Rosa's DopplerBench

Percentage Accurate: 73.0% → 98.1%

Time: 10.4s

Alternatives: 14

Speedup: 1.1×

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: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{t1 \cdot \frac{v}{t1 + u}}{-1}}{t1 + u} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (/ (/ (* t1 (/ v (+ t1 u))) -1.0) (+ t1 u)))

C

double code(double u, double v, double t1) {
	return ((t1 * (v / (t1 + u))) / -1.0) / (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))) / (-1.0d0)) / (t1 + u)
end function

Java

public static double code(double u, double v, double t1) {
	return ((t1 * (v / (t1 + u))) / -1.0) / (t1 + u);
}

Python

def code(u, v, t1):
	return ((t1 * (v / (t1 + u))) / -1.0) / (t1 + u)

Julia

function code(u, v, t1)
	return Float64(Float64(Float64(t1 * Float64(v / Float64(t1 + u))) / -1.0) / Float64(t1 + u))
end

MATLAB

function tmp = code(u, v, t1)
	tmp = ((t1 * (v / (t1 + u))) / -1.0) / (t1 + u);
end

Wolfram

code[u_, v_, t1_] := N[(N[(N[(t1 * N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / -1.0), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

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

   1. associate-/l* 76.9%

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

   2. distribute-lft-neg-out 76.9%

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

   3. distribute-rgt-neg-in 76.9%

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

   4. associate-/r* 88.0%

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

   5. distribute-neg-frac2 88.0%

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

3. Simplified 88.0%

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

   1. associate-*r/ 98.5%

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

   2. neg-mul-1 98.5%

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

   3. associate-/r* 98.5%

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

6. Applied egg-rr 98.5%

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

Alternative 2: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ t_2 := \frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{if}\;u \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;u \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;u \leq -2.4 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;u \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 6.2 \cdot 10^{+20} \lor \neg \left(u \leq 8.5 \cdot 10^{+138}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ v (* t1 (/ (- u t1) t1)))) (t_2 (* (/ v u) (/ t1 (- u)))))
   (if (<= u -1.05e+103)
     t_2
     (if (<= u -2.3e+48)
       t_1
       (if (<= u -2.4e-63)
         t_2
         (if (<= u 3.2e-45)
           (/ v (- t1))
           (if (or (<= u 6.2e+20) (not (<= u 8.5e+138))) t_2 t_1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = v / (t1 * ((u - t1) / t1));
	double t_2 = (v / u) * (t1 / -u);
	double tmp;
	if (u <= -1.05e+103) {
		tmp = t_2;
	} else if (u <= -2.3e+48) {
		tmp = t_1;
	} else if (u <= -2.4e-63) {
		tmp = t_2;
	} else if (u <= 3.2e-45) {
		tmp = v / -t1;
	} else if ((u <= 6.2e+20) || !(u <= 8.5e+138)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = v / (t1 * ((u - t1) / t1))
    t_2 = (v / u) * (t1 / -u)
    if (u <= (-1.05d+103)) then
        tmp = t_2
    else if (u <= (-2.3d+48)) then
        tmp = t_1
    else if (u <= (-2.4d-63)) then
        tmp = t_2
    else if (u <= 3.2d-45) then
        tmp = v / -t1
    else if ((u <= 6.2d+20) .or. (.not. (u <= 8.5d+138))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = v / (t1 * ((u - t1) / t1));
	double t_2 = (v / u) * (t1 / -u);
	double tmp;
	if (u <= -1.05e+103) {
		tmp = t_2;
	} else if (u <= -2.3e+48) {
		tmp = t_1;
	} else if (u <= -2.4e-63) {
		tmp = t_2;
	} else if (u <= 3.2e-45) {
		tmp = v / -t1;
	} else if ((u <= 6.2e+20) || !(u <= 8.5e+138)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = v / (t1 * ((u - t1) / t1))
	t_2 = (v / u) * (t1 / -u)
	tmp = 0
	if u <= -1.05e+103:
		tmp = t_2
	elif u <= -2.3e+48:
		tmp = t_1
	elif u <= -2.4e-63:
		tmp = t_2
	elif u <= 3.2e-45:
		tmp = v / -t1
	elif (u <= 6.2e+20) or not (u <= 8.5e+138):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(v / Float64(t1 * Float64(Float64(u - t1) / t1)))
	t_2 = Float64(Float64(v / u) * Float64(t1 / Float64(-u)))
	tmp = 0.0
	if (u <= -1.05e+103)
		tmp = t_2;
	elseif (u <= -2.3e+48)
		tmp = t_1;
	elseif (u <= -2.4e-63)
		tmp = t_2;
	elseif (u <= 3.2e-45)
		tmp = Float64(v / Float64(-t1));
	elseif ((u <= 6.2e+20) || !(u <= 8.5e+138))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = v / (t1 * ((u - t1) / t1));
	t_2 = (v / u) * (t1 / -u);
	tmp = 0.0;
	if (u <= -1.05e+103)
		tmp = t_2;
	elseif (u <= -2.3e+48)
		tmp = t_1;
	elseif (u <= -2.4e-63)
		tmp = t_2;
	elseif (u <= 3.2e-45)
		tmp = v / -t1;
	elseif ((u <= 6.2e+20) || ~((u <= 8.5e+138)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(v / N[(t1 * N[(N[(u - t1), $MachinePrecision] / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(v / u), $MachinePrecision] * N[(t1 / (-u)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[u, -1.05e+103], t$95$2, If[LessEqual[u, -2.3e+48], t$95$1, If[LessEqual[u, -2.4e-63], t$95$2, If[LessEqual[u, 3.2e-45], N[(v / (-t1)), $MachinePrecision], If[Or[LessEqual[u, 6.2e+20], N[Not[LessEqual[u, 8.5e+138]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if u < -1.0500000000000001e103 or -2.3e48 < u < -2.4000000000000001e-63 or 3.20000000000000007e-45 < u < 6.2e20 or 8.5000000000000006e138 < u

   1. Initial program 82.6%

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

      1. times-frac 98.4%

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

      2. distribute-frac-neg 98.4%

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

      3. distribute-neg-frac2 98.4%

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

      4. +-commutative 98.4%

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

      5. distribute-neg-in 98.4%

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

      6. unsub-neg 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t1 around 0 87.9%

