Rosa's DopplerBench

Percentage Accurate: 72.7% → 97.9%

Time: 8.1s

Alternatives: 13

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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. times-frac 98.5%

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

3. Simplified 98.5%

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

4. Final simplification 98.5%

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

Alternative 2: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{u} \cdot \frac{-t1}{u}\\ t_2 := \frac{v}{u \cdot -2 - t1}\\ \mathbf{if}\;t1 \leq -1600000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t1 \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq -1.22 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* (/ v u) (/ (- t1) u))) (t_2 (/ v (- (* u -2.0) t1))))
   (if (<= t1 -1600000.0)
     t_2
     (if (<= t1 -2.3e-28)
       t_1
       (if (<= t1 -1.22e-67) t_2 (if (<= t1 5.6e+164) t_1 (/ (- v) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = (v / u) * (-t1 / u);
	double t_2 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -1600000.0) {
		tmp = t_2;
	} else if (t1 <= -2.3e-28) {
		tmp = t_1;
	} else if (t1 <= -1.22e-67) {
		tmp = t_2;
	} else if (t1 <= 5.6e+164) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (v / u) * (-t1 / u)
    t_2 = v / ((u * (-2.0d0)) - t1)
    if (t1 <= (-1600000.0d0)) then
        tmp = t_2
    else if (t1 <= (-2.3d-28)) then
        tmp = t_1
    else if (t1 <= (-1.22d-67)) then
        tmp = t_2
    else if (t1 <= 5.6d+164) then
        tmp = t_1
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = (v / u) * (-t1 / u);
	double t_2 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -1600000.0) {
		tmp = t_2;
	} else if (t1 <= -2.3e-28) {
		tmp = t_1;
	} else if (t1 <= -1.22e-67) {
		tmp = t_2;
	} else if (t1 <= 5.6e+164) {
		tmp = t_1;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = (v / u) * (-t1 / u)
	t_2 = v / ((u * -2.0) - t1)
	tmp = 0
	if t1 <= -1600000.0:
		tmp = t_2
	elif t1 <= -2.3e-28:
		tmp = t_1
	elif t1 <= -1.22e-67:
		tmp = t_2
	elif t1 <= 5.6e+164:
		tmp = t_1
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(v / u) * Float64(Float64(-t1) / u))
	t_2 = Float64(v / Float64(Float64(u * -2.0) - t1))
	tmp = 0.0
	if (t1 <= -1600000.0)
		tmp = t_2;
	elseif (t1 <= -2.3e-28)
		tmp = t_1;
	elseif (t1 <= -1.22e-67)
		tmp = t_2;
	elseif (t1 <= 5.6e+164)
		tmp = t_1;
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = (v / u) * (-t1 / u);
	t_2 = v / ((u * -2.0) - t1);
	tmp = 0.0;
	if (t1 <= -1600000.0)
		tmp = t_2;
	elseif (t1 <= -2.3e-28)
		tmp = t_1;
	elseif (t1 <= -1.22e-67)
		tmp = t_2;
	elseif (t1 <= 5.6e+164)
		tmp = t_1;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(N[(v / u), $MachinePrecision] * N[((-t1) / u), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(v / N[(N[(u * -2.0), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -1600000.0], t$95$2, If[LessEqual[t1, -2.3e-28], t$95$1, If[LessEqual[t1, -1.22e-67], t$95$2, If[LessEqual[t1, 5.6e+164], t$95$1, N[((-v) / t1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.6e6 or -2.29999999999999986e-28 < t1 < -1.22e-67

   1. Initial program 75.5%

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

      1. associate-/r* 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/l* 99.9%

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

      4. associate-/l/ 98.8%

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

      5. +-commutative 98.8%

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

      6. remove-double-neg 98.8%

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

      7. unsub-neg 98.8%

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

      8. div-sub 98.8%

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

      9. sub-neg 98.8%

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

      10. *-inverses 98.8%

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

      11. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t1 around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

      3. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -1.6e6 < t1 < -2.29999999999999986e-28 or -1.22e-67 < t1 < 5.6000000000000004e164

   1. Initial program 75.5%

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

      1. times-frac 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t1 around 0 75.0%

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

   5. Taylor expanded in t1 around 0 75.9%

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

      1. associate-*r/ 75.9%

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

      2. mul-1-neg 75.9%

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

   7. Simplified 75.9%

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

   if 5.6000000000000004e164 < t1

   1. Initial program 34.4%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t1 around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

