Rosa's DopplerBench

Percentage Accurate: 72.7% → 97.7%

Time: 11.7s

Alternatives: 19

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: 72.7% 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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.2%

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

   1. associate-/l* 74.8%

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

   2. distribute-lft-neg-out 74.8%

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

   3. distribute-rgt-neg-in 74.8%

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

   4. associate-/r* 85.4%

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

   5. distribute-neg-frac2 85.4%

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

3. Simplified 85.4%

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

   1. associate-*r/ 98.7%

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

   2. frac-2neg 98.7%

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

   3. remove-double-neg 98.7%

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

6. Applied egg-rr 98.7%

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

7. Final simplification 98.7%

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

Alternative 2: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -3.75 \cdot 10^{+81}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 5 \cdot 10^{+191}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{t1 + u}}{\left(-t1\right) - u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -3.75e+81)
   (/ v (- (- t1) (* u 2.0)))
   (if (<= t1 5e+191) (* t1 (/ (/ v (+ t1 u)) (- (- t1) u))) (/ v (- t1)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -3.75e+81) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 5e+191) {
		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 (t1 <= (-3.75d+81)) then
        tmp = v / (-t1 - (u * 2.0d0))
    else if (t1 <= 5d+191) 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 (t1 <= -3.75e+81) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 5e+191) {
		tmp = t1 * ((v / (t1 + u)) / (-t1 - u));
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -3.75e+81:
		tmp = v / (-t1 - (u * 2.0))
	elif t1 <= 5e+191:
		tmp = t1 * ((v / (t1 + u)) / (-t1 - u))
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -3.75e+81)
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	elseif (t1 <= 5e+191)
		tmp = Float64(t1 * Float64(Float64(v / Float64(t1 + u)) / Float64(Float64(-t1) - u)));
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -3.75e+81)
		tmp = v / (-t1 - (u * 2.0));
	elseif (t1 <= 5e+191)
		tmp = t1 * ((v / (t1 + u)) / (-t1 - u));
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -3.75e+81], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 5e+191], N[(t1 * N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] / N[((-t1) - u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -3.74999999999999986e81

   1. Initial program 64.0%

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

      1. associate-/l* 65.0%

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

      2. distribute-lft-neg-out 65.0%

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

      3. distribute-rgt-neg-in 65.0%

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

      4. associate-/r* 85.5%

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

      5. distribute-neg-frac2 85.5%

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

   3. Simplified 85.5%

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

      1. associate-*r/ 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. associate-*l/ 100.0%

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

      6. frac-2neg 100.0%

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

      7. clear-num 100.0%

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

      8. frac-times 100.0%

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

      9. *-un-lft-identity 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. sub-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in u around 0 96.5%

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

      1. *-commutative 96.5%

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

   9. Simplified 96.5%

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

   if -3.74999999999999986e81 < t1 < 5.0000000000000002e191

   1. Initial program 80.7%

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

      1. associate-/l* 84.0%

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

      2. distribute-lft-neg-out 84.0%

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

      3. distribute-rgt-neg-in 84.0%

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

      4. associate-/r* 91.2%

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

      5. distribute-neg-frac2 91.2%

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

   3. Simplified 91.2%

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

   if 5.0000000000000002e191 < t1

   1. Initial program 41.0%

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

      1. associate-/l* 42.6%

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

      2. distribute-lft-neg-out 42.6%

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

      3. distribute-rgt-neg-in 42.6%

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

      4. associate-/r* 54.8%

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

      5. distribute-neg-frac2 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in t1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -3.75 \cdot 10^{+81}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 5 \cdot 10^{+191}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{t1 + u}}{\left(-t1\right) - u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{-111} \lor \neg \left(t1 \leq 9.5 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{v}{u \cdot \left(\left(-t1\right) - u\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -1.3e-111) (not (<= t1 9.5e-104)))
   (/ v (- (- t1) (* u 2.0)))
   (* t1 (/ v (* u (- (- t1) u))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.3e-111) || !(t1 <= 9.5e-104)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * (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 ((t1 <= (-1.3d-111)) .or. (.not. (t1 <= 9.5d-104))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = t1 * (v / (u * (-t1 - u)))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.3e-111) || !(t1 <= 9.5e-104)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * (v / (u * (-t1 - u)));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -1.3e-111) or not (t1 <= 9.5e-104):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = t1 * (v / (u * (-t1 - u)))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -1.3e-111) || !(t1 <= 9.5e-104))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(t1 * Float64(v / Float64(u * Float64(Float64(-t1) - u))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -1.3e-111) || ~((t1 <= 9.5e-104)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = t1 * (v / (u * (-t1 - u)));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -1.3e-111], N[Not[LessEqual[t1, 9.5e-104]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t1 * N[(v / N[(u * N[((-t1) - u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -1.29999999999999991e-111 or 9.5000000000000002e-104 < t1

   1. Initial program 69.3%

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

      1. associate-/l* 70.9%

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

      2. distribute-lft-neg-out 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. associate-/r* 84.1%

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

      5. distribute-neg-frac2 84.1%

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

   3. Simplified 84.1%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 97.7%

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

      9. *-un-lft-identity 97.7%

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

      10. +-commutative 97.7%

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

      11. distribute-neg-in 97.7%

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

      12. sub-neg 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in u around 0 88.0%

