Rosa's DopplerBench

Percentage Accurate: 72.7% → 98.2%

Time: 17.3s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.9%

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

   1. associate-/l* 75.0%

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

   2. distribute-lft-neg-out 75.0%

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

   3. distribute-rgt-neg-in 75.0%

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

   4. associate-/r* 85.4%

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

   5. distribute-neg-frac2 85.4%

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

3. Simplified 85.4%

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

   1. associate-*r/ 98.9%

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

   2. neg-mul-1 98.9%

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

   3. associate-/r* 98.9%

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

6. Applied egg-rr 98.9%

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

7. Taylor expanded in v around 0 83.6%

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

   1. *-commutative 83.6%

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

   2. associate-*r/ 98.9%

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

   3. associate-*r* 98.9%

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

   4. *-commutative 98.9%

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

   5. associate-*r/ 98.9%

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

   6. mul-1-neg 98.9%

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

9. Simplified 98.9%

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

10. Final simplification 98.9%

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

Alternative 2: 90.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 3 \cdot 10^{+97}:\\ \;\;\;\;t1 \cdot \left(-\frac{\frac{v}{t1 + u}}{t1 + u}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -2.15e+101)
   (/ v (- (- t1) (* u 2.0)))
   (if (<= t1 3e+97) (* t1 (- (/ (/ v (+ t1 u)) (+ t1 u)))) (/ v (- u t1)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.15e+101) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 3e+97) {
		tmp = t1 * -((v / (t1 + u)) / (t1 + u));
	} else {
		tmp = 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 <= (-2.15d+101)) then
        tmp = v / (-t1 - (u * 2.0d0))
    else if (t1 <= 3d+97) then
        tmp = t1 * -((v / (t1 + u)) / (t1 + u))
    else
        tmp = v / (u - t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.15e+101) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 3e+97) {
		tmp = t1 * -((v / (t1 + u)) / (t1 + u));
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -2.15e+101:
		tmp = v / (-t1 - (u * 2.0))
	elif t1 <= 3e+97:
		tmp = t1 * -((v / (t1 + u)) / (t1 + u))
	else:
		tmp = v / (u - t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -2.15e+101)
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	elseif (t1 <= 3e+97)
		tmp = Float64(t1 * Float64(-Float64(Float64(v / Float64(t1 + u)) / Float64(t1 + u))));
	else
		tmp = Float64(v / Float64(u - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -2.15e+101)
		tmp = v / (-t1 - (u * 2.0));
	elseif (t1 <= 3e+97)
		tmp = t1 * -((v / (t1 + u)) / (t1 + u));
	else
		tmp = v / (u - t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -2.15e+101], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 3e+97], N[(t1 * (-N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -2.15e101

   1. Initial program 54.2%

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

      1. associate-/l* 51.4%

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

      2. distribute-lft-neg-out 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      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/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.8%

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

      8. frac-times 97.9%

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

      9. *-un-lft-identity 97.9%

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

      10. +-commutative 97.9%

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

      11. distribute-neg-in 97.9%

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

      12. sub-neg 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in u around 0 91.7%

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

      1. *-commutative 91.7%

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

   9. Simplified 91.7%

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

   if -2.15e101 < t1 < 2.9999999999999998e97

   1. Initial program 85.4%

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

      1. associate-/l* 86.3%

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

      2. distribute-lft-neg-out 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

      4. associate-/r* 91.9%

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

      5. distribute-neg-frac2 91.9%

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

   3. Simplified 91.9%

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

   if 2.9999999999999998e97 < t1

   1. Initial program 45.9%

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

      1. times-frac 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t1 around inf 91.1%

