Rosa's DopplerBench

Percentage Accurate: 72.3% → 98.0%

Time: 10.2s

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: 72.3% 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 71.1%

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

   1. times-frac 98.2%

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

3. Simplified 98.2%

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

5. Final simplification 98.2%

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

Alternative 2: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -4.9 \cdot 10^{-12} \lor \neg \left(u \leq 2.2 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t1 \cdot \frac{v}{t1 + u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -4.9e-12) (not (<= u 2.2e+77)))
   (/ (* t1 (/ v (+ t1 u))) (- u))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -4.9e-12) || !(u <= 2.2e+77)) {
		tmp = (t1 * (v / (t1 + u))) / -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 <= (-4.9d-12)) .or. (.not. (u <= 2.2d+77))) then
        tmp = (t1 * (v / (t1 + u))) / -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 <= -4.9e-12) || !(u <= 2.2e+77)) {
		tmp = (t1 * (v / (t1 + u))) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -4.9e-12) or not (u <= 2.2e+77):
		tmp = (t1 * (v / (t1 + u))) / -u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -4.9e-12) || !(u <= 2.2e+77))
		tmp = Float64(Float64(t1 * Float64(v / Float64(t1 + u))) / Float64(-u));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -4.9e-12) || ~((u <= 2.2e+77)))
		tmp = (t1 * (v / (t1 + u))) / -u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -4.9e-12], N[Not[LessEqual[u, 2.2e+77]], $MachinePrecision]], N[(N[(t1 * N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -4.89999999999999972e-12 or 2.2e77 < u

   1. Initial program 74.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   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 87.6%

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

      1. associate-*r/ 87.6%

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

      2. mul-1-neg 87.6%

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

   7. Simplified 87.6%

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

      1. frac-2neg 87.6%

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

      2. remove-double-neg 87.6%

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

      3. associate-*l/ 89.5%

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

   9. Applied egg-rr 89.5%

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

   if -4.89999999999999972e-12 < u < 2.2e77

   1. Initial program 68.5%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. neg-mul-1 79.7%

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

   7. Simplified 79.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -4.9 \cdot 10^{-12} \lor \neg \left(u \leq 2.2 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t1 \cdot \frac{v}{t1 + u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.2 \cdot 10^{-11} \lor \neg \left(u \leq 4.6 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{-v}{u} \cdot \frac{t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.2e-11) (not (<= u 4.6e+77)))
   (* (/ (- v) u) (/ t1 u))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.2e-11) || !(u <= 4.6e+77)) {
		tmp = (-v / 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 <= (-1.2d-11)) .or. (.not. (u <= 4.6d+77))) then
        tmp = (-v / 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 <= -1.2e-11) || !(u <= 4.6e+77)) {
		tmp = (-v / u) * (t1 / u);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.2e-11) or not (u <= 4.6e+77):
		tmp = (-v / u) * (t1 / u)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.2e-11) || !(u <= 4.6e+77))
		tmp = Float64(Float64(Float64(-v) / 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 <= -1.2e-11) || ~((u <= 4.6e+77)))
		tmp = (-v / u) * (t1 / u);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.2e-11], N[Not[LessEqual[u, 4.6e+77]], $MachinePrecision]], N[(N[((-v) / u), $MachinePrecision] * N[(t1 / u), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.2000000000000001e-11 or 4.5999999999999999e77 < u

   1. Initial program 73.8%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   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 87.5%

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

      1. associate-*r/ 87.5%

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

      2. mul-1-neg 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in t1 around 0 84.3%