   6. Simplified 92.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1600000:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{-t1}{u}\\ \mathbf{elif}\;t1 \leq -1.22 \cdot 10^{-67}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{-t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t1 \cdot \frac{v}{u}}{-u}\\ t_2 := \frac{v}{u \cdot -2 - t1}\\ \mathbf{if}\;t1 \leq -480000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t1 \leq -1.2 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq -1.15 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ (* t1 (/ v u)) (- u))) (t_2 (/ v (- (* u -2.0) t1))))
   (if (<= t1 -480000.0)
     t_2
     (if (<= t1 -1.2e-28)
       t_1
       (if (<= t1 -1.15e-72) t_2 (if (<= t1 5.6e+164) t_1 (/ (- v) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = (t1 * (v / u)) / -u;
	double t_2 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -480000.0) {
		tmp = t_2;
	} else if (t1 <= -1.2e-28) {
		tmp = t_1;
	} else if (t1 <= -1.15e-72) {
		tmp = t_2;
	} else if (t1 <= 5.6e+164) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t1 * (v / u)) / -u
    t_2 = v / ((u * (-2.0d0)) - t1)
    if (t1 <= (-480000.0d0)) then
        tmp = t_2
    else if (t1 <= (-1.2d-28)) then
        tmp = t_1
    else if (t1 <= (-1.15d-72)) then
        tmp = t_2
    else if (t1 <= 5.6d+164) then
        tmp = t_1
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = (t1 * (v / u)) / -u;
	double t_2 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -480000.0) {
		tmp = t_2;
	} else if (t1 <= -1.2e-28) {
		tmp = t_1;
	} else if (t1 <= -1.15e-72) {
		tmp = t_2;
	} else if (t1 <= 5.6e+164) {
		tmp = t_1;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = (t1 * (v / u)) / -u
	t_2 = v / ((u * -2.0) - t1)
	tmp = 0
	if t1 <= -480000.0:
		tmp = t_2
	elif t1 <= -1.2e-28:
		tmp = t_1
	elif t1 <= -1.15e-72:
		tmp = t_2
	elif t1 <= 5.6e+164:
		tmp = t_1
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(t1 * Float64(v / u)) / Float64(-u))
	t_2 = Float64(v / Float64(Float64(u * -2.0) - t1))
	tmp = 0.0
	if (t1 <= -480000.0)
		tmp = t_2;
	elseif (t1 <= -1.2e-28)
		tmp = t_1;
	elseif (t1 <= -1.15e-72)
		tmp = t_2;
	elseif (t1 <= 5.6e+164)
		tmp = t_1;
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = (t1 * (v / u)) / -u;
	t_2 = v / ((u * -2.0) - t1);
	tmp = 0.0;
	if (t1 <= -480000.0)
		tmp = t_2;
	elseif (t1 <= -1.2e-28)
		tmp = t_1;
	elseif (t1 <= -1.15e-72)
		tmp = t_2;
	elseif (t1 <= 5.6e+164)
		tmp = t_1;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision]}, Block[{t$95$2 = N[(v / N[(N[(u * -2.0), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -480000.0], t$95$2, If[LessEqual[t1, -1.2e-28], t$95$1, If[LessEqual[t1, -1.15e-72], t$95$2, If[LessEqual[t1, 5.6e+164], t$95$1, N[((-v) / t1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -4.8e5 or -1.2000000000000001e-28 < t1 < -1.14999999999999997e-72

   1. Initial program 75.5%

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

      1. associate-/r* 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/l* 99.9%

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

      4. associate-/l/ 98.8%

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

      5. +-commutative 98.8%

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

      6. remove-double-neg 98.8%

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

      7. unsub-neg 98.8%

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

      8. div-sub 98.8%

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

      9. sub-neg 98.8%

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

      10. *-inverses 98.8%

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

      11. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t1 around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

      3. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -4.8e5 < t1 < -1.2000000000000001e-28 or -1.14999999999999997e-72 < t1 < 5.6000000000000004e164

   1. Initial program 75.5%

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

      1. times-frac 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t1 around 0 75.0%

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

   5. Taylor expanded in t1 around 0 75.9%

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

      1. associate-*r/ 75.9%

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

      2. mul-1-neg 75.9%

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

   7. Simplified 75.9%

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

      1. frac-2neg 75.9%

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

      2. remove-double-neg 75.9%

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

      3. associate-*l/ 76.6%

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

   9. Applied egg-rr 76.6%

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

   if 5.6000000000000004e164 < t1

   1. Initial program 34.4%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t1 around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