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

   6. Taylor expanded in v around 0 91.1%

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

      1. associate-*r/ 91.1%

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

      2. mul-1-neg 91.1%

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

   8. Simplified 91.1%

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

      1. frac-2neg 91.1%

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

      2. div-inv 90.7%

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

      3. remove-double-neg 90.7%

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

      4. +-commutative 90.7%

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

      5. distribute-neg-in 90.7%

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

      6. add-sqr-sqrt 48.6%

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

      7. sqrt-unprod 88.0%

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

      8. sqr-neg 88.0%

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

      9. sqrt-unprod 42.2%

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

      10. add-sqr-sqrt 91.1%

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

   10. Applied egg-rr 91.1%

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

       1. associate-*r/ 91.5%

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

       2. *-rgt-identity 91.5%

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

       3. sub-neg 91.5%

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

   12. Simplified 91.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 3 \cdot 10^{+97}:\\ \;\;\;\;t1 \cdot \left(-\frac{\frac{v}{t1 + u}}{t1 + u}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.32 \cdot 10^{+90}:\\ \;\;\;\;t1 \cdot \left(-\frac{\frac{v}{u}}{t1 + u}\right)\\ \mathbf{elif}\;u \leq 3 \cdot 10^{-39}:\\ \;\;\;\;\frac{v}{-t1} \cdot \frac{t1}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u} \cdot \frac{t1}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -1.32e+90)
   (* t1 (- (/ (/ v u) (+ t1 u))))
   (if (<= u 3e-39)
     (* (/ v (- t1)) (/ t1 (+ t1 u)))
     (* (/ (- v) (+ t1 u)) (/ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.32e+90) {
		tmp = t1 * -((v / u) / (t1 + u));
	} else if (u <= 3e-39) {
		tmp = (v / -t1) * (t1 / (t1 + u));
	} else {
		tmp = (-v / (t1 + u)) * (t1 / u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (u <= (-1.32d+90)) then
        tmp = t1 * -((v / u) / (t1 + u))
    else if (u <= 3d-39) then
        tmp = (v / -t1) * (t1 / (t1 + u))
    else
        tmp = (-v / (t1 + u)) * (t1 / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -1.32e+90) {
		tmp = t1 * -((v / u) / (t1 + u));
	} else if (u <= 3e-39) {
		tmp = (v / -t1) * (t1 / (t1 + u));
	} else {
		tmp = (-v / (t1 + u)) * (t1 / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -1.32e+90:
		tmp = t1 * -((v / u) / (t1 + u))
	elif u <= 3e-39:
		tmp = (v / -t1) * (t1 / (t1 + u))
	else:
		tmp = (-v / (t1 + u)) * (t1 / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -1.32e+90)
		tmp = Float64(t1 * Float64(-Float64(Float64(v / u) / Float64(t1 + u))));
	elseif (u <= 3e-39)
		tmp = Float64(Float64(v / Float64(-t1)) * Float64(t1 / Float64(t1 + u)));
	else
		tmp = Float64(Float64(Float64(-v) / Float64(t1 + u)) * Float64(t1 / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -1.32e+90)
		tmp = t1 * -((v / u) / (t1 + u));
	elseif (u <= 3e-39)
		tmp = (v / -t1) * (t1 / (t1 + u));
	else
		tmp = (-v / (t1 + u)) * (t1 / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -1.32e+90], N[(t1 * (-N[(N[(v / u), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[u, 3e-39], N[(N[(v / (-t1)), $MachinePrecision] * N[(t1 / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(t1 / u), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -1.3199999999999999e90

   1. Initial program 81.4%

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

      1. associate-/l* 81.8%

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

      2. distribute-lft-neg-out 81.8%

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

      3. distribute-rgt-neg-in 81.8%

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

      4. associate-/r* 94.7%

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

      5. distribute-neg-frac2 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t1 around 0 90.3%

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

   if -1.3199999999999999e90 < u < 3.00000000000000028e-39

   1. Initial program 70.5%

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

      1. times-frac 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 79.9%

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

   if 3.00000000000000028e-39 < u

   1. Initial program 79.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   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 84.6%

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

      1. associate-*r/ 84.6%

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

      2. mul-1-neg 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.32 \cdot 10^{+90}:\\ \;\;\;\;t1 \cdot \left(-\frac{\frac{v}{u}}{t1 + u}\right)\\ \mathbf{elif}\;u \leq 3 \cdot 10^{-39}:\\ \;\;\;\;\frac{v}{-t1} \cdot \frac{t1}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u} \cdot \frac{t1}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;\left(v \cdot \frac{t1}{u}\right) \cdot \frac{-1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1} \cdot \frac{t1}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -7.2e-32)
   (/ v (- (- t1) (* u 2.0)))
   (if (<= t1 2.4e-55)
     (* (* v (/ t1 u)) (/ -1.0 u))
     (* (/ v (- t1)) (/ t1 (+ t1 u))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -7.2e-32) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 2.4e-55) {
		tmp = (v * (t1 / u)) * (-1.0 / u);
	} else {
		tmp = (v / -t1) * (t1 / (t1 + u));
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-7.2d-32)) then
        tmp = v / (-t1 - (u * 2.0d0))
    else if (t1 <= 2.4d-55) then
        tmp = (v * (t1 / u)) * ((-1.0d0) / u)
    else
        tmp = (v / -t1) * (t1 / (t1 + u))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -7.2e-32) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 2.4e-55) {
		tmp = (v * (t1 / u)) * (-1.0 / u);
	} else {
		tmp = (v / -t1) * (t1 / (t1 + u));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -7.2e-32:
		tmp = v / (-t1 - (u * 2.0))
	elif t1 <= 2.4e-55:
		tmp = (v * (t1 / u)) * (-1.0 / u)
	else:
		tmp = (v / -t1) * (t1 / (t1 + u))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -7.2e-32)
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	elseif (t1 <= 2.4e-55)
		tmp = Float64(Float64(v * Float64(t1 / u)) * Float64(-1.0 / u));
	else
		tmp = Float64(Float64(v / Float64(-t1)) * Float64(t1 / Float64(t1 + u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -7.2e-32)
		tmp = v / (-t1 - (u * 2.0));
	elseif (t1 <= 2.4e-55)
		tmp = (v * (t1 / u)) * (-1.0 / u);
	else
		tmp = (v / -t1) * (t1 / (t1 + u));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -7.2e-32], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.4e-55], N[(N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / u), $MachinePrecision]), $MachinePrecision], N[(N[(v / (-t1)), $MachinePrecision] * N[(t1 / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -7.19999999999999986e-32