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

   6. Taylor expanded in t1 around 0 87.9%

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

      1. associate-*r/ 87.9%

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

      2. mul-1-neg 87.9%

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

   8. Simplified 87.9%

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

   if -1.0500000000000001e103 < u < -2.3e48 or 6.2e20 < u < 8.5000000000000006e138

   1. Initial program 64.8%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around inf 75.8%

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

      1. clear-num 75.8%

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

      2. frac-times 81.4%

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

      3. *-un-lft-identity 81.4%

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

      4. add-sqr-sqrt 30.7%

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

      5. sqrt-unprod 81.5%

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

      6. sqr-neg 81.5%

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

      7. sqrt-unprod 50.8%

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

      8. add-sqr-sqrt 81.9%

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

   7. Applied egg-rr 81.9%

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

   if -2.4000000000000001e-63 < u < 3.20000000000000007e-45

   1. Initial program 73.8%

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

      1. associate-/l* 72.0%

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

      2. distribute-lft-neg-out 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-/r* 82.5%

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

      5. distribute-neg-frac2 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t1 around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{elif}\;u \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;\frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ \mathbf{elif}\;u \leq -2.4 \cdot 10^{-63}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{elif}\;u \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 6.2 \cdot 10^{+20} \lor \neg \left(u \leq 8.5 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ t_2 := \left(-u\right) - t1\\ t_3 := t1 \cdot \frac{\frac{v}{u}}{t\_2}\\ \mathbf{if}\;u \leq -1.75 \cdot 10^{+104}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{t\_2}\\ \mathbf{elif}\;u \leq -3.9 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;u \leq -7.8 \cdot 10^{-62}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;u \leq 1.45 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;u \leq 9.2 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ v (* t1 (/ (- u t1) t1))))
        (t_2 (- (- u) t1))
        (t_3 (* t1 (/ (/ v u) t_2))))
   (if (<= u -1.75e+104)
     (/ (* t1 (/ v u)) t_2)
     (if (<= u -3.9e+48)
       t_1
       (if (<= u -7.8e-62)
         t_3
         (if (<= u 1.45e-45)
           (/ v (- t1))
           (if (<= u 1.05e+22)
             t_3
             (if (<= u 9.2e+134) t_1 (* (/ v u) (/ t1 (- u)))))))))))

C

double code(double u, double v, double t1) {
	double t_1 = v / (t1 * ((u - t1) / t1));
	double t_2 = -u - t1;
	double t_3 = t1 * ((v / u) / t_2);
	double tmp;
	if (u <= -1.75e+104) {
		tmp = (t1 * (v / u)) / t_2;
	} else if (u <= -3.9e+48) {
		tmp = t_1;
	} else if (u <= -7.8e-62) {
		tmp = t_3;
	} else if (u <= 1.45e-45) {
		tmp = v / -t1;
	} else if (u <= 1.05e+22) {
		tmp = t_3;
	} else if (u <= 9.2e+134) {
		tmp = t_1;
	} else {
		tmp = (v / u) * (t1 / -u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = v / (t1 * ((u - t1) / t1))
    t_2 = -u - t1
    t_3 = t1 * ((v / u) / t_2)
    if (u <= (-1.75d+104)) then
        tmp = (t1 * (v / u)) / t_2
    else if (u <= (-3.9d+48)) then
        tmp = t_1
    else if (u <= (-7.8d-62)) then
        tmp = t_3
    else if (u <= 1.45d-45) then
        tmp = v / -t1
    else if (u <= 1.05d+22) then
        tmp = t_3
    else if (u <= 9.2d+134) then
        tmp = t_1
    else
        tmp = (v / u) * (t1 / -u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = v / (t1 * ((u - t1) / t1));
	double t_2 = -u - t1;
	double t_3 = t1 * ((v / u) / t_2);
	double tmp;
	if (u <= -1.75e+104) {
		tmp = (t1 * (v / u)) / t_2;
	} else if (u <= -3.9e+48) {
		tmp = t_1;
	} else if (u <= -7.8e-62) {
		tmp = t_3;
	} else if (u <= 1.45e-45) {
		tmp = v / -t1;
	} else if (u <= 1.05e+22) {
		tmp = t_3;
	} else if (u <= 9.2e+134) {
		tmp = t_1;
	} else {
		tmp = (v / u) * (t1 / -u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = v / (t1 * ((u - t1) / t1))
	t_2 = -u - t1
	t_3 = t1 * ((v / u) / t_2)
	tmp = 0
	if u <= -1.75e+104:
		tmp = (t1 * (v / u)) / t_2
	elif u <= -3.9e+48:
		tmp = t_1
	elif u <= -7.8e-62:
		tmp = t_3
	elif u <= 1.45e-45:
		tmp = v / -t1
	elif u <= 1.05e+22:
		tmp = t_3
	elif u <= 9.2e+134:
		tmp = t_1
	else:
		tmp = (v / u) * (t1 / -u)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(v / Float64(t1 * Float64(Float64(u - t1) / t1)))
	t_2 = Float64(Float64(-u) - t1)
	t_3 = Float64(t1 * Float64(Float64(v / u) / t_2))
	tmp = 0.0
	if (u <= -1.75e+104)
		tmp = Float64(Float64(t1 * Float64(v / u)) / t_2);
	elseif (u <= -3.9e+48)
		tmp = t_1;
	elseif (u <= -7.8e-62)
		tmp = t_3;
	elseif (u <= 1.45e-45)
		tmp = Float64(v / Float64(-t1));
	elseif (u <= 1.05e+22)
		tmp = t_3;
	elseif (u <= 9.2e+134)
		tmp = t_1;
	else
		tmp = Float64(Float64(v / u) * Float64(t1 / Float64(-u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = v / (t1 * ((u - t1) / t1));
	t_2 = -u - t1;
	t_3 = t1 * ((v / u) / t_2);
	tmp = 0.0;
	if (u <= -1.75e+104)
		tmp = (t1 * (v / u)) / t_2;
	elseif (u <= -3.9e+48)
		tmp = t_1;
	elseif (u <= -7.8e-62)
		tmp = t_3;
	elseif (u <= 1.45e-45)
		tmp = v / -t1;
	elseif (u <= 1.05e+22)
		tmp = t_3;
	elseif (u <= 9.2e+134)
		tmp = t_1;
	else
		tmp = (v / u) * (t1 / -u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(v / N[(t1 * N[(N[(u - t1), $MachinePrecision] / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-u) - t1), $MachinePrecision]}, Block[{t$95$3 = N[(t1 * N[(N[(v / u), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[u, -1.75e+104], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[u, -3.9e+48], t$95$1, If[LessEqual[u, -7.8e-62], t$95$3, If[LessEqual[u, 1.45e-45], N[(v / (-t1)), $MachinePrecision], If[LessEqual[u, 1.05e+22], t$95$3, If[LessEqual[u, 9.2e+134], t$95$1, N[(N[(v / u), $MachinePrecision] * N[(t1 / (-u)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if u < -1.7500000000000001e104