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

      1. *-commutative 88.0%

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

   9. Simplified 88.0%

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

   if -1.29999999999999991e-111 < t1 < 9.5000000000000002e-104

   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. associate-/l* 82.4%

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

      2. distribute-lft-neg-out 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 84.5%

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

   6. Taylor expanded in v around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. neg-mul-1 81.1%

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

   8. Simplified 81.1%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{-111} \lor \neg \left(t1 \leq 9.5 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{v}{u \cdot \left(\left(-t1\right) - u\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -6.8 \cdot 10^{-108} \lor \neg \left(t1 \leq 8.5 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{\left(-t1\right) - u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -6.8e-108) (not (<= t1 8.5e-104)))
   (/ v (- (- t1) (* u 2.0)))
   (* t1 (/ (/ v u) (- (- t1) u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -6.8e-108) || !(t1 <= 8.5e-104)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * ((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 ((t1 <= (-6.8d-108)) .or. (.not. (t1 <= 8.5d-104))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = t1 * ((v / u) / (-t1 - u))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -6.8e-108) || !(t1 <= 8.5e-104)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * ((v / u) / (-t1 - u));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -6.8e-108) or not (t1 <= 8.5e-104):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = t1 * ((v / u) / (-t1 - u))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -6.8e-108) || !(t1 <= 8.5e-104))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(t1 * Float64(Float64(v / u) / Float64(Float64(-t1) - u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -6.8e-108) || ~((t1 <= 8.5e-104)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = t1 * ((v / u) / (-t1 - u));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -6.8e-108], N[Not[LessEqual[t1, 8.5e-104]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t1 * N[(N[(v / u), $MachinePrecision] / N[((-t1) - u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -6.80000000000000004e-108 or 8.50000000000000007e-104 < t1

   1. Initial program 69.3%

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

      1. associate-/l* 70.9%

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

      2. distribute-lft-neg-out 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. associate-/r* 84.1%

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

      5. distribute-neg-frac2 84.1%

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

   3. Simplified 84.1%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 97.7%

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

      9. *-un-lft-identity 97.7%

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

      10. +-commutative 97.7%

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

      11. distribute-neg-in 97.7%

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

      12. sub-neg 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in u around 0 88.0%

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

      1. *-commutative 88.0%

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

   9. Simplified 88.0%

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

   if -6.80000000000000004e-108 < t1 < 8.50000000000000007e-104

   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. associate-/l* 82.4%

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

      2. distribute-lft-neg-out 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 84.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -6.8 \cdot 10^{-108} \lor \neg \left(t1 \leq 8.5 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{\left(-t1\right) - u}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -9.5 \cdot 10^{-110} \lor \neg \left(t1 \leq 1.15 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -9.5e-110) (not (<= t1 1.15e-101)))
   (/ v (- (- t1) (* u 2.0)))
   (* (/ (- t1) (+ t1 u)) (/ v u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -9.5e-110) || !(t1 <= 1.15e-101)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (-t1 / (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 <= (-9.5d-110)) .or. (.not. (t1 <= 1.15d-101))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (-t1 / (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 <= -9.5e-110) || !(t1 <= 1.15e-101)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (-t1 / (t1 + u)) * (v / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -9.5e-110) or not (t1 <= 1.15e-101):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (-t1 / (t1 + u)) * (v / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -9.5e-110) || !(t1 <= 1.15e-101))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(Float64(-t1) / Float64(t1 + u)) * Float64(v / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -9.5e-110) || ~((t1 <= 1.15e-101)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (-t1 / (t1 + u)) * (v / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -9.5e-110], N[Not[LessEqual[t1, 1.15e-101]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-t1) / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -9.50000000000000004e-110 or 1.15e-101 < t1

   1. Initial program 69.3%

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

      1. associate-/l* 70.9%

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

      2. distribute-lft-neg-out 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. associate-/r* 84.1%

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

      5. distribute-neg-frac2 84.1%

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

   3. Simplified 84.1%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 97.7%

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

      9. *-un-lft-identity 97.7%

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

      10. +-commutative 97.7%

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

      11. distribute-neg-in 97.7%

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

      12. sub-neg 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in u around 0 88.0%