   1. Initial program 66.2%

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

      1. associate-/l* 67.9%

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

      2. distribute-lft-neg-out 67.9%

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

      3. distribute-rgt-neg-in 67.9%

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

      4. associate-/r* 78.4%

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

      5. distribute-neg-frac2 78.4%

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

   3. Simplified 78.4%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.8%

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

      8. frac-times 98.7%

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

      9. *-un-lft-identity 98.7%

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

      10. +-commutative 98.7%

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

      11. distribute-neg-in 98.7%

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

      12. sub-neg 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in u around 0 86.0%

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

      1. *-commutative 86.0%

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

   9. Simplified 86.0%

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

   if -7.19999999999999986e-32 < t1 < 2.39999999999999991e-55

   1. Initial program 83.4%

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

   3. Taylor expanded in t1 around 0 73.8%

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

      1. times-frac 81.5%

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

      2. div-inv 81.4%

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

      3. associate-*r* 81.0%

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

      4. add-sqr-sqrt 33.4%

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

      5. sqrt-unprod 52.2%

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

      6. sqr-neg 52.2%

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

      7. sqrt-unprod 29.5%

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

      8. add-sqr-sqrt 48.5%

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

      9. frac-2neg 48.5%

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

      10. metadata-eval 48.5%

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

      11. add-sqr-sqrt 17.5%

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

      12. sqrt-unprod 60.0%

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

      13. sqr-neg 60.0%

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

      14. sqrt-unprod 46.4%

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

      15. add-sqr-sqrt 81.0%

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

   5. Applied egg-rr 81.0%

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

   6. Taylor expanded in t1 around 0 83.9%

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

   if 2.39999999999999991e-55 < t1

   1. Initial program 70.8%

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

      1. 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 78.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;\left(v \cdot \frac{t1}{u}\right) \cdot \frac{-1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1} \cdot \frac{t1}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.8 \cdot 10^{-32} \lor \neg \left(t1 \leq 2.95 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(v \cdot \frac{t1}{u}\right) \cdot \frac{-1}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -1.8e-32) (not (<= t1 2.95e-55)))
   (/ v (- (- t1) (* u 2.0)))
   (* (* v (/ t1 u)) (/ -1.0 u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.8e-32) || !(t1 <= 2.95e-55)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v * (t1 / u)) * (-1.0 / u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-1.8d-32)) .or. (.not. (t1 <= 2.95d-55))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (v * (t1 / u)) * ((-1.0d0) / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.8e-32) || !(t1 <= 2.95e-55)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v * (t1 / u)) * (-1.0 / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -1.8e-32) or not (t1 <= 2.95e-55):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (v * (t1 / u)) * (-1.0 / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -1.8e-32) || !(t1 <= 2.95e-55))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(v * Float64(t1 / u)) * Float64(-1.0 / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -1.8e-32) || ~((t1 <= 2.95e-55)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (v * (t1 / u)) * (-1.0 / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -1.8e-32], N[Not[LessEqual[t1, 2.95e-55]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -1.79999999999999996e-32 or 2.9499999999999999e-55 < t1

   1. Initial program 68.4%

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

      1. associate-/l* 68.5%

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

      2. distribute-lft-neg-out 68.5%

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

      3. distribute-rgt-neg-in 68.5%

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

      4. associate-/r* 81.5%

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

      5. distribute-neg-frac2 81.5%

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

   3. Simplified 81.5%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.8%

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

      8. frac-times 95.4%

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

      9. *-un-lft-identity 95.4%

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

      10. +-commutative 95.4%

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

      11. distribute-neg-in 95.4%

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

      12. sub-neg 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in u around 0 82.1%

