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

   9. Applied egg-rr 80.9%

      \[\leadsto -1 \cdot \color{blue}{\frac{1}{\frac{t1 + u}{v}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq -3.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{\frac{t1 \cdot v}{u}}{t1 - u}\\ \mathbf{elif}\;t1 \leq -8 \cdot 10^{-45}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq 6.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{-t1}{u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t1 + u}{v}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq 6.2 \cdot 10^{+73}:\\ \;\;\;\;t1 \cdot \frac{-v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t1 + u}{v}}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -3.6e+98)
   (/ (- v) (+ t1 u))
   (if (<= t1 6.2e+73)
     (* t1 (/ (- v) (* (+ t1 u) (+ t1 u))))
     (/ -1.0 (/ (+ t1 u) v)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -3.6e+98) {
		tmp = -v / (t1 + u);
	} else if (t1 <= 6.2e+73) {
		tmp = t1 * (-v / ((t1 + u) * (t1 + u)));
	} else {
		tmp = -1.0 / ((t1 + u) / v);
	}
	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) :: tmp
    if (t1 <= (-3.6d+98)) then
        tmp = -v / (t1 + u)
    else if (t1 <= 6.2d+73) then
        tmp = t1 * (-v / ((t1 + u) * (t1 + u)))
    else
        tmp = (-1.0d0) / ((t1 + u) / v)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -3.6e+98) {
		tmp = -v / (t1 + u);
	} else if (t1 <= 6.2e+73) {
		tmp = t1 * (-v / ((t1 + u) * (t1 + u)));
	} else {
		tmp = -1.0 / ((t1 + u) / v);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -3.6e+98:
		tmp = -v / (t1 + u)
	elif t1 <= 6.2e+73:
		tmp = t1 * (-v / ((t1 + u) * (t1 + u)))
	else:
		tmp = -1.0 / ((t1 + u) / v)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -3.6e+98)
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	elseif (t1 <= 6.2e+73)
		tmp = Float64(t1 * Float64(Float64(-v) / Float64(Float64(t1 + u) * Float64(t1 + u))));
	else
		tmp = Float64(-1.0 / Float64(Float64(t1 + u) / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -3.6e+98)
		tmp = -v / (t1 + u);
	elseif (t1 <= 6.2e+73)
		tmp = t1 * (-v / ((t1 + u) * (t1 + u)));
	else
		tmp = -1.0 / ((t1 + u) / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -3.6e+98], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 6.2e+73], N[(t1 * N[((-v) / N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(t1 + u), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -3.59999999999999981e98

   1. Initial program 47.8%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around inf 89.1%

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

   if -3.59999999999999981e98 < t1 < 6.1999999999999999e73

   1. Initial program 82.9%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   if 6.1999999999999999e73 < t1

   1. Initial program 61.0%

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

      1. times-frac 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 98.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t1 around inf 91.8%

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

      1. associate-/r/ 92.3%

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

   9. Applied egg-rr 92.3%

      \[\leadsto -1 \cdot \color{blue}{\frac{1}{\frac{t1 + u}{v}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq 6.2 \cdot 10^{+73}:\\ \;\;\;\;t1 \cdot \frac{-v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t1 + u}{v}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -7.4 \cdot 10^{-56} \lor \neg \left(u \leq 1.02 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t1 \cdot \frac{v}{t1 + u}}{t1 - u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -7.4e-56) (not (<= u 1.02e-28)))
   (/ (* t1 (/ v (+ t1 u))) (- t1 u))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -7.4e-56) || !(u <= 1.02e-28)) {
		tmp = (t1 * (v / (t1 + u))) / (t1 - u);
	} else {
		tmp = -v / t1;
	}
	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) :: tmp
    if ((u <= (-7.4d-56)) .or. (.not. (u <= 1.02d-28))) then
        tmp = (t1 * (v / (t1 + u))) / (t1 - u)
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -7.4e-56) || !(u <= 1.02e-28)) {
		tmp = (t1 * (v / (t1 + u))) / (t1 - u);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -7.4e-56) or not (u <= 1.02e-28):
		tmp = (t1 * (v / (t1 + u))) / (t1 - u)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -7.4e-56) || !(u <= 1.02e-28))
		tmp = Float64(Float64(t1 * Float64(v / Float64(t1 + u))) / Float64(t1 - u));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -7.4e-56) || ~((u <= 1.02e-28)))
		tmp = (t1 * (v / (t1 + u))) / (t1 - u);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -7.4e-56], N[Not[LessEqual[u, 1.02e-28]], $MachinePrecision]], N[(N[(t1 * N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t1 - u), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -7.4000000000000004e-56 or 1.01999999999999997e-28 < u