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

   if -1.2000000000000001e-11 < u < 4.5999999999999999e77

   1. Initial program 68.7%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.2 \cdot 10^{-11} \lor \neg \left(u \leq 4.6 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{-v}{u} \cdot \frac{t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -6.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{-u}{v}}\\ \mathbf{elif}\;u \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u} \cdot \frac{t1}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -6.3e-12)
   (/ t1 (* u (/ (- u) v)))
   (if (<= u 4.8e+77) (/ (- v) t1) (* (/ (- v) u) (/ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -6.3e-12) {
		tmp = t1 / (u * (-u / v));
	} else if (u <= 4.8e+77) {
		tmp = -v / t1;
	} else {
		tmp = (-v / u) * (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 <= (-6.3d-12)) then
        tmp = t1 / (u * (-u / v))
    else if (u <= 4.8d+77) then
        tmp = -v / t1
    else
        tmp = (-v / u) * (t1 / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -6.3e-12) {
		tmp = t1 / (u * (-u / v));
	} else if (u <= 4.8e+77) {
		tmp = -v / t1;
	} else {
		tmp = (-v / u) * (t1 / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -6.3e-12:
		tmp = t1 / (u * (-u / v))
	elif u <= 4.8e+77:
		tmp = -v / t1
	else:
		tmp = (-v / u) * (t1 / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -6.3e-12)
		tmp = Float64(t1 / Float64(u * Float64(Float64(-u) / v)));
	elseif (u <= 4.8e+77)
		tmp = Float64(Float64(-v) / t1);
	else
		tmp = Float64(Float64(Float64(-v) / u) * Float64(t1 / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -6.3e-12)
		tmp = t1 / (u * (-u / v));
	elseif (u <= 4.8e+77)
		tmp = -v / t1;
	else
		tmp = (-v / u) * (t1 / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -6.3e-12], N[(t1 / N[(u * N[((-u) / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 4.8e+77], N[((-v) / t1), $MachinePrecision], N[(N[((-v) / u), $MachinePrecision] * N[(t1 / u), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -6.3000000000000002e-12

   1. Initial program 77.7%

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

      1. times-frac 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t1 around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. mul-1-neg 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t1 around 0 84.6%

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

      1. *-commutative 84.6%

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

      2. clear-num 84.5%

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

      3. frac-2neg 84.5%

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

      4. frac-times 86.3%

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

      5. *-un-lft-identity 86.3%

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

      6. remove-double-neg 86.3%

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

   10. Applied egg-rr 86.3%

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

   if -6.3000000000000002e-12 < u < 4.7999999999999997e77

   1. Initial program 68.7%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

   if 4.7999999999999997e77 < u

   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 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t1 around 0 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in t1 around 0 83.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -6.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{-u}{v}}\\ \mathbf{elif}\;u \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u} \cdot \frac{t1}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{-u}{v}}\\ \mathbf{elif}\;u \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -8.5e-12)
   (/ t1 (* u (/ (- u) v)))
   (if (<= u 4.6e+77) (/ (- v) t1) (/ (* t1 (/ v u)) (- u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -8.5e-12) {
		tmp = t1 / (u * (-u / v));
	} else if (u <= 4.6e+77) {
		tmp = -v / t1;
	} else {
		tmp = (t1 * (v / u)) / -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 <= (-8.5d-12)) then
        tmp = t1 / (u * (-u / v))
    else if (u <= 4.6d+77) then
        tmp = -v / t1
    else
        tmp = (t1 * (v / u)) / -u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -8.5e-12) {
		tmp = t1 / (u * (-u / v));
	} else if (u <= 4.6e+77) {
		tmp = -v / t1;
	} else {
		tmp = (t1 * (v / u)) / -u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -8.5e-12:
		tmp = t1 / (u * (-u / v))
	elif u <= 4.6e+77:
		tmp = -v / t1
	else:
		tmp = (t1 * (v / u)) / -u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -8.5e-12)
		tmp = Float64(t1 / Float64(u * Float64(Float64(-u) / v)));
	elseif (u <= 4.6e+77)
		tmp = Float64(Float64(-v) / t1);
	else
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -8.5e-12)
		tmp = t1 / (u * (-u / v));
	elseif (u <= 4.6e+77)
		tmp = -v / t1;
	else
		tmp = (t1 * (v / u)) / -u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -8.5e-12], N[(t1 / N[(u * N[((-u) / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 4.6e+77], N[((-v) / t1), $MachinePrecision], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -8.4999999999999997e-12

   1. Initial program 77.7%

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

      1. times-frac 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t1 around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. mul-1-neg 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t1 around 0 84.6%

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

      1. *-commutative 84.6%

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

      2. clear-num 84.5%

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

      3. frac-2neg 84.5%

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

      4. frac-times 86.3%

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

      5. *-un-lft-identity 86.3%

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

      6. remove-double-neg 86.3%

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

   10. Applied egg-rr 86.3%

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

   if -8.4999999999999997e-12 < u < 4.5999999999999999e77

   1. Initial program 68.7%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

   if 4.5999999999999999e77 < u

   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 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t1 around 0 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in t1 around 0 83.9%