   6. Simplified 92.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -480000:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq -1.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;t1 \leq -1.15 \cdot 10^{-72}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 4: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{u \cdot -2 - t1}\\ \mathbf{if}\;t1 \leq -3300000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq -7 \cdot 10^{-28}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;t1 \leq -6.3 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ v (- (* u -2.0) t1))))
   (if (<= t1 -3300000.0)
     t_1
     (if (<= t1 -7e-28)
       (/ (* t1 (/ v u)) (- u))
       (if (<= t1 -6.3e-68)
         t_1
         (if (<= t1 5.6e+164) (/ (/ t1 (/ u v)) (- u)) (/ (- v) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -3300000.0) {
		tmp = t_1;
	} else if (t1 <= -7e-28) {
		tmp = (t1 * (v / u)) / -u;
	} else if (t1 <= -6.3e-68) {
		tmp = t_1;
	} else if (t1 <= 5.6e+164) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = v / ((u * (-2.0d0)) - t1)
    if (t1 <= (-3300000.0d0)) then
        tmp = t_1
    else if (t1 <= (-7d-28)) then
        tmp = (t1 * (v / u)) / -u
    else if (t1 <= (-6.3d-68)) then
        tmp = t_1
    else if (t1 <= 5.6d+164) then
        tmp = (t1 / (u / v)) / -u
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -3300000.0) {
		tmp = t_1;
	} else if (t1 <= -7e-28) {
		tmp = (t1 * (v / u)) / -u;
	} else if (t1 <= -6.3e-68) {
		tmp = t_1;
	} else if (t1 <= 5.6e+164) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = v / ((u * -2.0) - t1)
	tmp = 0
	if t1 <= -3300000.0:
		tmp = t_1
	elif t1 <= -7e-28:
		tmp = (t1 * (v / u)) / -u
	elif t1 <= -6.3e-68:
		tmp = t_1
	elif t1 <= 5.6e+164:
		tmp = (t1 / (u / v)) / -u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(v / Float64(Float64(u * -2.0) - t1))
	tmp = 0.0
	if (t1 <= -3300000.0)
		tmp = t_1;
	elseif (t1 <= -7e-28)
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	elseif (t1 <= -6.3e-68)
		tmp = t_1;
	elseif (t1 <= 5.6e+164)
		tmp = Float64(Float64(t1 / Float64(u / v)) / Float64(-u));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = v / ((u * -2.0) - t1);
	tmp = 0.0;
	if (t1 <= -3300000.0)
		tmp = t_1;
	elseif (t1 <= -7e-28)
		tmp = (t1 * (v / u)) / -u;
	elseif (t1 <= -6.3e-68)
		tmp = t_1;
	elseif (t1 <= 5.6e+164)
		tmp = (t1 / (u / v)) / -u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(v / N[(N[(u * -2.0), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -3300000.0], t$95$1, If[LessEqual[t1, -7e-28], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], If[LessEqual[t1, -6.3e-68], t$95$1, If[LessEqual[t1, 5.6e+164], N[(N[(t1 / N[(u / v), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -3.3e6 or -6.9999999999999999e-28 < t1 < -6.2999999999999998e-68

   1. Initial program 75.5%

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

      1. associate-/r* 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/l* 99.9%

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

      4. associate-/l/ 98.8%

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

      5. +-commutative 98.8%

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

      6. remove-double-neg 98.8%

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

      7. unsub-neg 98.8%

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

      8. div-sub 98.8%

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

      9. sub-neg 98.8%

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

      10. *-inverses 98.8%

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

      11. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t1 around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

      3. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -3.3e6 < t1 < -6.9999999999999999e-28

   1. Initial program 78.9%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t1 around 0 88.7%

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

   5. Taylor expanded in t1 around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. mul-1-neg 89.0%

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

   7. Simplified 89.0%

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

      1. frac-2neg 89.0%

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

      2. remove-double-neg 89.0%

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

      3. associate-*l/ 89.2%

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

   9. Applied egg-rr 89.2%

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

   if -6.2999999999999998e-68 < t1 < 5.6000000000000004e164

   1. Initial program 75.2%

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

      1. times-frac 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t1 around 0 74.2%

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

   5. Taylor expanded in t1 around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

      1. frac-2neg 75.1%

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

      2. remove-double-neg 75.1%

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

      3. associate-*l/ 75.8%

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

   9. Applied egg-rr 75.8%

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

       1. clear-num 75.8%

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

       2. un-div-inv 75.8%

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

   11. Applied egg-rr 75.8%

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

   if 5.6000000000000004e164 < t1

   1. Initial program 34.4%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t1 around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