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

      1. *-commutative 82.1%

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

   9. Simplified 82.1%

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

   if -1.79999999999999996e-32 < t1 < 2.9499999999999999e-55

   1. Initial program 83.4%

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

   3. Taylor expanded in t1 around 0 73.8%

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

      1. times-frac 81.5%

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

      2. div-inv 81.4%

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

      3. associate-*r* 81.0%

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

      4. add-sqr-sqrt 33.4%

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

      5. sqrt-unprod 52.2%

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

      6. sqr-neg 52.2%

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

      7. sqrt-unprod 29.5%

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

      8. add-sqr-sqrt 48.5%

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

      9. frac-2neg 48.5%

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

      10. metadata-eval 48.5%

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

      11. add-sqr-sqrt 17.5%

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

      12. sqrt-unprod 60.0%

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

      13. sqr-neg 60.0%

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

      14. sqrt-unprod 46.4%

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

      15. add-sqr-sqrt 81.0%

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

   5. Applied egg-rr 81.0%

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

   6. Taylor expanded in t1 around 0 83.9%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.8 \cdot 10^{-32} \lor \neg \left(t1 \leq 2.95 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(v \cdot \frac{t1}{u}\right) \cdot \frac{-1}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8.5 \cdot 10^{-34} \lor \neg \left(t1 \leq 2.25 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{u}}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -8.5e-34) (not (<= t1 2.25e-55)))
   (/ v (- (- t1) (* u 2.0)))
   (* (- t1) (/ (/ v u) u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.5e-34) || !(t1 <= 2.25e-55)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = -t1 * ((v / u) / u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-8.5d-34)) .or. (.not. (t1 <= 2.25d-55))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = -t1 * ((v / u) / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.5e-34) || !(t1 <= 2.25e-55)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = -t1 * ((v / u) / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -8.5e-34) or not (t1 <= 2.25e-55):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = -t1 * ((v / u) / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -8.5e-34) || !(t1 <= 2.25e-55))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(-t1) * Float64(Float64(v / u) / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -8.5e-34) || ~((t1 <= 2.25e-55)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = -t1 * ((v / u) / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -8.5e-34], N[Not[LessEqual[t1, 2.25e-55]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t1) * N[(N[(v / u), $MachinePrecision] / u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -8.5000000000000001e-34 or 2.24999999999999985e-55 < t1

   1. Initial program 68.4%

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

      1. associate-/l* 68.5%

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

      2. distribute-lft-neg-out 68.5%

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

      3. distribute-rgt-neg-in 68.5%

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

      4. associate-/r* 81.5%

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

      5. distribute-neg-frac2 81.5%

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

   3. Simplified 81.5%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. frac-2neg 99.9%

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

      7. clear-num 99.8%

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

      8. frac-times 95.4%

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

      9. *-un-lft-identity 95.4%

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

      10. +-commutative 95.4%

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

      11. distribute-neg-in 95.4%

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

      12. sub-neg 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in u around 0 82.1%

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

      1. *-commutative 82.1%

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

   9. Simplified 82.1%

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

   if -8.5000000000000001e-34 < t1 < 2.24999999999999985e-55

   1. Initial program 83.4%

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

      1. associate-/l* 83.5%

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

      2. distribute-lft-neg-out 83.5%

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

      3. distribute-rgt-neg-in 83.5%

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

      4. associate-/r* 90.6%

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

      5. distribute-neg-frac2 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t1 around 0 80.6%

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

   6. Taylor expanded in t1 around 0 83.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8.5 \cdot 10^{-34} \lor \neg \left(t1 \leq 2.25 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{u}}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq 4 \cdot 10^{-55}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{u}}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -2.2e-33)
   (/ (- v) (+ t1 u))
   (if (<= t1 4e-55) (* (- t1) (/ (/ v u) u)) (/ v (- u t1)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.2e-33) {
		tmp = -v / (t1 + u);
	} else if (t1 <= 4e-55) {
		tmp = -t1 * ((v / u) / u);
	} else {
		tmp = 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 <= (-2.2d-33)) then
        tmp = -v / (t1 + u)
    else if (t1 <= 4d-55) then
        tmp = -t1 * ((v / u) / u)
    else
        tmp = v / (u - t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.2e-33) {
		tmp = -v / (t1 + u);
	} else if (t1 <= 4e-55) {
		tmp = -t1 * ((v / u) / u);
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -2.2e-33:
		tmp = -v / (t1 + u)
	elif t1 <= 4e-55:
		tmp = -t1 * ((v / u) / u)
	else:
		tmp = v / (u - t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -2.2e-33)
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	elseif (t1 <= 4e-55)
		tmp = Float64(Float64(-t1) * Float64(Float64(v / u) / u));
	else
		tmp = Float64(v / Float64(u - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -2.2e-33)
		tmp = -v / (t1 + u);
	elseif (t1 <= 4e-55)
		tmp = -t1 * ((v / u) / u);
	else
		tmp = v / (u - t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -2.2e-33], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 4e-55], N[((-t1) * N[(N[(v / u), $MachinePrecision] / u), $MachinePrecision]), $MachinePrecision], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -2.20000000000000005e-33

   1. Initial program 66.2%

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

      1. times-frac 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t1 around inf 84.6%