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

      1. frac-2neg 83.9%

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

      2. remove-double-neg 83.9%

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

      3. associate-*l/ 86.3%

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

   10. Applied egg-rr 86.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{-u}{v}}\\ \mathbf{elif}\;u \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1}{\frac{u}{v} \cdot \left(t1 - u\right)}\\ \mathbf{elif}\;u \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -1.9e-12)
   (/ t1 (* (/ u v) (- t1 u)))
   (if (<= u 4.6e+77) (/ (- v) t1) (/ (* t1 (/ v u)) (- u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.9e-12) {
		tmp = t1 / ((u / v) * (t1 - u));
	} else if (u <= 4.6e+77) {
		tmp = -v / t1;
	} else {
		tmp = (t1 * (v / u)) / -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 <= (-1.9d-12)) then
        tmp = t1 / ((u / v) * (t1 - u))
    else if (u <= 4.6d+77) then
        tmp = -v / t1
    else
        tmp = (t1 * (v / u)) / -u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.9e-12) {
		tmp = t1 / ((u / v) * (t1 - u));
	} else if (u <= 4.6e+77) {
		tmp = -v / t1;
	} else {
		tmp = (t1 * (v / u)) / -u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -1.9e-12:
		tmp = t1 / ((u / v) * (t1 - u))
	elif u <= 4.6e+77:
		tmp = -v / t1
	else:
		tmp = (t1 * (v / u)) / -u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -1.9e-12)
		tmp = Float64(t1 / Float64(Float64(u / v) * Float64(t1 - u)));
	elseif (u <= 4.6e+77)
		tmp = Float64(Float64(-v) / t1);
	else
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -1.9e-12)
		tmp = t1 / ((u / v) * (t1 - u));
	elseif (u <= 4.6e+77)
		tmp = -v / t1;
	else
		tmp = (t1 * (v / u)) / -u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -1.9e-12], N[(t1 / N[(N[(u / v), $MachinePrecision] * N[(t1 - u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 4.6e+77], N[((-v) / t1), $MachinePrecision], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -1.89999999999999998e-12

   1. Initial program 77.7%

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

      1. times-frac 98.4%

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

   3. Simplified 98.4%

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

      1. *-commutative 98.4%

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

      2. clear-num 98.2%

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

      3. frac-2neg 98.2%

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

      4. frac-times 95.3%

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

      5. *-un-lft-identity 95.3%

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

      6. remove-double-neg 95.3%

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

      7. distribute-neg-in 95.3%

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

      8. add-sqr-sqrt 60.7%

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

      9. sqrt-unprod 87.7%

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

      10. sqr-neg 87.7%

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

      11. sqrt-unprod 33.3%

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

      12. add-sqr-sqrt 87.6%

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

      13. sub-neg 87.6%

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

   6. Applied egg-rr 87.6%

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

   7. Taylor expanded in t1 around 0 87.6%

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

   if -1.89999999999999998e-12 < u < 4.5999999999999999e77

   1. Initial program 68.7%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

   if 4.5999999999999999e77 < u

   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 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t1 around 0 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in t1 around 0 83.9%