   1. Initial program 84.3%

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

      1. times-frac 96.2%

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

      2. distribute-frac-neg 96.2%

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

      3. distribute-neg-frac2 96.2%

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

      4. +-commutative 96.2%

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

      5. distribute-neg-in 96.2%

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

      6. unsub-neg 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t1 around 0 94.2%

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

      1. associate-*l/ 97.8%

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

      2. frac-2neg 97.8%

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

      3. sub-neg 97.8%

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

      4. distribute-neg-in 97.8%

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

      5. add-sqr-sqrt 97.7%

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

      6. sqrt-unprod 82.4%

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

      7. sqr-neg 82.4%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 69.1%

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

      10. distribute-neg-in 69.1%

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

      11. sub-neg 69.1%

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

      12. neg-sub0 69.1%

          \[\leadsto \frac{-t1 \cdot \frac{v}{u}}{\color{blue}{0 - \left(u - t1\right)}} \]

      13. associate-+l- 69.1%

          \[\leadsto \frac{-t1 \cdot \frac{v}{u}}{\color{blue}{\left(0 - u\right) + t1}} \]

      14. neg-sub0 69.1%

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

      15. add-sqr-sqrt 69.1%

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

      16. sqrt-unprod 69.4%

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

      17. sqr-neg 69.4%

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

      18. sqrt-unprod 0.0%

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

      19. add-sqr-sqrt 97.8%

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

      20. +-commutative 97.8%

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

   7. Applied egg-rr 97.8%

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

   if -1.7500000000000001e104 < u < -3.9000000000000001e48 or 1.0499999999999999e22 < u < 9.1999999999999992e134

   1. Initial program 64.8%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around inf 75.8%

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

      1. clear-num 75.8%

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

      2. frac-times 81.4%

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

      3. *-un-lft-identity 81.4%

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

      4. add-sqr-sqrt 30.7%

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

      5. sqrt-unprod 81.5%

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

      6. sqr-neg 81.5%

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

      7. sqrt-unprod 50.8%

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

      8. add-sqr-sqrt 81.9%

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

   7. Applied egg-rr 81.9%

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

   if -3.9000000000000001e48 < u < -7.8000000000000007e-62 or 1.45e-45 < u < 1.0499999999999999e22

   1. Initial program 87.8%

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

      1. associate-/l* 88.8%

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

      2. distribute-lft-neg-out 88.8%

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

      3. distribute-rgt-neg-in 88.8%

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

      4. associate-/r* 95.1%

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

      5. distribute-neg-frac2 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t1 around 0 77.7%

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

   if -7.8000000000000007e-62 < u < 1.45e-45

   1. Initial program 73.8%

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

      1. associate-/l* 72.0%

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

      2. distribute-lft-neg-out 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-/r* 82.5%

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

      5. distribute-neg-frac2 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t1 around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   7. Simplified 84.9%

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

   if 9.1999999999999992e134 < u

   1. Initial program 77.1%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around 0 93.2%

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

   6. Taylor expanded in t1 around 0 93.3%

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

      1. associate-*r/ 93.3%

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

      2. mul-1-neg 93.3%

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

   8. Simplified 93.3%

      \[\leadsto \color{blue}{\frac{-t1}{u}} \cdot \frac{v}{u} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.75 \cdot 10^{+104}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{\left(-u\right) - t1}\\ \mathbf{elif}\;u \leq -3.9 \cdot 10^{+48}:\\ \;\;\;\;\frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ \mathbf{elif}\;u \leq -7.8 \cdot 10^{-62}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{\left(-u\right) - t1}\\ \mathbf{elif}\;u \leq 1.45 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{\left(-u\right) - t1}\\ \mathbf{elif}\;u \leq 9.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t1 \cdot \frac{\frac{v}{u}}{\left(-u\right) - t1}\\ \mathbf{if}\;u \leq -1.1 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;u \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;u \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* t1 (/ (/ v u) (- (- u) t1)))))
   (if (<= u -1.1e-63)
     t_1
     (if (<= u 4.2e-45)
       (/ v (- t1))
       (if (<= u 5.8e+18)
         t_1
         (if (<= u 8.5e+134)
           (/ v (* t1 (/ (- u t1) t1)))
           (* (/ v u) (/ t1 (- u)))))))))