   6. Simplified 92.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -3300000:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq -7 \cdot 10^{-28}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;t1 \leq -6.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 5: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{u \cdot -2 - t1}\\ \mathbf{if}\;t1 \leq -260000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{t1}{\left(t1 - u\right) \cdot \frac{u}{v}}\\ \mathbf{elif}\;t1 \leq -1.2 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ v (- (* u -2.0) t1))))
   (if (<= t1 -260000.0)
     t_1
     (if (<= t1 -7.5e-29)
       (/ t1 (* (- t1 u) (/ u v)))
       (if (<= t1 -1.2e-67)
         t_1
         (if (<= t1 5.6e+164) (/ (/ t1 (/ u v)) (- u)) (/ (- v) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -260000.0) {
		tmp = t_1;
	} else if (t1 <= -7.5e-29) {
		tmp = t1 / ((t1 - u) * (u / v));
	} else if (t1 <= -1.2e-67) {
		tmp = t_1;
	} else if (t1 <= 5.6e+164) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = v / ((u * (-2.0d0)) - t1)
    if (t1 <= (-260000.0d0)) then
        tmp = t_1
    else if (t1 <= (-7.5d-29)) then
        tmp = t1 / ((t1 - u) * (u / v))
    else if (t1 <= (-1.2d-67)) then
        tmp = t_1
    else if (t1 <= 5.6d+164) then
        tmp = (t1 / (u / v)) / -u
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -260000.0) {
		tmp = t_1;
	} else if (t1 <= -7.5e-29) {
		tmp = t1 / ((t1 - u) * (u / v));
	} else if (t1 <= -1.2e-67) {
		tmp = t_1;
	} else if (t1 <= 5.6e+164) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = v / ((u * -2.0) - t1)
	tmp = 0
	if t1 <= -260000.0:
		tmp = t_1
	elif t1 <= -7.5e-29:
		tmp = t1 / ((t1 - u) * (u / v))
	elif t1 <= -1.2e-67:
		tmp = t_1
	elif t1 <= 5.6e+164:
		tmp = (t1 / (u / v)) / -u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(v / Float64(Float64(u * -2.0) - t1))
	tmp = 0.0
	if (t1 <= -260000.0)
		tmp = t_1;
	elseif (t1 <= -7.5e-29)
		tmp = Float64(t1 / Float64(Float64(t1 - u) * Float64(u / v)));
	elseif (t1 <= -1.2e-67)
		tmp = t_1;
	elseif (t1 <= 5.6e+164)
		tmp = Float64(Float64(t1 / Float64(u / v)) / Float64(-u));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = v / ((u * -2.0) - t1);
	tmp = 0.0;
	if (t1 <= -260000.0)
		tmp = t_1;
	elseif (t1 <= -7.5e-29)
		tmp = t1 / ((t1 - u) * (u / v));
	elseif (t1 <= -1.2e-67)
		tmp = t_1;
	elseif (t1 <= 5.6e+164)
		tmp = (t1 / (u / v)) / -u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(v / N[(N[(u * -2.0), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -260000.0], t$95$1, If[LessEqual[t1, -7.5e-29], N[(t1 / N[(N[(t1 - u), $MachinePrecision] * N[(u / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -1.2e-67], t$95$1, If[LessEqual[t1, 5.6e+164], N[(N[(t1 / N[(u / v), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -2.6e5 or -7.50000000000000006e-29 < t1 < -1.2e-67

   1. Initial program 75.5%

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

      1. associate-/r* 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/l* 99.9%

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

      4. associate-/l/ 98.8%

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

      5. +-commutative 98.8%

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

      6. remove-double-neg 98.8%

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

      7. unsub-neg 98.8%

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

      8. div-sub 98.8%

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

      9. sub-neg 98.8%

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

      10. *-inverses 98.8%

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

      11. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t1 around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

      3. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -2.6e5 < t1 < -7.50000000000000006e-29

   1. Initial program 78.9%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. clear-num 100.0%

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

      3. frac-2neg 100.0%

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

      4. frac-times 99.5%

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

      5. *-un-lft-identity 99.5%

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

      6. remove-double-neg 99.5%

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

      7. distribute-neg-in 99.5%

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

      8. add-sqr-sqrt 99.5%

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

      9. sqrt-unprod 99.5%

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

      10. sqr-neg 99.5%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 88.8%

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

      13. sub-neg 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in t1 around 0 89.2%

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

   if -1.2e-67 < t1 < 5.6000000000000004e164

   1. Initial program 75.2%

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

      1. times-frac 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t1 around 0 74.2%

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

   5. Taylor expanded in t1 around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

      1. frac-2neg 75.1%

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

      2. remove-double-neg 75.1%

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

      3. associate-*l/ 75.8%

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

   9. Applied egg-rr 75.8%

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

       1. clear-num 75.8%

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

       2. un-div-inv 75.8%

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

   11. Applied egg-rr 75.8%

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

   if 5.6000000000000004e164 < t1

   1. Initial program 34.4%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t1 around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