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

      1. frac-2neg 83.9%

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

      2. remove-double-neg 83.9%

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

      3. associate-*l/ 86.3%

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

   10. Applied egg-rr 86.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1}{\frac{u}{v} \cdot \left(t1 - u\right)}\\ \mathbf{elif}\;u \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -3 \cdot 10^{-11}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{-t1}{u}\\ \mathbf{elif}\;u \leq 5 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -3e-11)
   (* (/ v (+ t1 u)) (/ (- t1) u))
   (if (<= u 5e+77) (/ (- v) t1) (/ (* t1 (/ v u)) (- u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -3e-11) {
		tmp = (v / (t1 + u)) * (-t1 / u);
	} else if (u <= 5e+77) {
		tmp = -v / t1;
	} else {
		tmp = (t1 * (v / u)) / -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 <= (-3d-11)) then
        tmp = (v / (t1 + u)) * (-t1 / u)
    else if (u <= 5d+77) then
        tmp = -v / t1
    else
        tmp = (t1 * (v / u)) / -u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -3e-11) {
		tmp = (v / (t1 + u)) * (-t1 / u);
	} else if (u <= 5e+77) {
		tmp = -v / t1;
	} else {
		tmp = (t1 * (v / u)) / -u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -3e-11:
		tmp = (v / (t1 + u)) * (-t1 / u)
	elif u <= 5e+77:
		tmp = -v / t1
	else:
		tmp = (t1 * (v / u)) / -u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -3e-11)
		tmp = Float64(Float64(v / Float64(t1 + u)) * Float64(Float64(-t1) / u));
	elseif (u <= 5e+77)
		tmp = Float64(Float64(-v) / t1);
	else
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -3e-11)
		tmp = (v / (t1 + u)) * (-t1 / u);
	elseif (u <= 5e+77)
		tmp = -v / t1;
	else
		tmp = (t1 * (v / u)) / -u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -3e-11], N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[((-t1) / u), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 5e+77], N[((-v) / t1), $MachinePrecision], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -3e-11

   1. Initial program 77.7%

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

      1. times-frac 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t1 around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. mul-1-neg 89.5%

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

   7. Simplified 89.5%

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

   if -3e-11 < u < 5.00000000000000004e77

   1. Initial program 68.7%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

   if 5.00000000000000004e77 < u

   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 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t1 around 0 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in t1 around 0 83.9%

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

      1. frac-2neg 83.9%

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

      2. remove-double-neg 83.9%

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

      3. associate-*l/ 86.3%

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

   10. Applied egg-rr 86.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -3 \cdot 10^{-11}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{-t1}{u}\\ \mathbf{elif}\;u \leq 5 \cdot 10^{+77}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.05 \cdot 10^{+65} \lor \neg \left(u \leq 3 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t1}{\frac{u}{\frac{v}{u}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.05e+65) (not (<= u 3e+77)))
   (/ t1 (/ u (/ v u)))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.05e+65) || !(u <= 3e+77)) {
		tmp = t1 / (u / (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 <= (-2.05d+65)) .or. (.not. (u <= 3d+77))) then
        tmp = t1 / (u / (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 <= -2.05e+65) || !(u <= 3e+77)) {
		tmp = t1 / (u / (v / u));
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.05e+65) or not (u <= 3e+77):
		tmp = t1 / (u / (v / u))
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.05e+65) || !(u <= 3e+77))
		tmp = Float64(t1 / Float64(u / 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 <= -2.05e+65) || ~((u <= 3e+77)))
		tmp = t1 / (u / (v / u));
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.05e+65], N[Not[LessEqual[u, 3e+77]], $MachinePrecision]], N[(t1 / N[(u / N[(v / u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2.0500000000000001e65 or 2.9999999999999998e77 < u

   1. Initial program 73.8%

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

      1. times-frac 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t1 around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. mul-1-neg 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in t1 around 0 85.6%

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

      1. associate-*l/ 87.6%

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

      2. associate-/l* 86.1%

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

      3. add-sqr-sqrt 52.4%

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

      4. sqrt-unprod 62.7%

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

      5. sqr-neg 62.7%

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

      6. sqrt-unprod 23.5%

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

      7. add-sqr-sqrt 61.0%

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

   10. Applied egg-rr 61.0%

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

   if -2.0500000000000001e65 < u < 2.9999999999999998e77

   1. Initial program 68.9%

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

      1. times-frac 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t1 around inf 77.4%