C

double code(double u, double v, double t1) {
	double t_1 = t1 * ((v / u) / (-u - t1));
	double tmp;
	if (u <= -1.1e-63) {
		tmp = t_1;
	} else if (u <= 4.2e-45) {
		tmp = v / -t1;
	} else if (u <= 5.8e+18) {
		tmp = t_1;
	} else if (u <= 8.5e+134) {
		tmp = v / (t1 * ((u - t1) / t1));
	} else {
		tmp = (v / u) * (t1 / -u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t1 * ((v / u) / (-u - t1))
    if (u <= (-1.1d-63)) then
        tmp = t_1
    else if (u <= 4.2d-45) then
        tmp = v / -t1
    else if (u <= 5.8d+18) then
        tmp = t_1
    else if (u <= 8.5d+134) then
        tmp = v / (t1 * ((u - t1) / t1))
    else
        tmp = (v / u) * (t1 / -u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = t1 * ((v / u) / (-u - t1));
	double tmp;
	if (u <= -1.1e-63) {
		tmp = t_1;
	} else if (u <= 4.2e-45) {
		tmp = v / -t1;
	} else if (u <= 5.8e+18) {
		tmp = t_1;
	} else if (u <= 8.5e+134) {
		tmp = v / (t1 * ((u - t1) / t1));
	} else {
		tmp = (v / u) * (t1 / -u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = t1 * ((v / u) / (-u - t1))
	tmp = 0
	if u <= -1.1e-63:
		tmp = t_1
	elif u <= 4.2e-45:
		tmp = v / -t1
	elif u <= 5.8e+18:
		tmp = t_1
	elif u <= 8.5e+134:
		tmp = v / (t1 * ((u - t1) / t1))
	else:
		tmp = (v / u) * (t1 / -u)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(t1 * Float64(Float64(v / u) / Float64(Float64(-u) - t1)))
	tmp = 0.0
	if (u <= -1.1e-63)
		tmp = t_1;
	elseif (u <= 4.2e-45)
		tmp = Float64(v / Float64(-t1));
	elseif (u <= 5.8e+18)
		tmp = t_1;
	elseif (u <= 8.5e+134)
		tmp = Float64(v / Float64(t1 * Float64(Float64(u - t1) / t1)));
	else
		tmp = Float64(Float64(v / u) * Float64(t1 / Float64(-u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = t1 * ((v / u) / (-u - t1));
	tmp = 0.0;
	if (u <= -1.1e-63)
		tmp = t_1;
	elseif (u <= 4.2e-45)
		tmp = v / -t1;
	elseif (u <= 5.8e+18)
		tmp = t_1;
	elseif (u <= 8.5e+134)
		tmp = v / (t1 * ((u - t1) / t1));
	else
		tmp = (v / u) * (t1 / -u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(t1 * N[(N[(v / u), $MachinePrecision] / N[((-u) - t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[u, -1.1e-63], t$95$1, If[LessEqual[u, 4.2e-45], N[(v / (-t1)), $MachinePrecision], If[LessEqual[u, 5.8e+18], t$95$1, If[LessEqual[u, 8.5e+134], N[(v / N[(t1 * N[(N[(u - t1), $MachinePrecision] / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(v / u), $MachinePrecision] * N[(t1 / (-u)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if u < -1.1e-63 or 4.1999999999999999e-45 < u < 5.8e18

   1. Initial program 83.5%

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

      1. associate-/l* 84.1%

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

      2. distribute-lft-neg-out 84.1%

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

      3. distribute-rgt-neg-in 84.1%

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

      4. associate-/r* 94.2%

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

      5. distribute-neg-frac2 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t1 around 0 82.7%

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

   if -1.1e-63 < u < 4.1999999999999999e-45

   1. Initial program 73.8%

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

      1. associate-/l* 72.0%

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

      2. distribute-lft-neg-out 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-/r* 82.5%

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

      5. distribute-neg-frac2 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t1 around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   7. Simplified 84.9%

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

   if 5.8e18 < u < 8.50000000000000024e134

   1. Initial program 60.3%

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

      1. times-frac 99.7%

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

      2. distribute-frac-neg 99.7%

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

      3. distribute-neg-frac2 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-neg-in 99.7%

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

      6. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t1 around inf 78.3%

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

      1. clear-num 78.3%

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

      2. frac-times 83.0%

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

      3. *-un-lft-identity 83.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 83.1%

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

      6. sqr-neg 83.1%

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

      7. sqrt-unprod 83.1%

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

      8. add-sqr-sqrt 83.1%

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

   7. Applied egg-rr 83.1%

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

   if 8.50000000000000024e134 < u

   1. Initial program 77.1%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around 0 93.2%

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

   6. Taylor expanded in t1 around 0 93.3%

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

      1. associate-*r/ 93.3%

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

      2. mul-1-neg 93.3%

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

   8. Simplified 93.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.1 \cdot 10^{-63}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{\left(-u\right) - t1}\\ \mathbf{elif}\;u \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{\left(-u\right) - t1}\\ \mathbf{elif}\;u \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{v}{t1 \cdot \frac{u - t1}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{if}\;u \leq -7.8 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;u \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 68000000000000 \lor \neg \left(u \leq 5.1 \cdot 10^{+65}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u \cdot \left(-2\right) - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* (/ v u) (/ t1 (- u)))))
   (if (<= u -7.8e-62)
     t_1
     (if (<= u 1.25e-45)
       (/ v (- t1))
       (if (or (<= u 68000000000000.0) (not (<= u 5.1e+65)))
         t_1
         (/ v (- (* u (- 2.0)) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = (v / u) * (t1 / -u);
	double tmp;
	if (u <= -7.8e-62) {
		tmp = t_1;
	} else if (u <= 1.25e-45) {
		tmp = v / -t1;
	} else if ((u <= 68000000000000.0) || !(u <= 5.1e+65)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (v / u) * (t1 / -u)
    if (u <= (-7.8d-62)) then
        tmp = t_1
    else if (u <= 1.25d-45) then
        tmp = v / -t1
    else if ((u <= 68000000000000.0d0) .or. (.not. (u <= 5.1d+65))) then
        tmp = t_1
    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 t_1 = (v / u) * (t1 / -u);
	double tmp;
	if (u <= -7.8e-62) {
		tmp = t_1;
	} else if (u <= 1.25e-45) {
		tmp = v / -t1;
	} else if ((u <= 68000000000000.0) || !(u <= 5.1e+65)) {
		tmp = t_1;
	} else {
		tmp = v / ((u * -2.0) - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = (v / u) * (t1 / -u)
	tmp = 0
	if u <= -7.8e-62:
		tmp = t_1
	elif u <= 1.25e-45:
		tmp = v / -t1
	elif (u <= 68000000000000.0) or not (u <= 5.1e+65):
		tmp = t_1
	else:
		tmp = v / ((u * -2.0) - t1)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(v / u) * Float64(t1 / Float64(-u)))
	tmp = 0.0
	if (u <= -7.8e-62)
		tmp = t_1;
	elseif (u <= 1.25e-45)
		tmp = Float64(v / Float64(-t1));
	elseif ((u <= 68000000000000.0) || !(u <= 5.1e+65))
		tmp = t_1;
	else
		tmp = Float64(v / Float64(Float64(u * Float64(-2.0)) - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = (v / u) * (t1 / -u);
	tmp = 0.0;
	if (u <= -7.8e-62)
		tmp = t_1;
	elseif (u <= 1.25e-45)
		tmp = v / -t1;
	elseif ((u <= 68000000000000.0) || ~((u <= 5.1e+65)))
		tmp = t_1;
	else
		tmp = v / ((u * -2.0) - 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]}, If[LessEqual[u, -7.8e-62], t$95$1, If[LessEqual[u, 1.25e-45], N[(v / (-t1)), $MachinePrecision], If[Or[LessEqual[u, 68000000000000.0], N[Not[LessEqual[u, 5.1e+65]], $MachinePrecision]], t$95$1, N[(v / N[(N[(u * (-2.0)), $MachinePrecision] - t1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if u < -7.8000000000000007e-62 or 1.24999999999999994e-45 < u < 6.8e13 or 5.09999999999999989e65 < u