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

   6. Taylor expanded in v around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. mul-1-neg 84.6%

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

   8. Simplified 84.6%

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

   if -2.20000000000000005e-33 < t1 < 3.99999999999999998e-55

   1. Initial program 83.4%

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

      1. associate-/l* 83.5%

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

      2. distribute-lft-neg-out 83.5%

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

      3. distribute-rgt-neg-in 83.5%

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

      4. associate-/r* 90.6%

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

      5. distribute-neg-frac2 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t1 around 0 80.6%

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

   6. Taylor expanded in t1 around 0 83.5%

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

   if 3.99999999999999998e-55 < t1

   1. Initial program 70.8%

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

      1. 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 78.0%

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

   6. Taylor expanded in v around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. mul-1-neg 77.5%

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

   8. Simplified 77.5%

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

      1. frac-2neg 77.5%

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

      2. div-inv 77.1%

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

      3. remove-double-neg 77.1%

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

      4. +-commutative 77.1%

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

      5. distribute-neg-in 77.1%

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

      6. add-sqr-sqrt 37.4%

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

      7. sqrt-unprod 77.7%

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

      8. sqr-neg 77.7%

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

      9. sqrt-unprod 39.5%

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

      10. add-sqr-sqrt 77.2%

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

   10. Applied egg-rr 77.2%

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

       1. associate-*r/ 77.5%

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

       2. *-rgt-identity 77.5%

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

       3. sub-neg 77.5%

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

   12. Simplified 77.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \mathbf{elif}\;t1 \leq 4 \cdot 10^{-55}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{u}}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -9.5 \cdot 10^{+132} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{t1 \cdot v}{u \cdot u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -9.5e+132) (not (<= u 6.8e+41)))
   (/ (* t1 v) (* u u))
   (/ (- v) (+ t1 u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -9.5e+132) || !(u <= 6.8e+41)) {
		tmp = (t1 * v) / (u * u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-9.5d+132)) .or. (.not. (u <= 6.8d+41))) then
        tmp = (t1 * v) / (u * u)
    else
        tmp = -v / (t1 + u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -9.5e+132) || !(u <= 6.8e+41)) {
		tmp = (t1 * v) / (u * u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -9.5e+132) or not (u <= 6.8e+41):
		tmp = (t1 * v) / (u * u)
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -9.5e+132) || !(u <= 6.8e+41))
		tmp = Float64(Float64(t1 * v) / Float64(u * u));
	else
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -9.5e+132) || ~((u <= 6.8e+41)))
		tmp = (t1 * v) / (u * u);
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -9.5e+132], N[Not[LessEqual[u, 6.8e+41]], $MachinePrecision]], N[(N[(t1 * v), $MachinePrecision] / N[(u * u), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -9.5000000000000005e132 or 6.79999999999999996e41 < u

   1. Initial program 78.0%

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

   3. Taylor expanded in t1 around 0 78.0%

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

   4. Taylor expanded in t1 around 0 76.0%

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

      1. add-sqr-sqrt 28.9%

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

      2. sqrt-unprod 58.9%

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

      3. sqr-neg 58.9%

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

      4. sqrt-unprod 38.9%

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

      5. add-sqr-sqrt 64.5%

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

      6. pow1 64.5%

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

   6. Applied egg-rr 64.5%

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

      1. unpow1 64.5%

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

   8. Simplified 64.5%

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

   if -9.5000000000000005e132 < u < 6.79999999999999996e41

   1. Initial program 73.2%

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

      1. times-frac 99.1%

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

      2. distribute-frac-neg 99.1%

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

      3. distribute-neg-frac2 99.1%

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

      4. +-commutative 99.1%

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

      5. distribute-neg-in 99.1%

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

      6. unsub-neg 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t1 around inf 73.1%

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

   6. Taylor expanded in v around 0 72.0%

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

      1. associate-*r/ 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -9.5 \cdot 10^{+132} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{t1 \cdot v}{u \cdot u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -9.6 \cdot 10^{+132} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -9.6e+132) (not (<= u 6.8e+41)))
   (* (/ v u) (/ t1 u))
   (/ (- v) (+ t1 u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -9.6e+132) || !(u <= 6.8e+41)) {
		tmp = (v / u) * (t1 / u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-9.6d+132)) .or. (.not. (u <= 6.8d+41))) then
        tmp = (v / u) * (t1 / u)
    else
        tmp = -v / (t1 + u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -9.6e+132) || !(u <= 6.8e+41)) {
		tmp = (v / u) * (t1 / u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -9.6e+132) or not (u <= 6.8e+41):
		tmp = (v / u) * (t1 / u)
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -9.6e+132) || !(u <= 6.8e+41))
		tmp = Float64(Float64(v / u) * Float64(t1 / u));
	else
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -9.6e+132) || ~((u <= 6.8e+41)))
		tmp = (v / u) * (t1 / u);
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -9.6e+132], N[Not[LessEqual[u, 6.8e+41]], $MachinePrecision]], N[(N[(v / u), $MachinePrecision] * N[(t1 / u), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -9.6000000000000004e132 or 6.79999999999999996e41 < u