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

      1. *-commutative 88.0%

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

   9. Simplified 88.0%

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

   if -9.50000000000000004e-110 < t1 < 1.15e-101

   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 95.5%

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

      2. distribute-frac-neg 95.5%

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

      3. distribute-neg-frac2 95.5%

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

      4. +-commutative 95.5%

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

      5. distribute-neg-in 95.5%

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

      6. unsub-neg 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t1 around 0 85.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -9.5 \cdot 10^{-110} \lor \neg \left(t1 \leq 1.15 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.8 \cdot 10^{-110} \lor \neg \left(t1 \leq 2 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{\left(-t1\right) - u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -2.8e-110) (not (<= t1 2e-101)))
   (/ v (- (- t1) (* u 2.0)))
   (/ (/ t1 (/ u v)) (- (- t1) u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -2.8e-110) || !(t1 <= 2e-101)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (t1 / (u / 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 ((t1 <= (-2.8d-110)) .or. (.not. (t1 <= 2d-101))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (t1 / (u / v)) / (-t1 - u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -2.8e-110) || !(t1 <= 2e-101)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (t1 / (u / v)) / (-t1 - u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -2.8e-110) or not (t1 <= 2e-101):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (t1 / (u / v)) / (-t1 - u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -2.8e-110) || !(t1 <= 2e-101))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(t1 / Float64(u / v)) / Float64(Float64(-t1) - u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -2.8e-110) || ~((t1 <= 2e-101)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (t1 / (u / v)) / (-t1 - u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -2.8e-110], N[Not[LessEqual[t1, 2e-101]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t1 / N[(u / v), $MachinePrecision]), $MachinePrecision] / N[((-t1) - u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -2.8e-110 or 2.0000000000000001e-101 < t1

   1. Initial program 69.3%

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

      1. associate-/l* 70.9%

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

      2. distribute-lft-neg-out 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. associate-/r* 84.1%

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

      5. distribute-neg-frac2 84.1%

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

   3. Simplified 84.1%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 97.7%

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

      9. *-un-lft-identity 97.7%

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

      10. +-commutative 97.7%

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

      11. distribute-neg-in 97.7%

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

      12. sub-neg 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in u around 0 88.0%

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

      1. *-commutative 88.0%

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

   9. Simplified 88.0%

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

   if -2.8e-110 < t1 < 2.0000000000000001e-101

   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. associate-/l* 82.4%

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

      2. distribute-lft-neg-out 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

      1. associate-*r/ 96.3%

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

      2. frac-2neg 96.3%

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

      3. remove-double-neg 96.3%

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

   6. Applied egg-rr 96.3%

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

      1. clear-num 96.3%

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

      2. un-div-inv 96.4%

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

   8. Applied egg-rr 96.4%

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

   9. Taylor expanded in t1 around 0 86.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.8 \cdot 10^{-110} \lor \neg \left(t1 \leq 2 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{\left(-t1\right) - u}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.82 \cdot 10^{-177} \lor \neg \left(t1 \leq 1.45 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -1.82e-177) (not (<= t1 1.45e-147)))
   (/ v (- (- t1) (* u 2.0)))
   (* t1 (/ (/ v u) (+ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.82e-177) || !(t1 <= 1.45e-147)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * ((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 ((t1 <= (-1.82d-177)) .or. (.not. (t1 <= 1.45d-147))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = t1 * ((v / u) / (t1 + u))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.82e-177) || !(t1 <= 1.45e-147)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * ((v / u) / (t1 + u));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -1.82e-177) or not (t1 <= 1.45e-147):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = t1 * ((v / u) / (t1 + u))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -1.82e-177) || !(t1 <= 1.45e-147))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(t1 * Float64(Float64(v / u) / Float64(t1 + u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -1.82e-177) || ~((t1 <= 1.45e-147)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = t1 * ((v / u) / (t1 + u));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -1.82e-177], N[Not[LessEqual[t1, 1.45e-147]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t1 * N[(N[(v / u), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -1.81999999999999993e-177 or 1.4500000000000001e-147 < t1

   1. Initial program 71.3%

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

      1. associate-/l* 71.8%

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

      2. distribute-lft-neg-out 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-/r* 84.4%

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

      5. distribute-neg-frac2 84.4%

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

   3. Simplified 84.4%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 96.4%

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

      9. *-un-lft-identity 96.4%

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

      10. +-commutative 96.4%

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

      11. distribute-neg-in 96.4%

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

      12. sub-neg 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in u around 0 84.8%

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

      1. *-commutative 84.8%

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

   9. Simplified 84.8%

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

   if -1.81999999999999993e-177 < t1 < 1.4500000000000001e-147

   1. Initial program 74.5%

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

      1. associate-/l* 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 83.7%

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

      1. distribute-frac-neg2 83.7%

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

      2. distribute-frac-neg 83.7%

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

      3. associate-*r/ 86.2%

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

      4. distribute-neg-frac2 86.2%

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

      5. add-sqr-sqrt 52.2%

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

      6. sqrt-unprod 68.5%

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

      7. sqr-neg 68.5%

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

      8. sqrt-unprod 20.4%

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

      9. add-sqr-sqrt 50.8%

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

   7. Applied egg-rr 50.8%

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

      1. associate-/l* 50.4%

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

   9. Simplified 50.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.82 \cdot 10^{-177} \lor \neg \left(t1 \leq 1.45 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -5.8 \cdot 10^{-178} \lor \neg \left(t1 \leq 2.8 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;v \cdot \frac{t1}{u \cdot \left(t1 + u\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -5.8e-178) (not (<= t1 2.8e-104)))
   (/ v (- (- t1) (* u 2.0)))
   (* v (/ t1 (* u (+ t1 u))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -5.8e-178) || !(t1 <= 2.8e-104)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = v * (t1 / (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 ((t1 <= (-5.8d-178)) .or. (.not. (t1 <= 2.8d-104))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = v * (t1 / (u * (t1 + u)))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -5.8e-178) || !(t1 <= 2.8e-104)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = v * (t1 / (u * (t1 + u)));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -5.8e-178) or not (t1 <= 2.8e-104):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = v * (t1 / (u * (t1 + u)))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -5.8e-178) || !(t1 <= 2.8e-104))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(v * Float64(t1 / Float64(u * Float64(t1 + u))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -5.8e-178) || ~((t1 <= 2.8e-104)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = v * (t1 / (u * (t1 + u)));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -5.8e-178], N[Not[LessEqual[t1, 2.8e-104]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v * N[(t1 / N[(u * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -5.7999999999999995e-178 or 2.8e-104 < t1