   1. Initial program 79.7%

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

      1. times-frac 98.7%

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

      2. distribute-frac-neg 98.7%

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

      3. distribute-neg-frac2 98.7%

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

      4. +-commutative 98.7%

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

      5. distribute-neg-in 98.7%

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

      6. unsub-neg 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t1 around 0 82.0%

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

   6. Taylor expanded in t1 around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. mul-1-neg 82.2%

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

   8. Simplified 82.2%

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

   if -7.8000000000000007e-62 < u < 1.24999999999999994e-45

   1. Initial program 73.8%

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

      1. associate-/l* 72.0%

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

      2. distribute-lft-neg-out 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-/r* 82.5%

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

      5. distribute-neg-frac2 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t1 around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   7. Simplified 84.9%

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

   if 6.8e13 < u < 5.09999999999999989e65

   1. Initial program 57.5%

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

      1. associate-/l* 68.9%

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

      2. distribute-lft-neg-out 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. associate-/r* 68.9%

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

      5. distribute-neg-frac2 68.9%

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

   3. Simplified 68.9%

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

      1. associate-*r/ 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. associate-*l/ 100.0%

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

      6. clear-num 100.0%

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

      7. frac-2neg 100.0%

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

      8. frac-times 100.0%

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

      9. *-un-lft-identity 100.0%

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

      10. frac-2neg 100.0%

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

      11. sub-neg 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. remove-double-neg 100.0%

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

      15. add-sqr-sqrt 32.7%

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

      16. sqrt-unprod 56.2%

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

      17. sqr-neg 56.2%

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

      18. sqrt-unprod 34.6%

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

      19. add-sqr-sqrt 35.5%

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

      20. add-sqr-sqrt 0.9%

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

      21. sqrt-unprod 47.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in u around 0 90.7%

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

      1. *-commutative 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -7.8 \cdot 10^{-62}:\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{elif}\;u \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;u \leq 68000000000000 \lor \neg \left(u \leq 5.1 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u \cdot \left(-2\right) - t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -6.2 \cdot 10^{-62} \lor \neg \left(u \leq 5.1 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -6.2e-62) (not (<= u 5.1e-45)))
   (* (/ v u) (/ t1 (- u)))
   (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -6.2e-62) || !(u <= 5.1e-45)) {
		tmp = (v / u) * (t1 / -u);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-6.2d-62)) .or. (.not. (u <= 5.1d-45))) then
        tmp = (v / u) * (t1 / -u)
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -6.2e-62) || !(u <= 5.1e-45)) {
		tmp = (v / u) * (t1 / -u);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -6.2e-62) or not (u <= 5.1e-45):
		tmp = (v / u) * (t1 / -u)
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -6.2e-62) || !(u <= 5.1e-45))
		tmp = Float64(Float64(v / u) * Float64(t1 / Float64(-u)));
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -6.2e-62) || ~((u <= 5.1e-45)))
		tmp = (v / u) * (t1 / -u);
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -6.2e-62], N[Not[LessEqual[u, 5.1e-45]], $MachinePrecision]], N[(N[(v / u), $MachinePrecision] * N[(t1 / (-u)), $MachinePrecision]), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -6.1999999999999999e-62 or 5.0999999999999997e-45 < u

   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 98.7%

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

      2. distribute-frac-neg 98.7%

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

      3. distribute-neg-frac2 98.7%

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

      4. +-commutative 98.7%

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

      5. distribute-neg-in 98.7%

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

      6. unsub-neg 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t1 around 0 79.3%

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

   6. Taylor expanded in t1 around 0 79.5%

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

      1. associate-*r/ 79.5%

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

      2. mul-1-neg 79.5%

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

   8. Simplified 79.5%

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

   if -6.1999999999999999e-62 < u < 5.0999999999999997e-45

   1. Initial program 73.8%

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

      1. associate-/l* 72.0%

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

      2. distribute-lft-neg-out 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-/r* 82.5%

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

      5. distribute-neg-frac2 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t1 around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -6.2 \cdot 10^{-62} \lor \neg \left(u \leq 5.1 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -4 \cdot 10^{-203} \lor \neg \left(t1 \leq 4.8 \cdot 10^{-188}\right):\\ \;\;\;\;\frac{v}{\left(-u\right) - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -4e-203) (not (<= t1 4.8e-188)))
   (/ v (- (- u) t1))
   (/ (* t1 (/ v u)) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -4e-203) || !(t1 <= 4.8e-188)) {
		tmp = v / (-u - t1);
	} else {
		tmp = (t1 * (v / u)) / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-4d-203)) .or. (.not. (t1 <= 4.8d-188))) then
        tmp = v / (-u - t1)
    else
        tmp = (t1 * (v / u)) / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -4e-203) || !(t1 <= 4.8e-188)) {
		tmp = v / (-u - t1);
	} else {
		tmp = (t1 * (v / u)) / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -4e-203) or not (t1 <= 4.8e-188):
		tmp = v / (-u - t1)
	else:
		tmp = (t1 * (v / u)) / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -4e-203) || !(t1 <= 4.8e-188))
		tmp = Float64(v / Float64(Float64(-u) - t1));
	else
		tmp = Float64(Float64(t1 * Float64(v / u)) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -4e-203) || ~((t1 <= 4.8e-188)))
		tmp = v / (-u - t1);
	else
		tmp = (t1 * (v / u)) / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -4e-203], N[Not[LessEqual[t1, 4.8e-188]], $MachinePrecision]], N[(v / N[((-u) - t1), $MachinePrecision]), $MachinePrecision], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -4.0000000000000001e-203 or 4.8e-188 < t1