   1. Initial program 77.4%

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

      1. associate-/l* 79.6%

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

   3. Simplified 79.6%

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

      1. associate-*r/ 77.4%

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

      2. frac-times 97.9%

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

      3. frac-2neg 97.9%

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

      4. remove-double-neg 97.9%

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

      5. associate-*l/ 99.3%

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

      6. distribute-neg-in 99.3%

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

      7. add-sqr-sqrt 52.6%

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

      8. sqrt-unprod 82.5%

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

      9. sqr-neg 82.5%

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

      10. sqrt-unprod 37.3%

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

      11. add-sqr-sqrt 81.6%

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

      12. sub-neg 81.6%

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

   6. Applied egg-rr 81.6%

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

   if -7.4000000000000004e-56 < u < 1.01999999999999997e-28

   1. Initial program 65.2%

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

      1. associate-/l* 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in t1 around inf 83.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{v}{t1}} \]
   6. Step-by-step derivation

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{-v}{t1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -7.4 \cdot 10^{-56} \lor \neg \left(u \leq 1.02 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t1 \cdot \frac{v}{t1 + u}}{t1 - u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -5.2 \cdot 10^{-56} \lor \neg \left(u \leq 6.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{-t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -5.2e-56) (not (<= u 6.2e-30)))
   (* (/ v (+ t1 u)) (/ (- t1) u))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -5.2e-56) || !(u <= 6.2e-30)) {
		tmp = (v / (t1 + u)) * (-t1 / u);
	} else {
		tmp = -v / t1;
	}
	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) :: tmp
    if ((u <= (-5.2d-56)) .or. (.not. (u <= 6.2d-30))) then
        tmp = (v / (t1 + u)) * (-t1 / u)
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -5.2e-56) || !(u <= 6.2e-30)) {
		tmp = (v / (t1 + u)) * (-t1 / u);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -5.2e-56) or not (u <= 6.2e-30):
		tmp = (v / (t1 + u)) * (-t1 / u)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -5.2e-56) || !(u <= 6.2e-30))
		tmp = Float64(Float64(v / Float64(t1 + u)) * Float64(Float64(-t1) / u));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -5.2e-56) || ~((u <= 6.2e-30)))
		tmp = (v / (t1 + u)) * (-t1 / u);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -5.2e-56], N[Not[LessEqual[u, 6.2e-30]], $MachinePrecision]], N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[((-t1) / u), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -5.19999999999999994e-56 or 6.19999999999999982e-30 < u

   1. Initial program 77.4%

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

      1. times-frac 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around 0 79.5%

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

      1. associate-*r/ 79.5%

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

      2. neg-mul-1 79.5%

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

   7. Simplified 79.5%

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

   if -5.19999999999999994e-56 < u < 6.19999999999999982e-30

   1. Initial program 65.2%

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

      1. associate-/l* 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in t1 around inf 83.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{v}{t1}} \]
   6. Step-by-step derivation