   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. associate-/l* 71.6%

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

      2. distribute-lft-neg-out 71.6%

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

      3. distribute-rgt-neg-in 71.6%

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

      4. associate-/r* 84.3%

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

      5. distribute-neg-frac2 84.3%

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

   3. Simplified 84.3%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 97.3%

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

      9. *-un-lft-identity 97.3%

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

      10. +-commutative 97.3%

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

      11. distribute-neg-in 97.3%

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

      12. sub-neg 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in u around 0 86.9%

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

      1. *-commutative 86.9%

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

   9. Simplified 86.9%

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

   if -5.7999999999999995e-178 < t1 < 2.8e-104

   1. Initial program 75.8%

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

      1. associate-/l* 81.9%

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

      2. distribute-lft-neg-out 81.9%

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

      3. distribute-rgt-neg-in 81.9%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-/l/ 80.5%

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

      3. associate-*l/ 73.3%

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

      4. add-sqr-sqrt 42.6%

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

      5. sqrt-unprod 63.4%

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

      6. sqr-neg 63.4%

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

      7. sqrt-unprod 20.8%

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

      8. add-sqr-sqrt 49.4%

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

   7. Applied egg-rr 49.4%

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

      1. associate-/l* 49.3%

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

      2. *-commutative 49.3%

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

      3. *-commutative 49.3%

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

   9. Applied egg-rr 49.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -5.8 \cdot 10^{-178} \lor \neg \left(t1 \leq 2.8 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;v \cdot \frac{t1}{u \cdot \left(t1 + u\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.6 \cdot 10^{-177} \lor \neg \left(t1 \leq 7.5 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{t1}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -2.6e-177) (not (<= t1 7.5e-147)))
   (/ v (- (- t1) (* u 2.0)))
   (* (/ v (+ t1 u)) (/ t1 u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -2.6e-177) || !(t1 <= 7.5e-147)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v / (t1 + 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 ((t1 <= (-2.6d-177)) .or. (.not. (t1 <= 7.5d-147))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (v / (t1 + u)) * (t1 / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -2.6e-177) || !(t1 <= 7.5e-147)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v / (t1 + u)) * (t1 / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -2.6e-177) or not (t1 <= 7.5e-147):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (v / (t1 + u)) * (t1 / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -2.6e-177) || !(t1 <= 7.5e-147))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(v / Float64(t1 + u)) * Float64(t1 / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -2.6e-177) || ~((t1 <= 7.5e-147)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (v / (t1 + u)) * (t1 / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -2.6e-177], N[Not[LessEqual[t1, 7.5e-147]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(t1 / u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -2.6000000000000001e-177 or 7.50000000000000047e-147 < t1

   1. Initial program 71.3%

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

      1. associate-/l* 71.8%

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

      2. distribute-lft-neg-out 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-/r* 84.4%

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

      5. distribute-neg-frac2 84.4%

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

   3. Simplified 84.4%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 96.4%

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

      9. *-un-lft-identity 96.4%

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

      10. +-commutative 96.4%

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

      11. distribute-neg-in 96.4%

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

      12. sub-neg 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in u around 0 84.8%

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

      1. *-commutative 84.8%

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

   9. Simplified 84.8%

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

   if -2.6000000000000001e-177 < t1 < 7.50000000000000047e-147

   1. Initial program 74.5%

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

      1. associate-/l* 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-/l/ 80.9%

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

      3. associate-*l/ 72.9%

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

      4. add-sqr-sqrt 43.1%

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

      5. sqrt-unprod 64.8%

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

      6. sqr-neg 64.8%

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

      7. sqrt-unprod 21.6%

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

      8. add-sqr-sqrt 50.5%

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

   7. Applied egg-rr 50.5%

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

      1. times-frac 50.8%

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

   9. Applied egg-rr 50.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.6 \cdot 10^{-177} \lor \neg \left(t1 \leq 7.5 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{t1}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8.1 \cdot 10^{-178} \lor \neg \left(t1 \leq 1.45 \cdot 10^{-148}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -8.1e-178) (not (<= t1 1.45e-148)))
   (/ v (- (- t1) (* u 2.0)))
   (/ (* v (/ t1 u)) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.1e-178) || !(t1 <= 1.45e-148)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v * (t1 / u)) / 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 ((t1 <= (-8.1d-178)) .or. (.not. (t1 <= 1.45d-148))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (v * (t1 / u)) / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.1e-178) || !(t1 <= 1.45e-148)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v * (t1 / u)) / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -8.1e-178) or not (t1 <= 1.45e-148):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (v * (t1 / u)) / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -8.1e-178) || !(t1 <= 1.45e-148))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(v * Float64(t1 / u)) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -8.1e-178) || ~((t1 <= 1.45e-148)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (v * (t1 / u)) / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -8.1e-178], N[Not[LessEqual[t1, 1.45e-148]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision] / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -8.0999999999999997e-178 or 1.4499999999999999e-148 < t1