   1. Initial program 73.3%

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

      1. times-frac 99.2%

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

      2. distribute-frac-neg 99.2%

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

      3. distribute-neg-frac2 99.2%

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

      4. +-commutative 99.2%

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

      5. distribute-neg-in 99.2%

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

      6. unsub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t1 around inf 70.6%

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

   6. Taylor expanded in v around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   8. Simplified 68.4%

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

   if -4.0000000000000001e-203 < t1 < 4.8e-188

   1. Initial program 89.7%

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

      1. times-frac 93.6%

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

      2. distribute-frac-neg 93.6%

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

      3. distribute-neg-frac2 93.6%

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

      4. +-commutative 93.6%

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

      5. distribute-neg-in 93.6%

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

      6. unsub-neg 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in t1 around inf 49.2%

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

      1. frac-times 44.5%

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

      2. associate-/r* 62.4%

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

      3. sub-neg 62.4%

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

      4. distribute-neg-in 62.4%

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

      5. +-commutative 62.4%

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

      6. neg-mul-1 62.4%

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

      7. associate-/l/ 62.4%

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

      8. associate-*r/ 64.4%

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

      9. associate-/l* 64.4%

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

      10. associate-/l/ 64.4%

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

      11. neg-mul-1 64.4%

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

      12. +-commutative 64.4%

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

      13. distribute-neg-in 64.4%

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

      14. sub-neg 64.4%

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

      15. add-sqr-sqrt 28.1%

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

      16. sqrt-unprod 67.3%

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

      17. sqr-neg 67.3%

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

      18. sqrt-unprod 35.9%

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

      19. add-sqr-sqrt 62.0%

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

   7. Applied egg-rr 62.0%

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

   8. Taylor expanded in u around inf 56.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -4 \cdot 10^{-203} \lor \neg \left(t1 \leq 4.8 \cdot 10^{-188}\right):\\ \;\;\;\;\frac{v}{\left(-u\right) - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.6 \cdot 10^{+125} \lor \neg \left(u \leq 3.5 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.6e+125) (not (<= u 3.5e+191))) (/ v u) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.6e+125) || !(u <= 3.5e+191)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-2.6d+125)) .or. (.not. (u <= 3.5d+191))) then
        tmp = v / u
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.6e+125) || !(u <= 3.5e+191)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.6e+125) or not (u <= 3.5e+191):
		tmp = v / u
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.6e+125) || !(u <= 3.5e+191))
		tmp = Float64(v / u);
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.6e+125) || ~((u <= 3.5e+191)))
		tmp = v / u;
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.6e+125], N[Not[LessEqual[u, 3.5e+191]], $MachinePrecision]], N[(v / u), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2.60000000000000003e125 or 3.4999999999999997e191 < u

   1. Initial program 80.6%

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

      1. associate-/l* 80.9%

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

      2. distribute-lft-neg-out 80.9%

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

      3. distribute-rgt-neg-in 80.9%

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

      4. associate-/r* 94.9%

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

      5. distribute-neg-frac2 94.9%

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

   3. Simplified 94.9%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. div-inv 99.9%

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

      2. associate-/l* 99.9%

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

      3. associate-*l* 94.9%

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

      4. associate-/l/ 94.9%

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

      5. neg-mul-1 94.9%

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

      6. +-commutative 94.9%

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

      7. distribute-neg-in 94.9%

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

      8. sub-neg 94.9%

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

      9. add-sqr-sqrt 49.0%

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

      10. sqrt-unprod 80.9%

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

      11. sqr-neg 80.9%

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

      12. sqrt-unprod 40.0%

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

      13. add-sqr-sqrt 78.8%

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

      14. frac-2neg 78.8%

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

      15. metadata-eval 78.8%

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

      16. +-commutative 78.8%

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

      17. distribute-neg-in 78.8%

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

      18. sub-neg 78.8%

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

      19. add-sqr-sqrt 38.8%

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

      20. sqrt-unprod 78.1%

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

      21. sqr-neg 78.1%

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

      22. sqrt-unprod 45.4%

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

      23. add-sqr-sqrt 94.5%

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

   8. Applied egg-rr 94.5%

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

      1. associate-*r* 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*l/ 99.5%

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

      4. neg-mul-1 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r/ 96.2%

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

      7. distribute-frac-neg 96.2%

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

      8. div-sub 96.2%

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

      9. sub-neg 96.2%

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

      10. *-inverses 96.2%

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

      11. metadata-eval 96.2%

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

   10. Simplified 96.2%

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

   11. Taylor expanded in u around 0 41.9%

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

   12. Taylor expanded in u around inf 41.1%

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

   if -2.60000000000000003e125 < u < 3.4999999999999997e191

   1. Initial program 75.0%

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

      1. associate-/l* 75.5%

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

      2. distribute-lft-neg-out 75.5%

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

      3. distribute-rgt-neg-in 75.5%

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

      4. associate-/r* 85.4%

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

      5. distribute-neg-frac2 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t1 around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. neg-mul-1 66.0%

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

   7. Simplified 66.0%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.6 \cdot 10^{+125} \lor \neg \left(u \leq 3.5 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -4 \cdot 10^{+122}:\\ \;\;\;\;\frac{v}{-u}\\ \mathbf{elif}\;u \leq 3.5 \cdot 10^{+191}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -4e+122) (/ v (- u)) (if (<= u 3.5e+191) (/ v (- t1)) (/ v u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -4e+122) {
		tmp = v / -u;
	} else if (u <= 3.5e+191) {
		tmp = v / -t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (u <= (-4d+122)) then
        tmp = v / -u
    else if (u <= 3.5d+191) then
        tmp = v / -t1
    else
        tmp = v / u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -4e+122) {
		tmp = v / -u;
	} else if (u <= 3.5e+191) {
		tmp = v / -t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -4e+122:
		tmp = v / -u
	elif u <= 3.5e+191:
		tmp = v / -t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -4e+122)
		tmp = Float64(v / Float64(-u));
	elseif (u <= 3.5e+191)
		tmp = Float64(v / Float64(-t1));
	else
		tmp = Float64(v / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -4e+122)
		tmp = v / -u;
	elseif (u <= 3.5e+191)
		tmp = v / -t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -4e+122], N[(v / (-u)), $MachinePrecision], If[LessEqual[u, 3.5e+191], N[(v / (-t1)), $MachinePrecision], N[(v / u), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -4.00000000000000006e122