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{-v}{t1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -5.2 \cdot 10^{-56} \lor \neg \left(u \leq 6.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{-t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -3.9 \cdot 10^{+133} \lor \neg \left(u \leq 1.02 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -3.9e+133) (not (<= u 1.02e+75)))
   (/ t1 (* u (/ u v)))
   (/ (- v) (+ t1 u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -3.9e+133) || !(u <= 1.02e+75)) {
		tmp = t1 / (u * (u / v));
	} else {
		tmp = -v / (t1 + u);
	}
	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) :: tmp
    if ((u <= (-3.9d+133)) .or. (.not. (u <= 1.02d+75))) then
        tmp = t1 / (u * (u / v))
    else
        tmp = -v / (t1 + u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -3.9e+133) || !(u <= 1.02e+75)) {
		tmp = t1 / (u * (u / v));
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -3.9e+133) or not (u <= 1.02e+75):
		tmp = t1 / (u * (u / v))
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -3.9e+133) || !(u <= 1.02e+75))
		tmp = Float64(t1 / Float64(u * Float64(u / v)));
	else
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -3.9e+133) || ~((u <= 1.02e+75)))
		tmp = t1 / (u * (u / v));
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -3.9e+133], N[Not[LessEqual[u, 1.02e+75]], $MachinePrecision]], N[(t1 / N[(u * N[(u / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -3.90000000000000014e133 or 1.0200000000000001e75 < u

   1. Initial program 77.6%

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

      1. times-frac 96.5%

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

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around 0 88.7%

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

      1. associate-*r/ 88.7%

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

      2. neg-mul-1 88.7%

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

   7. Simplified 88.7%

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

   8. Taylor expanded in t1 around 0 88.8%

      \[\leadsto \frac{-t1}{u} \cdot \color{blue}{\frac{v}{u}} \]
   9. Step-by-step derivation

      1. *-commutative 88.8%

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

      2. clear-num 88.7%

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

      3. frac-times 84.5%

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

      4. *-un-lft-identity 84.5%

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

      5. add-sqr-sqrt 42.4%

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

      6. sqrt-unprod 63.3%

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

      7. sqr-neg 63.3%

         \[\leadsto \frac{\sqrt{\color{blue}{t1 \cdot t1}}}{\frac{u}{v} \cdot u} \]

      8. sqrt-unprod 34.7%

         \[\leadsto \frac{\color{blue}{\sqrt{t1} \cdot \sqrt{t1}}}{\frac{u}{v} \cdot u} \]

      9. add-sqr-sqrt 68.3%

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

   10. Applied egg-rr 68.3%

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

   if -3.90000000000000014e133 < u < 1.0200000000000001e75

   1. Initial program 69.8%

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

      1. times-frac 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around inf 69.9%

      \[\leadsto \color{blue}{-1} \cdot \frac{v}{t1 + u} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -3.9 \cdot 10^{+133} \lor \neg \left(u \leq 1.02 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.4 \cdot 10^{+178} \lor \neg \left(u \leq 3.5 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.4e+178) (not (<= u 3.5e+143))) (/ v u) (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.4e+178) || !(u <= 3.5e+143)) {
		tmp = v / u;
	} else {
		tmp = -v / t1;
	}
	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) :: tmp
    if ((u <= (-1.4d+178)) .or. (.not. (u <= 3.5d+143))) then
        tmp = v / u
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.4e+178) || !(u <= 3.5e+143)) {
		tmp = v / u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.4e+178) or not (u <= 3.5e+143):
		tmp = v / u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.4e+178) || !(u <= 3.5e+143))
		tmp = Float64(v / u);
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.4e+178) || ~((u <= 3.5e+143)))
		tmp = v / u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.4e+178], N[Not[LessEqual[u, 3.5e+143]], $MachinePrecision]], N[(v / u), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.39999999999999997e178 or 3.50000000000000008e143 < u

   1. Initial program 77.8%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
   4. Add Preprocessing

   5. Taylor expanded in t1 around 0 96.4%

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

      1. associate-*r/ 96.4%

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

      2. neg-mul-1 96.4%

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

   7. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{-t1}{u}} \cdot \frac{v}{t1 + u} \]
   8. Step-by-step derivation