   1. Initial program 71.3%

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

      1. associate-/l* 71.8%

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

      2. distribute-lft-neg-out 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-/r* 84.4%

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

      5. distribute-neg-frac2 84.4%

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

   3. Simplified 84.4%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.9%

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

      8. frac-times 96.4%

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

      9. *-un-lft-identity 96.4%

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

      10. +-commutative 96.4%

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

      11. distribute-neg-in 96.4%

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

      12. sub-neg 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in u around 0 84.8%

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

      1. *-commutative 84.8%

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

   9. Simplified 84.8%

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

   if -8.0999999999999997e-178 < t1 < 1.4499999999999999e-148

   1. Initial program 74.5%

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

      1. associate-/l* 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 83.7%

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

   6. Taylor expanded in u around 0 12.8%

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

      1. mul-1-neg 12.8%

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

      2. associate-/r* 12.9%

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

      3. distribute-neg-frac2 12.9%

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

   8. Simplified 12.9%

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

      1. div-inv 12.9%

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

      2. associate-/l* 12.8%

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

      3. add-sqr-sqrt 9.9%

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

      4. sqrt-unprod 25.1%

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

      5. sqr-neg 25.1%

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

      6. sqrt-unprod 2.9%

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

      7. add-sqr-sqrt 15.6%

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

   10. Applied egg-rr 15.6%

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

       1. associate-/r* 15.6%

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

       2. associate-*r/ 15.6%

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

       3. *-rgt-identity 15.6%

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

   12. Simplified 15.6%

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

       1. associate-*r/ 28.8%

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

       2. *-commutative 28.8%

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

       3. associate-/r* 40.3%

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

       4. associate-*l/ 50.2%

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

       5. *-commutative 50.2%

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

   14. Applied egg-rr 50.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8.1 \cdot 10^{-178} \lor \neg \left(t1 \leq 1.45 \cdot 10^{-148}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.95 \cdot 10^{-178} \lor \neg \left(t1 \leq 2.1 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -1.95e-178) (not (<= t1 2.1e-152)))
   (/ v (- (- t1) u))
   (/ (* v (/ t1 u)) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.95e-178) || !(t1 <= 2.1e-152)) {
		tmp = v / (-t1 - u);
	} else {
		tmp = (v * (t1 / u)) / 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 ((t1 <= (-1.95d-178)) .or. (.not. (t1 <= 2.1d-152))) then
        tmp = v / (-t1 - u)
    else
        tmp = (v * (t1 / u)) / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.95e-178) || !(t1 <= 2.1e-152)) {
		tmp = v / (-t1 - u);
	} else {
		tmp = (v * (t1 / u)) / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -1.95e-178) or not (t1 <= 2.1e-152):
		tmp = v / (-t1 - u)
	else:
		tmp = (v * (t1 / u)) / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -1.95e-178) || !(t1 <= 2.1e-152))
		tmp = Float64(v / Float64(Float64(-t1) - u));
	else
		tmp = Float64(Float64(v * Float64(t1 / u)) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -1.95e-178) || ~((t1 <= 2.1e-152)))
		tmp = v / (-t1 - u);
	else
		tmp = (v * (t1 / u)) / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -1.95e-178], N[Not[LessEqual[t1, 2.1e-152]], $MachinePrecision]], N[(v / N[((-t1) - u), $MachinePrecision]), $MachinePrecision], N[(N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision] / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -1.95000000000000013e-178 or 2.09999999999999999e-152 < t1

   1. Initial program 71.3%

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

      1. associate-/l* 71.8%

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

      2. distribute-lft-neg-out 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-/r* 84.4%

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

      5. distribute-neg-frac2 84.4%

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

   3. Simplified 84.4%

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

      1. associate-*r/ 99.9%

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

      2. frac-2neg 99.9%

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

      3. remove-double-neg 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t1 around inf 84.7%

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

   if -1.95000000000000013e-178 < t1 < 2.09999999999999999e-152

   1. Initial program 74.5%

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

      1. associate-/l* 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. associate-/r* 87.8%

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

      5. distribute-neg-frac2 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t1 around 0 83.7%