   1. Initial program 81.9%

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

      1. times-frac 95.6%

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

      2. distribute-frac-neg 95.6%

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

      3. distribute-neg-frac2 95.6%

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

      4. +-commutative 95.6%

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

      5. distribute-neg-in 95.6%

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

      6. unsub-neg 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t1 around inf 49.7%

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

   6. Taylor expanded in t1 around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. neg-mul-1 35.2%

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

   8. Simplified 35.2%

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

   if -4.00000000000000006e122 < u < 3.4999999999999997e191

   1. Initial program 74.7%

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

      1. associate-/l* 75.2%

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

      2. distribute-lft-neg-out 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

      4. associate-/r* 85.2%

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

      5. distribute-neg-frac2 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in t1 around inf 66.6%

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

      1. associate-*r/ 66.6%

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

      2. neg-mul-1 66.6%

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

   7. Simplified 66.6%

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

   if 3.4999999999999997e191 < u

   1. Initial program 80.4%

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

      1. associate-/l* 80.6%

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

      2. distribute-lft-neg-out 80.6%

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

      3. distribute-rgt-neg-in 80.6%

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

      4. associate-/r* 94.6%

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

      5. distribute-neg-frac2 94.6%

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

   3. Simplified 94.6%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. div-inv 100.0%

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

      2. associate-/l* 100.0%

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

      3. associate-*l* 94.5%

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

      4. associate-/l/ 94.5%

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

      5. neg-mul-1 94.5%

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

      6. +-commutative 94.5%

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

      7. distribute-neg-in 94.5%

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

      8. sub-neg 94.5%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 80.6%

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

      11. sqr-neg 80.6%

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

      12. sqrt-unprod 82.3%

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

      13. add-sqr-sqrt 82.3%

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

      14. frac-2neg 82.3%

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

      15. metadata-eval 82.3%

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

      16. +-commutative 82.3%

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

      17. distribute-neg-in 82.3%

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

      18. sub-neg 82.3%

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

      19. add-sqr-sqrt 0.0%

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

      20. sqrt-unprod 80.6%

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

      21. sqr-neg 80.6%

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

      22. sqrt-unprod 93.4%

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

      23. add-sqr-sqrt 93.6%

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

   8. Applied egg-rr 93.6%

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

      1. associate-*r* 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l/ 99.0%

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

      4. neg-mul-1 99.0%

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

      5. *-commutative 99.0%

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

      6. associate-/r/ 98.9%

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

      7. distribute-frac-neg 98.9%

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

      8. div-sub 98.9%

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

      9. sub-neg 98.9%

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

      10. *-inverses 98.9%

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

      11. metadata-eval 98.9%

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

   10. Simplified 98.9%

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

   11. Taylor expanded in u around 0 47.9%

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

   12. Taylor expanded in u around inf 46.2%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -4 \cdot 10^{+122}:\\ \;\;\;\;\frac{v}{-u}\\ \mathbf{elif}\;u \leq 3.5 \cdot 10^{+191}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. times-frac 98.1%

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

   2. distribute-frac-neg 98.1%

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

   3. distribute-neg-frac2 98.1%

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

   4. +-commutative 98.1%

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

   5. distribute-neg-in 98.1%

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

   6. unsub-neg 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 11: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{v}{u - t1}}{1 - \frac{u}{t1}} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ (/ v (- u t1)) (- 1.0 (/ u t1))))

C

double code(double u, double v, double t1) {
	return (v / (u - t1)) / (1.0 - (u / 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 / (u - t1)) / (1.0d0 - (u / t1))
end function

Java

public static double code(double u, double v, double t1) {
	return (v / (u - t1)) / (1.0 - (u / t1));
}

Python

def code(u, v, t1):
	return (v / (u - t1)) / (1.0 - (u / t1))

Julia

function code(u, v, t1)
	return Float64(Float64(v / Float64(u - t1)) / Float64(1.0 - Float64(u / t1)))
end

MATLAB

function tmp = code(u, v, t1)
	tmp = (v / (u - t1)) / (1.0 - (u / t1));
end

Wolfram

code[u_, v_, t1_] := N[(N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(u / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