      1. associate-*r/ 96.3%

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

      2. frac-2neg 96.3%

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

      3. add-sqr-sqrt 51.9%

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

      4. sqrt-unprod 76.9%

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

      5. sqr-neg 76.9%

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

      6. sqrt-unprod 42.1%

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

      7. add-sqr-sqrt 77.9%

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

      8. distribute-lft-neg-out 77.9%

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

      9. distribute-frac-neg 77.9%

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

      10. *-commutative 77.9%

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

      11. add-sqr-sqrt 35.8%

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

      12. sqrt-unprod 64.1%

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

      13. sqr-neg 64.1%

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

      14. sqrt-unprod 44.4%

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

      15. add-sqr-sqrt 96.3%

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

      16. distribute-neg-in 96.3%

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

      17. add-sqr-sqrt 51.9%

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

      18. sqrt-unprod 90.5%

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

      19. sqr-neg 90.5%

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

      20. sqrt-unprod 44.6%

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

      21. add-sqr-sqrt 96.4%

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

      22. sub-neg 96.4%

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

   9. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{\frac{v \cdot \frac{t1}{u}}{t1 - u}} \]
   10. Step-by-step derivation

       1. associate-/l* 85.8%

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

   11. Simplified 85.8%

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

   12. Taylor expanded in t1 around inf 46.1%

       \[\leadsto \color{blue}{\frac{v}{u}} \]

   if -1.39999999999999997e178 < u < 3.50000000000000008e143

   1. Initial program 70.8%

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

      1. associate-/l* 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in t1 around inf 64.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{v}{t1}} \]
   6. Step-by-step derivation

      1. associate-*r/ 64.5%

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

      2. neg-mul-1 64.5%

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

   7. Simplified 64.5%

      \[\leadsto \color{blue}{\frac{-v}{t1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.4 \cdot 10^{+178} \lor \neg \left(u \leq 3.5 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{-v}{t1 + u} \end{array} \]

FPCore

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

C

double code(double u, double v, double t1) {
	return -v / (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 = -v / (t1 + u)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.4%

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

   1. times-frac 98.0%

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

3. Simplified 98.0%

   \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
4. Add Preprocessing

5. Taylor expanded in t1 around inf 61.2%

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

6. Final simplification 61.2%

   \[\leadsto \frac{-v}{t1 + u} \]
7. Add Preprocessing

Alternative 11: 17.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \frac{v}{u} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ v u))

C

double code(double u, double v, double t1) {
	return v / 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 = v / u
end function

Java

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

Python

def code(u, v, t1):
	return v / u

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.4%

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

   1. times-frac 98.0%

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

3. Simplified 98.0%

   \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}} \]
4. Add Preprocessing

5. Taylor expanded in t1 around 0 55.5%

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

   1. associate-*r/ 55.5%

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

   2. neg-mul-1 55.5%

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

7. Simplified 55.5%

   \[\leadsto \color{blue}{\frac{-t1}{u}} \cdot \frac{v}{t1 + u} \]
8. Step-by-step derivation

   1. associate-*r/ 51.7%

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

   2. frac-2neg 51.7%

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

   3. add-sqr-sqrt 25.9%

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

   4. sqrt-unprod 32.0%

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

   5. sqr-neg 32.0%

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

   6. sqrt-unprod 14.7%

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

   7. add-sqr-sqrt 31.7%

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

   8. distribute-lft-neg-out 31.7%

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

   9. distribute-frac-neg 31.7%

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

   10. *-commutative 31.7%

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

   11. add-sqr-sqrt 16.9%

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

   12. sqrt-unprod 31.0%

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

   13. sqr-neg 31.0%

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

   14. sqrt-unprod 25.7%

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

   15. add-sqr-sqrt 51.7%

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

   16. distribute-neg-in 51.7%

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

   17. add-sqr-sqrt 25.9%

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

   18. sqrt-unprod 54.2%

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

   19. sqr-neg 54.2%

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

   20. sqrt-unprod 24.6%

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

   21. add-sqr-sqrt 52.3%

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

   22. sub-neg 52.3%

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

9. Applied egg-rr 52.3%

   \[\leadsto \color{blue}{\frac{v \cdot \frac{t1}{u}}{t1 - u}} \]
10. Step-by-step derivation

    1. associate-/l* 49.4%

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

11. Simplified 49.4%

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

12. Taylor expanded in t1 around inf 18.8%

    \[\leadsto \color{blue}{\frac{v}{u}} \]

13. Final simplification 18.8%

    \[\leadsto \frac{v}{u} \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))