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

      1. associate-*r/ 77.4%

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

      2. neg-mul-1 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.05 \cdot 10^{+65} \lor \neg \left(u \leq 3 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t1}{\frac{u}{\frac{v}{u}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2 \cdot 10^{+104} \lor \neg \left(u \leq 4.5 \cdot 10^{+218}\right):\\ \;\;\;\;\frac{v}{u} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2e+104) (not (<= u 4.5e+218))) (* (/ v u) -0.5) (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2e+104) || !(u <= 4.5e+218)) {
		tmp = (v / u) * -0.5;
	} 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 <= (-2d+104)) .or. (.not. (u <= 4.5d+218))) then
        tmp = (v / u) * (-0.5d0)
    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 <= -2e+104) || !(u <= 4.5e+218)) {
		tmp = (v / u) * -0.5;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2e+104) or not (u <= 4.5e+218):
		tmp = (v / u) * -0.5
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2e+104) || !(u <= 4.5e+218))
		tmp = Float64(Float64(v / u) * -0.5);
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2e+104) || ~((u <= 4.5e+218)))
		tmp = (v / u) * -0.5;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2e+104], N[Not[LessEqual[u, 4.5e+218]], $MachinePrecision]], N[(N[(v / u), $MachinePrecision] * -0.5), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2e104 or 4.50000000000000008e218 < u

   1. Initial program 72.7%

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

      1. associate-/r* 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-/l* 98.5%

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

      4. associate-/l/ 82.7%

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

      5. +-commutative 82.7%

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

      6. remove-double-neg 82.7%

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

      7. unsub-neg 82.7%

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

      8. div-sub 82.8%

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

      9. sub-neg 82.8%

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

      10. *-inverses 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in t1 around inf 44.0%

      \[\leadsto \frac{v}{\color{blue}{-2 \cdot u + -1 \cdot t1}} \]
   6. Step-by-step derivation

      1. mul-1-neg 44.0%

         \[\leadsto \frac{v}{-2 \cdot u + \color{blue}{\left(-t1\right)}} \]

      2. unsub-neg 44.0%

         \[\leadsto \frac{v}{\color{blue}{-2 \cdot u - t1}} \]

      3. *-commutative 44.0%

         \[\leadsto \frac{v}{\color{blue}{u \cdot -2} - t1} \]

   7. Simplified 44.0%

      \[\leadsto \frac{v}{\color{blue}{u \cdot -2 - t1}} \]

   8. Taylor expanded in u around inf 38.7%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{v}{u}} \]

   if -2e104 < u < 4.50000000000000008e218

   1. Initial program 70.5%

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

      1. times-frac 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t1 around inf 65.1%

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

      1. associate-*r/ 65.1%

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

      2. neg-mul-1 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2 \cdot 10^{+104} \lor \neg \left(u \leq 4.5 \cdot 10^{+218}\right):\\ \;\;\;\;\frac{v}{u} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2 \cdot 10^{+104} \lor \neg \left(u \leq 1.85 \cdot 10^{+217}\right):\\ \;\;\;\;\frac{-v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2e+104) (not (<= u 1.85e+217))) (/ (- v) u) (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2e+104) || !(u <= 1.85e+217)) {
		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 <= (-2d+104)) .or. (.not. (u <= 1.85d+217))) 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 <= -2e+104) || !(u <= 1.85e+217)) {
		tmp = -v / u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2e+104) or not (u <= 1.85e+217):
		tmp = -v / u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2e+104) || !(u <= 1.85e+217))
		tmp = Float64(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 <= -2e+104) || ~((u <= 1.85e+217)))
		tmp = -v / u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2e+104], N[Not[LessEqual[u, 1.85e+217]], $MachinePrecision]], N[((-v) / u), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2e104 or 1.85000000000000005e217 < u

   1. Initial program 72.7%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t1 around 0 92.3%

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

      1. associate-*r/ 92.3%

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

      2. mul-1-neg 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in t1 around inf 38.7%

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

      1. associate-*r/ 38.7%

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

      2. neg-mul-1 38.7%

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

   10. Simplified 38.7%

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

   if -2e104 < u < 1.85000000000000005e217

   1. Initial program 70.5%

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

      1. times-frac 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t1 around inf 65.1%

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

      1. associate-*r/ 65.1%

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

      2. neg-mul-1 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2 \cdot 10^{+104} \lor \neg \left(u \leq 1.85 \cdot 10^{+217}\right):\\ \;\;\;\;\frac{-v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.8% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.1%

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

   1. times-frac 98.2%

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

3. Simplified 98.2%

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

5. Taylor expanded in t1 around inf 51.8%

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

   1. associate-*r/ 51.8%

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

   2. neg-mul-1 51.8%

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

7. Simplified 51.8%

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

8. Final simplification 51.8%

   \[\leadsto \frac{-v}{t1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))