   1. Initial program 78.0%

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

   3. Taylor expanded in t1 around 0 78.0%

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

   4. Taylor expanded in t1 around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. times-frac 85.4%

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

      3. add-sqr-sqrt 31.9%

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

      4. sqrt-unprod 62.9%

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

      5. sqr-neg 62.9%

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

      6. sqrt-unprod 38.9%

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

      7. add-sqr-sqrt 62.5%

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

   6. Applied egg-rr 62.5%

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

   if -9.6000000000000004e132 < u < 6.79999999999999996e41

   1. Initial program 73.2%

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

      1. times-frac 99.1%

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

      2. distribute-frac-neg 99.1%

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

      3. distribute-neg-frac2 99.1%

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

      4. +-commutative 99.1%

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

      5. distribute-neg-in 99.1%

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

      6. unsub-neg 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t1 around inf 73.1%

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

   6. Taylor expanded in v around 0 72.0%

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

      1. associate-*r/ 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -9.6 \cdot 10^{+132} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -5.5 \cdot 10^{+92} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{v}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -5.5e+92) (not (<= u 6.8e+41))) (/ v (+ t1 u)) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -5.5e+92) || !(u <= 6.8e+41)) {
		tmp = v / (t1 + u);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-5.5d+92)) .or. (.not. (u <= 6.8d+41))) then
        tmp = v / (t1 + u)
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -5.5e+92) || !(u <= 6.8e+41)) {
		tmp = v / (t1 + u);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -5.5e+92) or not (u <= 6.8e+41):
		tmp = v / (t1 + u)
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -5.5e+92) || !(u <= 6.8e+41))
		tmp = Float64(v / Float64(t1 + u));
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -5.5e+92) || ~((u <= 6.8e+41)))
		tmp = v / (t1 + u);
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -5.5e+92], N[Not[LessEqual[u, 6.8e+41]], $MachinePrecision]], N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -5.50000000000000053e92 or 6.79999999999999996e41 < u

   1. Initial program 80.3%

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

      1. times-frac 97.3%

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

      2. distribute-frac-neg 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. +-commutative 97.3%

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

      5. distribute-neg-in 97.3%

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

      6. unsub-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t1 around inf 49.6%

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

      1. frac-2neg 49.6%

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

      2. frac-times 38.7%

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

      3. add-sqr-sqrt 19.2%

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

      4. sqrt-unprod 39.9%

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

      5. sqr-neg 39.9%

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

      6. sqrt-unprod 19.3%

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

      7. add-sqr-sqrt 38.6%

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

      8. sub-neg 38.6%

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

      9. distribute-neg-in 38.6%

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

      10. +-commutative 38.6%

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

      11. remove-double-neg 38.6%

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

   7. Applied egg-rr 38.6%

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

      1. *-commutative 38.6%

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

      2. times-frac 35.2%

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

      3. *-inverses 35.2%

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

      4. *-lft-identity 35.2%

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

   9. Simplified 35.2%

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

   if -5.50000000000000053e92 < u < 6.79999999999999996e41

   1. Initial program 71.3%

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

      1. associate-/l* 71.3%

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

      2. distribute-lft-neg-out 71.3%

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

      3. distribute-rgt-neg-in 71.3%

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

      4. associate-/r* 81.2%

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

      5. distribute-neg-frac2 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t1 around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. neg-mul-1 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -5.5 \cdot 10^{+92} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{v}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.5 \cdot 10^{+189} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.5e+189) (not (<= u 6.8e+41))) (/ 1.0 (/ u v)) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.5e+189) || !(u <= 6.8e+41)) {
		tmp = 1.0 / (u / v);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-1.5d+189)) .or. (.not. (u <= 6.8d+41))) then
        tmp = 1.0d0 / (u / v)
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.5e+189) || !(u <= 6.8e+41)) {
		tmp = 1.0 / (u / v);
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.5e+189) or not (u <= 6.8e+41):
		tmp = 1.0 / (u / v)
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.5e+189) || !(u <= 6.8e+41))
		tmp = Float64(1.0 / Float64(u / v));
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.5e+189) || ~((u <= 6.8e+41)))
		tmp = 1.0 / (u / v);
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.5e+189], N[Not[LessEqual[u, 6.8e+41]], $MachinePrecision]], N[(1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.4999999999999999e189 or 6.79999999999999996e41 < u

   1. Initial program 77.6%

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

      1. associate-/l* 77.8%

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

      2. distribute-lft-neg-out 77.8%

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

      3. distribute-rgt-neg-in 77.8%

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

      4. associate-/r* 89.6%

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

      5. distribute-neg-frac2 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t1 around 0 84.8%