   6. Simplified 92.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -260000:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{t1}{\left(t1 - u\right) \cdot \frac{u}{v}}\\ \mathbf{elif}\;t1 \leq -1.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{u \cdot -2 - t1}\\ \mathbf{if}\;t1 \leq -250000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{t1 - u}\\ \mathbf{elif}\;t1 \leq -1.22 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ v (- (* u -2.0) t1))))
   (if (<= t1 -250000.0)
     t_1
     (if (<= t1 -4.8e-28)
       (/ (* t1 (/ v u)) (- t1 u))
       (if (<= t1 -1.22e-67)
         t_1
         (if (<= t1 5.6e+164) (/ (/ t1 (/ u v)) (- u)) (/ (- v) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -250000.0) {
		tmp = t_1;
	} else if (t1 <= -4.8e-28) {
		tmp = (t1 * (v / u)) / (t1 - u);
	} else if (t1 <= -1.22e-67) {
		tmp = t_1;
	} else if (t1 <= 5.6e+164) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = v / ((u * (-2.0d0)) - t1)
    if (t1 <= (-250000.0d0)) then
        tmp = t_1
    else if (t1 <= (-4.8d-28)) then
        tmp = (t1 * (v / u)) / (t1 - u)
    else if (t1 <= (-1.22d-67)) then
        tmp = t_1
    else if (t1 <= 5.6d+164) then
        tmp = (t1 / (u / v)) / -u
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = v / ((u * -2.0) - t1);
	double tmp;
	if (t1 <= -250000.0) {
		tmp = t_1;
	} else if (t1 <= -4.8e-28) {
		tmp = (t1 * (v / u)) / (t1 - u);
	} else if (t1 <= -1.22e-67) {
		tmp = t_1;
	} else if (t1 <= 5.6e+164) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = v / ((u * -2.0) - t1)
	tmp = 0
	if t1 <= -250000.0:
		tmp = t_1
	elif t1 <= -4.8e-28:
		tmp = (t1 * (v / u)) / (t1 - u)
	elif t1 <= -1.22e-67:
		tmp = t_1
	elif t1 <= 5.6e+164:
		tmp = (t1 / (u / v)) / -u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(v / Float64(Float64(u * -2.0) - t1))
	tmp = 0.0
	if (t1 <= -250000.0)
		tmp = t_1;
	elseif (t1 <= -4.8e-28)
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(t1 - u));
	elseif (t1 <= -1.22e-67)
		tmp = t_1;
	elseif (t1 <= 5.6e+164)
		tmp = Float64(Float64(t1 / Float64(u / v)) / Float64(-u));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = v / ((u * -2.0) - t1);
	tmp = 0.0;
	if (t1 <= -250000.0)
		tmp = t_1;
	elseif (t1 <= -4.8e-28)
		tmp = (t1 * (v / u)) / (t1 - u);
	elseif (t1 <= -1.22e-67)
		tmp = t_1;
	elseif (t1 <= 5.6e+164)
		tmp = (t1 / (u / v)) / -u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(v / N[(N[(u * -2.0), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -250000.0], t$95$1, If[LessEqual[t1, -4.8e-28], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / N[(t1 - u), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -1.22e-67], t$95$1, If[LessEqual[t1, 5.6e+164], N[(N[(t1 / N[(u / v), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -2.5e5 or -4.8000000000000004e-28 < t1 < -1.22e-67

   1. Initial program 75.5%

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

      1. associate-/r* 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/l* 99.9%

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

      4. associate-/l/ 98.8%

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

      5. +-commutative 98.8%

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

      6. remove-double-neg 98.8%

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

      7. unsub-neg 98.8%

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

      8. div-sub 98.8%

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

      9. sub-neg 98.8%

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

      10. *-inverses 98.8%

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

      11. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t1 around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

      3. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -2.5e5 < t1 < -4.8000000000000004e-28

   1. Initial program 78.9%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t1 around 0 88.7%

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

      1. distribute-frac-neg 88.7%

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

      2. frac-2neg 88.7%

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

      3. distribute-frac-neg 88.7%

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

      4. remove-double-neg 88.7%

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

      5. associate-*l/ 88.9%

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

      6. distribute-neg-in 88.9%

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

      7. add-sqr-sqrt 88.9%

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

      8. sqrt-unprod 88.9%

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

      9. sqr-neg 88.9%

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

      10. sqrt-unprod 0.0%

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

      11. add-sqr-sqrt 89.3%

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

      12. sub-neg 89.3%

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

   6. Applied egg-rr 89.3%

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

   if -1.22e-67 < t1 < 5.6000000000000004e164

   1. Initial program 75.2%

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

      1. times-frac 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t1 around 0 74.2%

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

   5. Taylor expanded in t1 around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

      1. frac-2neg 75.1%

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

      2. remove-double-neg 75.1%

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

      3. associate-*l/ 75.8%

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

   9. Applied egg-rr 75.8%

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

       1. clear-num 75.8%

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

       2. un-div-inv 75.8%

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

   11. Applied egg-rr 75.8%

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

   if 5.6000000000000004e164 < t1

   1. Initial program 34.4%

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

      1. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t1 around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