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

   6. Taylor expanded in u around 0 12.8%

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

      1. mul-1-neg 12.8%

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

      2. associate-/r* 12.9%

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

      3. distribute-neg-frac2 12.9%

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

   8. Simplified 12.9%

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

      1. div-inv 12.9%

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

      2. associate-/l* 12.8%

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

      3. add-sqr-sqrt 9.9%

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

      4. sqrt-unprod 25.1%

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

      5. sqr-neg 25.1%

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

      6. sqrt-unprod 2.9%

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

      7. add-sqr-sqrt 15.6%

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

   10. Applied egg-rr 15.6%

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

       1. associate-/r* 15.6%

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

       2. associate-*r/ 15.6%

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

       3. *-rgt-identity 15.6%

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

   12. Simplified 15.6%

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

       1. associate-*r/ 28.8%

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

       2. *-commutative 28.8%

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

       3. associate-/r* 40.3%

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

       4. associate-*l/ 50.2%

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

       5. *-commutative 50.2%

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

   14. Applied egg-rr 50.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.95 \cdot 10^{-178} \lor \neg \left(t1 \leq 2.1 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+54} \lor \neg \left(u \leq 2.5 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.1e+54) (not (<= u 2.5e+142))) (/ 1.0 (/ u v)) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.1e+54) || !(u <= 2.5e+142)) {
		tmp = 1.0 / (u / v);
	} 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 <= (-2.1d+54)) .or. (.not. (u <= 2.5d+142))) then
        tmp = 1.0d0 / (u / v)
    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 <= -2.1e+54) || !(u <= 2.5e+142)) {
		tmp = 1.0 / (u / v);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.1e+54) or not (u <= 2.5e+142):
		tmp = 1.0 / (u / v)
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.1e+54) || !(u <= 2.5e+142))
		tmp = Float64(1.0 / Float64(u / v));
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.1e+54) || ~((u <= 2.5e+142)))
		tmp = 1.0 / (u / v);
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.1e+54], N[Not[LessEqual[u, 2.5e+142]], $MachinePrecision]], N[(1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2.09999999999999986e54 or 2.5000000000000001e142 < u

   1. Initial program 83.9%

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

      1. associate-/l* 84.2%

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

      2. distribute-lft-neg-out 84.2%

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

      3. distribute-rgt-neg-in 84.2%

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

      4. associate-/r* 93.3%

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

      5. distribute-neg-frac2 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t1 around 0 91.3%

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

   6. Taylor expanded in u around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. associate-/r* 49.1%

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

      3. distribute-neg-frac2 49.1%

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

   8. Simplified 49.1%

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

      1. clear-num 49.1%

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

      2. un-div-inv 49.1%

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

      3. associate-/r/ 49.5%

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

      4. add-sqr-sqrt 27.5%

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

      5. sqrt-unprod 66.8%

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

      6. sqr-neg 66.8%

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

      7. sqrt-unprod 21.9%

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

      8. add-sqr-sqrt 49.9%

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

   10. Applied egg-rr 49.9%

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

       1. *-commutative 49.9%

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

       2. associate-/r* 47.3%

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

       3. *-inverses 47.3%

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

   12. Simplified 47.3%

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

   if -2.09999999999999986e54 < u < 2.5000000000000001e142

   1. Initial program 67.6%

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

      1. associate-/l* 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. distribute-rgt-neg-in 71.1%

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

      4. associate-/r* 82.2%

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

      5. distribute-neg-frac2 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in t1 around inf 72.1%

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

      1. associate-*r/ 72.1%

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

      2. neg-mul-1 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+54} \lor \neg \left(u \leq 2.5 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{elif}\;u \leq 4.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{u}{v}}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -2.1e+54)
   (/ 1.0 (/ u v))
   (if (<= u 4.2e+143) (/ v (- t1)) (/ -1.0 (/ u v)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2.1e+54) {
		tmp = 1.0 / (u / v);
	} else if (u <= 4.2e+143) {
		tmp = v / -t1;
	} else {
		tmp = -1.0 / (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 (u <= (-2.1d+54)) then
        tmp = 1.0d0 / (u / v)
    else if (u <= 4.2d+143) then
        tmp = v / -t1
    else
        tmp = (-1.0d0) / (u / v)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2.1e+54) {
		tmp = 1.0 / (u / v);
	} else if (u <= 4.2e+143) {
		tmp = v / -t1;
	} else {
		tmp = -1.0 / (u / v);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -2.1e+54:
		tmp = 1.0 / (u / v)
	elif u <= 4.2e+143:
		tmp = v / -t1
	else:
		tmp = -1.0 / (u / v)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -2.1e+54)
		tmp = Float64(1.0 / Float64(u / v));
	elseif (u <= 4.2e+143)
		tmp = Float64(v / Float64(-t1));
	else
		tmp = Float64(-1.0 / Float64(u / v));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -2.1e+54)
		tmp = 1.0 / (u / v);
	elseif (u <= 4.2e+143)
		tmp = v / -t1;
	else
		tmp = -1.0 / (u / v);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -2.1e+54], N[(1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 4.2e+143], N[(v / (-t1)), $MachinePrecision], N[(-1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -2.09999999999999986e54

   1. Initial program 86.0%

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

      1. associate-/l* 86.1%

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

      2. distribute-lft-neg-out 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

      4. associate-/r* 95.3%

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

      5. distribute-neg-frac2 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t1 around 0 94.1%

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

   6. Taylor expanded in u around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. associate-/r* 47.8%

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

      3. distribute-neg-frac2 47.8%

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

   8. Simplified 47.8%

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

      1. clear-num 47.8%

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

      2. un-div-inv 47.8%

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

      3. associate-/r/ 48.3%

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

      4. add-sqr-sqrt 48.3%

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

      5. sqrt-unprod 60.3%

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

      6. sqr-neg 60.3%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 49.0%

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

   10. Applied egg-rr 49.0%

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

       1. *-commutative 49.0%

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

       2. associate-/r* 46.9%

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

       3. *-inverses 46.9%

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

   12. Simplified 46.9%

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

   if -2.09999999999999986e54 < u < 4.19999999999999975e143

   1. Initial program 67.6%

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

      1. associate-/l* 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. distribute-rgt-neg-in 71.1%