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

   6. Taylor expanded in t1 around inf 32.6%

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

      1. neg-mul-1 32.6%

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

      2. distribute-neg-frac 32.6%

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

   8. Simplified 32.6%

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

      1. clear-num 34.8%

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

      2. inv-pow 34.8%

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

      3. add-sqr-sqrt 14.7%

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

      4. sqrt-unprod 37.7%

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

      5. sqr-neg 37.7%

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

      6. sqrt-unprod 20.2%

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

      7. add-sqr-sqrt 35.2%

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

   10. Applied egg-rr 35.2%

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

       1. unpow-1 35.2%

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

   12. Simplified 35.2%

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

   if -1.4999999999999999e189 < u < 6.79999999999999996e41

   1. Initial program 73.6%

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

      1. associate-/l* 73.7%

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

      2. distribute-lft-neg-out 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. associate-/r* 83.4%

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

      5. distribute-neg-frac2 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in t1 around inf 68.0%

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

      1. associate-*r/ 68.0%

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

      2. neg-mul-1 68.0%

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

   7. Simplified 68.0%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.5 \cdot 10^{+189} \lor \neg \left(u \leq 6.8 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 23.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8.5 \cdot 10^{+135} \lor \neg \left(t1 \leq 3.5 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -8.5e+135) (not (<= t1 3.5e+74))) (/ v t1) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.5e+135) || !(t1 <= 3.5e+74)) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-8.5d+135)) .or. (.not. (t1 <= 3.5d+74))) then
        tmp = v / t1
    else
        tmp = v / u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.5e+135) || !(t1 <= 3.5e+74)) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -8.5e+135) or not (t1 <= 3.5e+74):
		tmp = v / t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -8.5e+135) || !(t1 <= 3.5e+74))
		tmp = Float64(v / t1);
	else
		tmp = Float64(v / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -8.5e+135) || ~((t1 <= 3.5e+74)))
		tmp = v / t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -8.5e+135], N[Not[LessEqual[t1, 3.5e+74]], $MachinePrecision]], N[(v / t1), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -8.49999999999999992e135 or 3.50000000000000014e74 < t1

   1. Initial program 49.9%

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

      1. associate-/l* 48.7%

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

      2. distribute-lft-neg-out 48.7%

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

      3. distribute-rgt-neg-in 48.7%

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

      4. associate-/r* 71.9%

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

      5. distribute-neg-frac2 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in t1 around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   7. Simplified 87.6%

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

      1. distribute-frac-neg 87.6%

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

      2. div-inv 87.4%

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

      3. distribute-rgt-neg-in 87.4%

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

      4. frac-2neg 87.4%

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

      5. metadata-eval 87.4%

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

      6. add-sqr-sqrt 42.5%

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

      7. sqrt-unprod 40.5%

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

      8. sqr-neg 40.5%

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

      9. sqrt-unprod 16.4%

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

      10. add-sqr-sqrt 37.0%

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

   9. Applied egg-rr 37.0%

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

       1. distribute-rgt-neg-out 37.0%

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

       2. associate-*r/ 37.0%

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

       3. *-commutative 37.0%

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

       4. mul-1-neg 37.0%

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

       5. distribute-neg-frac 37.0%

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

       6. remove-double-neg 37.0%

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

   11. Simplified 37.0%

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

   if -8.49999999999999992e135 < t1 < 3.50000000000000014e74

   1. Initial program 84.7%

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

      1. times-frac 97.9%

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

      2. distribute-frac-neg 97.9%

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

      3. distribute-neg-frac2 97.9%

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

      4. +-commutative 97.9%

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

      5. distribute-neg-in 97.9%

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

      6. unsub-neg 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t1 around inf 55.2%

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

   6. Taylor expanded in v around 0 49.5%

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

      1. associate-*r/ 49.5%

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

      2. mul-1-neg 49.5%

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

   8. Simplified 49.5%

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

      1. clear-num 49.3%

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

      2. associate-/r/ 49.3%

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

      3. add-sqr-sqrt 26.2%

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

      4. sqrt-unprod 31.7%

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

      5. sqr-neg 31.7%

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

      6. sqrt-unprod 6.6%

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

      7. add-sqr-sqrt 15.4%

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

   10. Applied egg-rr 15.4%

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

   11. Taylor expanded in t1 around 0 16.7%

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

4. Final simplification 22.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8.5 \cdot 10^{+135} \lor \neg \left(t1 \leq 3.5 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.9%