   6. Simplified 92.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -250000:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{t1 - u}\\ \mathbf{elif}\;t1 \leq -1.22 \cdot 10^{-67}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 7: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -3.2 \cdot 10^{+148} \lor \neg \left(u \leq 1.5 \cdot 10^{+247}\right):\\ \;\;\;\;v \cdot \frac{\frac{t1}{u}}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -3.2e+148) (not (<= u 1.5e+247)))
   (* v (/ (/ t1 u) t1))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -3.2e+148) || !(u <= 1.5e+247)) {
		tmp = v * ((t1 / u) / t1);
	} 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 <= (-3.2d+148)) .or. (.not. (u <= 1.5d+247))) then
        tmp = v * ((t1 / u) / t1)
    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 <= -3.2e+148) || !(u <= 1.5e+247)) {
		tmp = v * ((t1 / u) / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -3.2e+148) or not (u <= 1.5e+247):
		tmp = v * ((t1 / u) / t1)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -3.2e+148) || !(u <= 1.5e+247))
		tmp = Float64(v * Float64(Float64(t1 / u) / t1));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -3.2e+148) || ~((u <= 1.5e+247)))
		tmp = v * ((t1 / u) / t1);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -3.2e+148], N[Not[LessEqual[u, 1.5e+247]], $MachinePrecision]], N[(v * N[(N[(t1 / u), $MachinePrecision] / t1), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -3.1999999999999999e148 or 1.5e247 < u

   1. Initial program 82.0%

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

      1. times-frac 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.5%

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

      3. frac-2neg 96.5%

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

      4. frac-times 92.9%

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

      5. *-un-lft-identity 92.9%

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

      6. remove-double-neg 92.9%

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

      7. distribute-neg-in 92.9%

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

      8. add-sqr-sqrt 45.5%

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

      9. sqrt-unprod 91.1%

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

      10. sqr-neg 91.1%

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

      11. sqrt-unprod 47.4%

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

      12. add-sqr-sqrt 92.9%

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

      13. sub-neg 92.9%

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

   5. Applied egg-rr 92.9%

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

   6. Taylor expanded in t1 around 0 92.9%

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

   7. Taylor expanded in u around 0 53.1%

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

      1. associate-/r/ 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-/r* 64.3%

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

   9. Applied egg-rr 64.3%

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

   if -3.1999999999999999e148 < u < 1.5e247

   1. Initial program 68.5%

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

      1. times-frac 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t1 around inf 61.3%

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

      1. associate-*r/ 61.3%

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

      2. neg-mul-1 61.3%

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

   6. Simplified 61.3%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -3.2 \cdot 10^{+148} \lor \neg \left(u \leq 1.5 \cdot 10^{+247}\right):\\ \;\;\;\;v \cdot \frac{\frac{t1}{u}}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 8: 69.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -6.8 \cdot 10^{+102} \lor \neg \left(u \leq 1.95 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{t1}{\frac{u}{\frac{v}{u}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -6.8e+102) (not (<= u 1.95e+90)))
   (/ t1 (/ u (/ v u)))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -6.8e+102) || !(u <= 1.95e+90)) {
		tmp = t1 / (u / (v / u));
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-6.8d+102)) .or. (.not. (u <= 1.95d+90))) then
        tmp = t1 / (u / (v / u))
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -6.8e+102) || !(u <= 1.95e+90)) {
		tmp = t1 / (u / (v / u));
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -6.8e+102) or not (u <= 1.95e+90):
		tmp = t1 / (u / (v / u))
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -6.8e+102) || !(u <= 1.95e+90))
		tmp = Float64(t1 / Float64(u / Float64(v / u)));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -6.8e+102) || ~((u <= 1.95e+90)))
		tmp = t1 / (u / (v / u));
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -6.8e+102], N[Not[LessEqual[u, 1.95e+90]], $MachinePrecision]], N[(t1 / N[(u / N[(v / u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -6.8000000000000001e102 or 1.9500000000000001e90 < u

   1. Initial program 70.0%

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

      1. times-frac 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t1 around 0 81.1%

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

   5. Taylor expanded in t1 around 0 81.0%

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

      1. associate-*r/ 81.0%

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

      2. mul-1-neg 81.0%

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

   7. Simplified 81.0%

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

      1. associate-*l/ 83.7%

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

      2. associate-/l* 80.5%

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

      3. add-sqr-sqrt 41.8%

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

      4. sqrt-unprod 62.7%

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

      5. sqr-neg 62.7%

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

      6. sqrt-unprod 30.7%

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

      7. add-sqr-sqrt 66.4%

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

   9. Applied egg-rr 66.4%

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

   if -6.8000000000000001e102 < u < 1.9500000000000001e90

   1. Initial program 72.1%

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

      1. times-frac 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in t1 around inf 67.5%