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

      4. associate-/r* 82.2%

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

      5. distribute-neg-frac2 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in t1 around inf 72.1%

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

      1. associate-*r/ 72.1%

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

      2. neg-mul-1 72.1%

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

   7. Simplified 72.1%

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

   if 4.19999999999999975e143 < u

   1. Initial program 81.1%

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

      1. associate-/l* 81.6%

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

      2. distribute-lft-neg-out 81.6%

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

      3. distribute-rgt-neg-in 81.6%

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

      4. associate-/r* 90.8%

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

      5. distribute-neg-frac2 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in t1 around 0 87.7%

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

   6. Taylor expanded in u around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate-/r* 50.9%

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

      3. distribute-neg-frac2 50.9%

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

   8. Simplified 50.9%

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

      1. associate-*r/ 47.9%

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

      2. distribute-frac-neg2 47.9%

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

      3. add-sqr-sqrt 47.9%

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

      4. sqrt-unprod 69.1%

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

      5. sqr-neg 69.1%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 47.8%

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

      8. associate-*r/ 50.9%

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

      9. clear-num 50.9%

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

      10. un-div-inv 50.9%

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

      11. associate-/r/ 51.0%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 75.5%

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

      14. sqr-neg 75.5%

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

      15. sqrt-unprod 51.0%

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

      16. add-sqr-sqrt 51.0%

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

   10. Applied egg-rr 51.0%

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

       1. *-commutative 51.0%

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

       2. associate-/r* 48.0%

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

       3. *-inverses 48.0%

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

   12. Simplified 48.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{elif}\;u \leq 4.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{u}{v}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+54} \lor \neg \left(u \leq 2.5 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.1e+54) (not (<= u 2.5e+175))) (/ v u) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.1e+54) || !(u <= 2.5e+175)) {
		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 <= (-2.1d+54)) .or. (.not. (u <= 2.5d+175))) 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 <= -2.1e+54) || !(u <= 2.5e+175)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.1e+54) or not (u <= 2.5e+175):
		tmp = v / u
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.1e+54) || !(u <= 2.5e+175))
		tmp = Float64(v / u);
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.1e+54) || ~((u <= 2.5e+175)))
		tmp = v / u;
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.1e+54], N[Not[LessEqual[u, 2.5e+175]], $MachinePrecision]], N[(v / u), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2.09999999999999986e54 or 2.5e175 < u

   1. Initial program 85.2%

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

      1. associate-/l* 85.4%

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

      2. distribute-lft-neg-out 85.4%

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

      3. distribute-rgt-neg-in 85.4%

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

      4. associate-/r* 92.7%

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

      5. distribute-neg-frac2 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in t1 around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/l/ 85.4%

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

      3. associate-*l/ 85.2%

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

      4. add-sqr-sqrt 52.5%

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

      5. sqrt-unprod 85.2%

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

      6. sqr-neg 85.2%

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

      7. sqrt-unprod 32.6%

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

      8. add-sqr-sqrt 79.3%

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

   7. Applied egg-rr 79.3%

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

   8. Taylor expanded in t1 around inf 48.8%

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

   if -2.09999999999999986e54 < u < 2.5e175

   1. Initial program 67.8%

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

      1. associate-/l* 71.2%

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

      2. distribute-lft-neg-out 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. associate-/r* 82.9%

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

      5. distribute-neg-frac2 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in t1 around inf 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+54} \lor \neg \left(u \leq 2.5 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2 \cdot 10^{+54}:\\ \;\;\;\;\frac{v}{u}\\ \mathbf{elif}\;u \leq 2.6 \cdot 10^{+174}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -2e+54) (/ v u) (if (<= u 2.6e+174) (/ v (- t1)) (/ (- v) u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2e+54) {
		tmp = v / u;
	} else if (u <= 2.6e+174) {
		tmp = v / -t1;
	} else {
		tmp = -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 (u <= (-2d+54)) then
        tmp = v / u
    else if (u <= 2.6d+174) then
        tmp = v / -t1
    else
        tmp = -v / u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2e+54) {
		tmp = v / u;
	} else if (u <= 2.6e+174) {
		tmp = v / -t1;
	} else {
		tmp = -v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -2e+54:
		tmp = v / u
	elif u <= 2.6e+174:
		tmp = v / -t1
	else:
		tmp = -v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -2e+54)
		tmp = Float64(v / u);
	elseif (u <= 2.6e+174)
		tmp = Float64(v / Float64(-t1));
	else
		tmp = Float64(Float64(-v) / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -2e+54)
		tmp = v / u;
	elseif (u <= 2.6e+174)
		tmp = v / -t1;
	else
		tmp = -v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -2e+54], N[(v / u), $MachinePrecision], If[LessEqual[u, 2.6e+174], N[(v / (-t1)), $MachinePrecision], N[((-v) / u), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -2.0000000000000002e54