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

   1. times-frac 98.5%

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

   2. distribute-frac-neg 98.5%

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

   3. distribute-neg-frac2 98.5%

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

   4. +-commutative 98.5%

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

   5. distribute-neg-in 98.5%

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

   6. unsub-neg 98.5%

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

3. Simplified 98.5%

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

5. Final simplification 98.5%

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

Alternative 14: 56.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (if (<= u 4.5e+108) (/ v (- t1)) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= 4.5e+108) {
		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 <= 4.5d+108) 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 <= 4.5e+108) {
		tmp = v / -t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= 4.5e+108:
		tmp = v / -t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= 4.5e+108)
		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 <= 4.5e+108)
		tmp = v / -t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, 4.5e+108], N[(v / (-t1)), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < 4.5e108

   1. Initial program 74.3%

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

      1. associate-/l* 74.4%

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

      2. distribute-lft-neg-out 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

      4. associate-/r* 84.9%

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

      5. distribute-neg-frac2 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in t1 around inf 59.5%

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

      1. associate-*r/ 59.5%

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

      2. neg-mul-1 59.5%

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

   7. Simplified 59.5%

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

   if 4.5e108 < u

   1. Initial program 77.6%

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

      1. times-frac 97.8%

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

      2. distribute-frac-neg 97.8%

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

      3. distribute-neg-frac2 97.8%

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

      4. +-commutative 97.8%

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

      5. distribute-neg-in 97.8%

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

      6. unsub-neg 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t1 around inf 53.9%

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

   6. Taylor expanded in v around 0 46.0%

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

      1. associate-*r/ 46.0%

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

      2. mul-1-neg 46.0%

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

   8. Simplified 46.0%

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

      1. clear-num 47.5%

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

      2. associate-/r/ 46.0%

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

      3. add-sqr-sqrt 23.2%

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

      4. sqrt-unprod 44.3%

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

      5. sqr-neg 44.3%

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

      6. sqrt-unprod 20.9%

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

      7. add-sqr-sqrt 40.7%

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

   10. Applied egg-rr 40.7%

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

   11. Taylor expanded in t1 around 0 37.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.9%

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

   1. times-frac 98.5%

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

   2. distribute-frac-neg 98.5%

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

   3. distribute-neg-frac2 98.5%

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

   4. +-commutative 98.5%

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

   5. distribute-neg-in 98.5%

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

   6. unsub-neg 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in t1 around inf 64.7%

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

6. Taylor expanded in v around 0 60.6%

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

   1. associate-*r/ 60.6%

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

   2. mul-1-neg 60.6%

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

8. Simplified 60.6%

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

Alternative 16: 61.5% 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 74.9%

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

   1. times-frac 98.5%

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

   2. distribute-frac-neg 98.5%

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

   3. distribute-neg-frac2 98.5%

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

   4. +-commutative 98.5%

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

   5. distribute-neg-in 98.5%

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

   6. unsub-neg 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in t1 around inf 64.7%

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

6. Taylor expanded in v around 0 60.6%

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

   1. associate-*r/ 60.6%

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

   2. mul-1-neg 60.6%

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

8. Simplified 60.6%

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

   1. frac-2neg 60.6%

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

   2. div-inv 60.4%

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

   3. remove-double-neg 60.4%

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

   4. +-commutative 60.4%

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

   5. distribute-neg-in 60.4%

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

   6. add-sqr-sqrt 27.5%

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

   7. sqrt-unprod 66.7%

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

   8. sqr-neg 66.7%

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

   9. sqrt-unprod 32.3%

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

   10. add-sqr-sqrt 60.1%

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

10. Applied egg-rr 60.1%

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

    1. associate-*r/ 60.3%

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

    2. *-rgt-identity 60.3%

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

    3. sub-neg 60.3%

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

12. Simplified 60.3%

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

Alternative 17: 14.5% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.9%

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

   1. associate-/l* 75.0%

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

   2. distribute-lft-neg-out 75.0%

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

   3. distribute-rgt-neg-in 75.0%

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

   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 52.6%

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

   1. associate-*r/ 52.6%

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

   2. neg-mul-1 52.6%

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

7. Simplified 52.6%

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

   1. distribute-frac-neg 52.6%

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

   2. div-inv 52.4%

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

   3. distribute-rgt-neg-in 52.4%

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

   4. frac-2neg 52.4%

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

   5. metadata-eval 52.4%

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

   6. add-sqr-sqrt 28.7%

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

   7. sqrt-unprod 28.3%

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

   8. sqr-neg 28.3%

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

   9. sqrt-unprod 5.9%

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

   10. add-sqr-sqrt 12.7%

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

9. Applied egg-rr 12.7%

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

    1. distribute-rgt-neg-out 12.7%

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

    2. associate-*r/ 12.7%

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

    3. *-commutative 12.7%

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

    4. mul-1-neg 12.7%

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

    5. distribute-neg-frac 12.7%

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

    6. remove-double-neg 12.7%

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

11. Simplified 12.7%

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

Reproduce

herbie shell --seed 2024118 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))