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

      1. associate-*r/ 67.5%

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

      2. neg-mul-1 67.5%

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

   6. Simplified 67.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -6.8 \cdot 10^{+102} \lor \neg \left(u \leq 1.95 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{t1}{\frac{u}{\frac{v}{u}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 9: 67.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -3.75 \cdot 10^{+149} \lor \neg \left(u \leq 1.5 \cdot 10^{+247}\right):\\ \;\;\;\;\frac{v}{u \cdot \frac{u}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -3.75e+149) (not (<= u 1.5e+247)))
   (/ v (* u (/ u t1)))
   (/ v (- (* u -2.0) t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -3.75e+149) || !(u <= 1.5e+247)) {
		tmp = v / (u * (u / t1));
	} else {
		tmp = v / ((u * -2.0) - 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 <= (-3.75d+149)) .or. (.not. (u <= 1.5d+247))) then
        tmp = v / (u * (u / t1))
    else
        tmp = v / ((u * (-2.0d0)) - t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -3.75e+149) || !(u <= 1.5e+247)) {
		tmp = v / (u * (u / t1));
	} else {
		tmp = v / ((u * -2.0) - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -3.75e+149) or not (u <= 1.5e+247):
		tmp = v / (u * (u / t1))
	else:
		tmp = v / ((u * -2.0) - t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -3.75e+149) || !(u <= 1.5e+247))
		tmp = Float64(v / Float64(u * Float64(u / t1)));
	else
		tmp = Float64(v / Float64(Float64(u * -2.0) - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -3.75e+149) || ~((u <= 1.5e+247)))
		tmp = v / (u * (u / t1));
	else
		tmp = v / ((u * -2.0) - t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -3.75e+149], N[Not[LessEqual[u, 1.5e+247]], $MachinePrecision]], N[(v / N[(u * N[(u / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v / N[(N[(u * -2.0), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -3.75000000000000016e149 or 1.5e247 < u

   1. Initial program 82.0%

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

      1. times-frac 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t1 around 0 94.7%

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

   5. Taylor expanded in t1 around 0 94.6%

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

      1. associate-*r/ 94.6%

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

      2. mul-1-neg 94.6%

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

   7. Simplified 94.6%

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

      1. clear-num 94.7%

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

      2. frac-times 82.3%

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

      3. *-un-lft-identity 82.3%

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

      4. add-sqr-sqrt 42.0%

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

      5. sqrt-unprod 69.1%

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

      6. sqr-neg 69.1%

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

      7. sqrt-unprod 40.3%

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

      8. add-sqr-sqrt 82.3%

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

   9. Applied egg-rr 82.3%

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

   if -3.75000000000000016e149 < u < 1.5e247

   1. Initial program 68.5%

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

      1. associate-/r* 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-/l* 98.6%

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

      4. associate-/l/ 98.0%

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

      5. +-commutative 98.0%

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

      6. remove-double-neg 98.0%

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

      7. unsub-neg 98.0%

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

      8. div-sub 98.0%

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

      9. sub-neg 98.0%

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

      10. *-inverses 98.0%

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

      11. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t1 around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

      3. *-commutative 64.3%

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

   6. Simplified 64.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -3.75 \cdot 10^{+149} \lor \neg \left(u \leq 1.5 \cdot 10^{+247}\right):\\ \;\;\;\;\frac{v}{u \cdot \frac{u}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \end{array} \]

Alternative 10: 57.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.08 \cdot 10^{+163}:\\ \;\;\;\;\frac{t1}{u} \cdot \frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -1.08e+163) (* (/ t1 u) (/ v t1)) (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.08e+163) {
		tmp = (t1 / u) * (v / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (u <= (-1.08d+163)) then
        tmp = (t1 / u) * (v / t1)
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.08e+163) {
		tmp = (t1 / u) * (v / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -1.08e+163:
		tmp = (t1 / u) * (v / t1)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -1.08e+163)
		tmp = Float64(Float64(t1 / u) * Float64(v / t1));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -1.08e+163)
		tmp = (t1 / u) * (v / t1);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -1.08e+163], N[(N[(t1 / u), $MachinePrecision] * N[(v / t1), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.0800000000000001e163

   1. Initial program 78.4%

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

      1. times-frac 94.7%

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

   3. Simplified 94.7%

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

      1. *-commutative 94.7%

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

      2. clear-num 94.7%

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

      3. frac-2neg 94.7%

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

      4. frac-times 91.9%

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

      5. *-un-lft-identity 91.9%

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

      6. remove-double-neg 91.9%

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

      7. distribute-neg-in 91.9%

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

      8. add-sqr-sqrt 43.0%

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

      9. sqrt-unprod 89.2%

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

      10. sqr-neg 89.2%

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

      11. sqrt-unprod 48.9%

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

      12. add-sqr-sqrt 91.9%

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

      13. sub-neg 91.9%

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

   5. Applied egg-rr 91.9%

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

   6. Taylor expanded in t1 around 0 91.9%

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

   7. Taylor expanded in u around 0 59.2%

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

      1. associate-/l* 56.4%

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

      2. *-commutative 56.4%

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

      3. times-frac 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -1.0800000000000001e163 < u

   1. Initial program 70.2%

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

      1. times-frac 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t1 around inf 58.8%