   1. Initial program 86.0%

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

      1. associate-/l* 86.1%

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

      2. distribute-lft-neg-out 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

      4. associate-/r* 95.3%

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

      5. distribute-neg-frac2 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t1 around 0 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-/l/ 86.1%

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

      3. associate-*l/ 86.0%

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

      4. add-sqr-sqrt 83.3%

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

      5. sqrt-unprod 86.0%

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

      6. sqr-neg 86.0%

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

      7. sqrt-unprod 2.7%

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

      8. add-sqr-sqrt 76.8%

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

   7. Applied egg-rr 76.8%

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

   8. Taylor expanded in t1 around inf 46.7%

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

   if -2.0000000000000002e54 < u < 2.5999999999999999e174

   1. Initial program 67.8%

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

      1. associate-/l* 71.2%

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

      2. distribute-lft-neg-out 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. associate-/r* 82.9%

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

      5. distribute-neg-frac2 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in t1 around inf 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

   7. Simplified 70.6%

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

   if 2.5999999999999999e174 < u

   1. Initial program 83.7%

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

      1. associate-/l* 84.3%

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

      2. distribute-lft-neg-out 84.3%

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

      3. distribute-rgt-neg-in 84.3%

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

      4. associate-/r* 88.2%

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

      5. distribute-neg-frac2 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t1 around 0 88.3%

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

   6. Taylor expanded in t1 around inf 52.9%

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

      1. associate-*r/ 52.9%

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

      2. neg-mul-1 52.9%

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

   8. Simplified 52.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2 \cdot 10^{+54}:\\ \;\;\;\;\frac{v}{u}\\ \mathbf{elif}\;u \leq 2.6 \cdot 10^{+174}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 23.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -3.6 \cdot 10^{+50} \lor \neg \left(t1 \leq 3.9 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -3.6e+50) (not (<= t1 3.9e+52))) (/ v t1) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -3.6e+50) || !(t1 <= 3.9e+52)) {
		tmp = v / t1;
	} else {
		tmp = 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 <= (-3.6d+50)) .or. (.not. (t1 <= 3.9d+52))) then
        tmp = v / t1
    else
        tmp = v / u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -3.6e+50) || !(t1 <= 3.9e+52)) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -3.6e+50) or not (t1 <= 3.9e+52):
		tmp = v / t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -3.6e+50) || !(t1 <= 3.9e+52))
		tmp = Float64(v / t1);
	else
		tmp = Float64(v / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -3.6e+50) || ~((t1 <= 3.9e+52)))
		tmp = v / t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -3.6e+50], N[Not[LessEqual[t1, 3.9e+52]], $MachinePrecision]], N[(v / t1), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -3.59999999999999986e50 or 3.9e52 < t1

   1. Initial program 56.3%

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

      1. times-frac 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t1 around inf 92.4%

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

   6. Taylor expanded in u around inf 38.2%

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

   if -3.59999999999999986e50 < t1 < 3.9e52

   1. Initial program 84.9%

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

      1. associate-/l* 86.9%

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

      2. distribute-lft-neg-out 86.9%

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

      3. distribute-rgt-neg-in 86.9%

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

      4. associate-/r* 90.9%

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

      5. distribute-neg-frac2 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t1 around 0 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-/l/ 64.0%

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

      3. associate-*l/ 60.1%

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

      4. add-sqr-sqrt 31.5%

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

      5. sqrt-unprod 50.1%

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

      6. sqr-neg 50.1%

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

      7. sqrt-unprod 18.6%

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

      8. add-sqr-sqrt 38.5%

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

   7. Applied egg-rr 38.5%

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

   8. Taylor expanded in t1 around inf 19.0%

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

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -3.6 \cdot 10^{+50} \lor \neg \left(t1 \leq 3.9 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.2%

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

   1. times-frac 98.4%

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

   2. distribute-frac-neg 98.4%

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

   3. distribute-neg-frac2 98.4%

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

   4. +-commutative 98.4%

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

   5. distribute-neg-in 98.4%

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

   6. unsub-neg 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 18: 61.6% accurate, 2.0× speedup

Math

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

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(v / Float64(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 72.2%

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

   1. associate-/l* 74.8%

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

   2. distribute-lft-neg-out 74.8%

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

   3. distribute-rgt-neg-in 74.8%

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

   4. associate-/r* 85.4%

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

   5. distribute-neg-frac2 85.4%

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

3. Simplified 85.4%

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

   1. associate-*r/ 98.7%

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

   2. frac-2neg 98.7%

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

   3. remove-double-neg 98.7%

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

6. Applied egg-rr 98.7%

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

7. Taylor expanded in t1 around inf 66.8%

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

8. Final simplification 66.8%

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

Alternative 19: 14.2% accurate, 4.0× 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(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 72.2%

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

   1. times-frac 98.4%

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

   2. distribute-frac-neg 98.4%

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

   3. distribute-neg-frac2 98.4%

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

   4. +-commutative 98.4%

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

   5. distribute-neg-in 98.4%

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

   6. unsub-neg 98.4%

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

3. Simplified 98.4%

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

5. Taylor expanded in t1 around inf 61.7%

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

6. Taylor expanded in u around inf 18.2%

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

7. Final simplification 18.2%

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

Reproduce

herbie shell --seed 2024071 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))