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

   1. associate-/l* 76.9%

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

   2. distribute-lft-neg-out 76.9%

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

   3. distribute-rgt-neg-in 76.9%

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

   4. associate-/r* 88.0%

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

   5. distribute-neg-frac2 88.0%

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

3. Simplified 88.0%

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

   1. associate-*r/ 98.5%

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

   2. neg-mul-1 98.5%

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

   3. associate-/r* 98.5%

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

6. Applied egg-rr 98.5%

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

   1. div-inv 98.3%

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

   2. associate-/l* 98.3%

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

   3. associate-*l* 87.9%

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

   4. associate-/l/ 87.9%

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

   5. neg-mul-1 87.9%

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

   6. +-commutative 87.9%

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

   7. distribute-neg-in 87.9%

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

   8. sub-neg 87.9%

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

   9. add-sqr-sqrt 44.8%

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

   10. sqrt-unprod 76.2%

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

   11. sqr-neg 76.2%

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

   12. sqrt-unprod 33.9%

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

   13. add-sqr-sqrt 68.3%

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

   14. frac-2neg 68.3%

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

   15. metadata-eval 68.3%

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

   16. +-commutative 68.3%

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

   17. distribute-neg-in 68.3%

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

   18. sub-neg 68.3%

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

   19. add-sqr-sqrt 34.3%

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

   20. sqrt-unprod 73.9%

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

   21. sqr-neg 73.9%

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

   22. sqrt-unprod 42.5%

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

   23. add-sqr-sqrt 86.8%

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

8. Applied egg-rr 86.8%

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

   1. associate-*r* 97.0%

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

   2. *-commutative 97.0%

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

   3. associate-*l/ 97.1%

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

   4. neg-mul-1 97.1%

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

   5. *-commutative 97.1%

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

   6. associate-/r/ 97.3%

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

   7. distribute-frac-neg 97.3%

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

   8. div-sub 97.3%

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

   9. sub-neg 97.3%

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

   10. *-inverses 97.3%

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

   11. metadata-eval 97.3%

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

10. Simplified 97.3%

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

11. Taylor expanded in v around 0 95.5%

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

    1. mul-1-neg 95.5%

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

    2. sub-neg 95.5%

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

    3. metadata-eval 95.5%

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

    4. associate-/r* 96.5%

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

    5. distribute-neg-frac2 96.5%

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

    6. +-commutative 96.5%

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

    7. distribute-neg-in 96.5%

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

    8. metadata-eval 96.5%

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

    9. unsub-neg 96.5%

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

13. Simplified 96.5%

    \[\leadsto \color{blue}{\frac{\frac{v}{u - t1}}{1 - \frac{u}{t1}}} \]
14. Add Preprocessing

Alternative 12: 62.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. times-frac 98.1%

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

   2. distribute-frac-neg 98.1%

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

   3. distribute-neg-frac2 98.1%

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

   4. +-commutative 98.1%

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

   5. distribute-neg-in 98.1%

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

   6. unsub-neg 98.1%

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

3. Simplified 98.1%

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

5. Taylor expanded in t1 around inf 66.3%

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

6. Taylor expanded in v around 0 60.8%

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

   1. associate-*r/ 60.8%

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

   2. neg-mul-1 60.8%

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

8. Simplified 60.8%

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

9. Final simplification 60.8%

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

Alternative 13: 62.3% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. associate-/l* 76.9%

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

   2. distribute-lft-neg-out 76.9%

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

   3. distribute-rgt-neg-in 76.9%

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

   4. associate-/r* 88.0%

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

   5. distribute-neg-frac2 88.0%

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

3. Simplified 88.0%

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

   1. associate-*r/ 98.5%

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

   2. neg-mul-1 98.5%

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

   3. associate-/r* 98.5%

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

6. Applied egg-rr 98.5%

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

   1. div-inv 98.3%

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

   2. associate-/l* 98.3%

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

   3. associate-*l* 87.9%

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

   4. associate-/l/ 87.9%

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

   5. neg-mul-1 87.9%

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

   6. +-commutative 87.9%

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

   7. distribute-neg-in 87.9%

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

   8. sub-neg 87.9%

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

   9. add-sqr-sqrt 44.8%

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

   10. sqrt-unprod 76.2%

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

   11. sqr-neg 76.2%

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

   12. sqrt-unprod 33.9%

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

   13. add-sqr-sqrt 68.3%

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

   14. frac-2neg 68.3%

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

   15. metadata-eval 68.3%

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

   16. +-commutative 68.3%

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

   17. distribute-neg-in 68.3%

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

   18. sub-neg 68.3%

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

   19. add-sqr-sqrt 34.3%

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

   20. sqrt-unprod 73.9%

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

   21. sqr-neg 73.9%

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

   22. sqrt-unprod 42.5%

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

   23. add-sqr-sqrt 86.8%

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

8. Applied egg-rr 86.8%

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

   1. associate-*r* 97.0%

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

   2. *-commutative 97.0%

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

   3. associate-*l/ 97.1%

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

   4. neg-mul-1 97.1%

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

   5. *-commutative 97.1%

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

   6. associate-/r/ 97.3%

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

   7. distribute-frac-neg 97.3%

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

   8. div-sub 97.3%

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

   9. sub-neg 97.3%

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

   10. *-inverses 97.3%

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

   11. metadata-eval 97.3%

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

10. Simplified 97.3%

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

11. Taylor expanded in u around 0 59.7%

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

Alternative 14: 16.9% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. associate-/l* 76.9%

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

   2. distribute-lft-neg-out 76.9%

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

   3. distribute-rgt-neg-in 76.9%

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

   4. associate-/r* 88.0%

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

   5. distribute-neg-frac2 88.0%

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

3. Simplified 88.0%

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

   1. associate-*r/ 98.5%

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

   2. neg-mul-1 98.5%

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

   3. associate-/r* 98.5%

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

6. Applied egg-rr 98.5%

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

   1. div-inv 98.3%

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

   2. associate-/l* 98.3%

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

   3. associate-*l* 87.9%

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

   4. associate-/l/ 87.9%

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

   5. neg-mul-1 87.9%

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

   6. +-commutative 87.9%

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

   7. distribute-neg-in 87.9%

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

   8. sub-neg 87.9%

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

   9. add-sqr-sqrt 44.8%

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

   10. sqrt-unprod 76.2%

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

   11. sqr-neg 76.2%

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

   12. sqrt-unprod 33.9%

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

   13. add-sqr-sqrt 68.3%

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

   14. frac-2neg 68.3%

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

   15. metadata-eval 68.3%

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

   16. +-commutative 68.3%

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

   17. distribute-neg-in 68.3%

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

   18. sub-neg 68.3%

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

   19. add-sqr-sqrt 34.3%

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

   20. sqrt-unprod 73.9%

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

   21. sqr-neg 73.9%

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

   22. sqrt-unprod 42.5%

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

   23. add-sqr-sqrt 86.8%

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

8. Applied egg-rr 86.8%

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

   1. associate-*r* 97.0%

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

   2. *-commutative 97.0%

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

   3. associate-*l/ 97.1%

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

   4. neg-mul-1 97.1%

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

   5. *-commutative 97.1%

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

   6. associate-/r/ 97.3%

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

   7. distribute-frac-neg 97.3%

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

   8. div-sub 97.3%

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

   9. sub-neg 97.3%

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

   10. *-inverses 97.3%

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

   11. metadata-eval 97.3%

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

10. Simplified 97.3%

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

11. Taylor expanded in u around 0 59.7%

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

12. Taylor expanded in u around inf 18.4%

    \[\leadsto \color{blue}{\frac{v}{u}} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))