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

      1. associate-*r/ 58.8%

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

      2. neg-mul-1 58.8%

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

   6. Simplified 58.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.08 \cdot 10^{+163}:\\ \;\;\;\;\frac{t1}{u} \cdot \frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 11: 23.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.5 \cdot 10^{+128} \lor \neg \left(t1 \leq 1.3 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -2.5e+128) (not (<= t1 1.3e+172))) (/ v t1) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -2.5e+128) || !(t1 <= 1.3e+172)) {
		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 <= (-2.5d+128)) .or. (.not. (t1 <= 1.3d+172))) 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 <= -2.5e+128) || !(t1 <= 1.3e+172)) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -2.5e+128) or not (t1 <= 1.3e+172):
		tmp = v / t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -2.5e+128) || !(t1 <= 1.3e+172))
		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 <= -2.5e+128) || ~((t1 <= 1.3e+172)))
		tmp = v / t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -2.5e+128], N[Not[LessEqual[t1, 1.3e+172]], $MachinePrecision]], N[(v / t1), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -2.5e128 or 1.3e172 < t1

   1. Initial program 51.1%

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

      1. times-frac 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

      3. associate-*l/ 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. frac-2neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. add-sqr-sqrt 61.4%

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

      8. sqrt-unprod 52.6%

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

      9. sqr-neg 52.6%

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

      10. sqrt-unprod 17.1%

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

      11. add-sqr-sqrt 54.3%

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

      12. sub-neg 54.3%

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

      13. remove-double-neg 54.3%

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

   5. Applied egg-rr 54.3%

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

   6. Taylor expanded in t1 around inf 49.8%

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

   if -2.5e128 < t1 < 1.3e172

   1. Initial program 78.1%

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

      1. times-frac 97.9%

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

   3. Simplified 97.9%

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

      1. *-commutative 97.9%

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

      2. clear-num 97.7%

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

      3. frac-2neg 97.7%

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

      4. frac-times 85.9%

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

      5. *-un-lft-identity 85.9%

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

      6. remove-double-neg 85.9%

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

      7. distribute-neg-in 85.9%

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

      8. add-sqr-sqrt 46.0%

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

      9. sqrt-unprod 76.0%

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

      10. sqr-neg 76.0%

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

      11. sqrt-unprod 29.4%

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

      12. add-sqr-sqrt 59.8%

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

      13. sub-neg 59.8%

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

   5. Applied egg-rr 59.8%

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

   6. Taylor expanded in t1 around 0 61.2%

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

   7. Taylor expanded in t1 around inf 17.7%

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

4. Final simplification 25.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.5 \cdot 10^{+128} \lor \neg \left(t1 \leq 1.3 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]

Alternative 12: 56.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.85 \cdot 10^{+163}:\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -1.85e+163) (/ v u) (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.85e+163) {
		tmp = v / u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (u <= (-1.85d+163)) then
        tmp = v / u
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.85e+163) {
		tmp = v / u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -1.85e+163:
		tmp = v / u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -1.85e+163)
		tmp = Float64(v / u);
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -1.85e+163)
		tmp = v / u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -1.85e+163], N[(v / u), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.84999999999999996e163

   1. Initial program 78.4%

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

      1. times-frac 94.7%

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

   3. Simplified 94.7%

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

      1. *-commutative 94.7%

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

      2. clear-num 94.7%

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

      3. frac-2neg 94.7%

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

      4. frac-times 91.9%

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

      5. *-un-lft-identity 91.9%

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

      6. remove-double-neg 91.9%

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

      7. distribute-neg-in 91.9%

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

      8. add-sqr-sqrt 43.0%

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

      9. sqrt-unprod 89.2%

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

      10. sqr-neg 89.2%

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

      11. sqrt-unprod 48.9%

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

      12. add-sqr-sqrt 91.9%

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

      13. sub-neg 91.9%

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

   5. Applied egg-rr 91.9%

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

   6. Taylor expanded in t1 around 0 91.9%

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

   7. Taylor expanded in t1 around inf 54.1%

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

   if -1.84999999999999996e163 < u

   1. Initial program 70.2%

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

      1. times-frac 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t1 around inf 58.8%

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

      1. associate-*r/ 58.8%

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

      2. neg-mul-1 58.8%

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

   6. Simplified 58.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.85 \cdot 10^{+163}:\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]

Alternative 13: 14.0% 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 71.3%

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

   1. times-frac 98.5%

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

3. Simplified 98.5%

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

   1. associate-*r/ 98.2%

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

   2. clear-num 98.2%

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

   3. associate-*l/ 98.2%

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

   4. *-un-lft-identity 98.2%

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

   5. frac-2neg 98.2%

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

   6. distribute-neg-in 98.2%

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

   7. add-sqr-sqrt 54.6%

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

   8. sqrt-unprod 74.5%

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

   9. sqr-neg 74.5%

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

   10. sqrt-unprod 27.9%

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

   11. add-sqr-sqrt 61.9%

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

   12. sub-neg 61.9%

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

   13. remove-double-neg 61.9%

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

5. Applied egg-rr 61.9%

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

6. Taylor expanded in t1 around inf 16.2%

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

7. Final simplification 16.2%

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

Reproduce

herbie shell --seed 2023333 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))