Rosa's DopplerBench

Percentage Accurate: 73.4% → 98.3%

Time: 17.6s

Alternatives: 16

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: 73.4% 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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. 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* 81.3%

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

   5. distribute-neg-frac2 81.3%

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

3. Simplified 81.3%

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

   1. distribute-frac-neg2 81.3%

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

   2. distribute-rgt-neg-out 81.3%

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

   3. associate-/r* 71.3%

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

   4. distribute-lft-neg-out 71.3%

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

   5. associate-/l* 71.3%

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

   6. times-frac 98.1%

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

   7. frac-2neg 98.1%

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

   8. associate-*r/ 99.4%

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

   9. add-sqr-sqrt 51.2%

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

   10. sqrt-unprod 49.4%

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

   11. sqr-neg 49.4%

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

   12. sqrt-unprod 22.6%

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

   13. add-sqr-sqrt 39.5%

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

   14. add-sqr-sqrt 23.9%

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

   15. sqrt-unprod 57.5%

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

   16. sqr-neg 57.5%

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

   17. sqrt-prod 39.5%

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

   18. add-sqr-sqrt 99.4%

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

6. Applied egg-rr 99.4%

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

Alternative 2: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -6 \cdot 10^{-13}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;u \leq 1.4 \cdot 10^{+63}:\\ \;\;\;\;-\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{v}{1 - \frac{u}{t1}}}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -6e-13)
   (/ (* t1 (/ v u)) (- u))
   (if (<= u 1.4e+63) (- (/ v t1)) (/ (/ v (- 1.0 (/ u t1))) u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -6e-13) {
		tmp = (t1 * (v / u)) / -u;
	} else if (u <= 1.4e+63) {
		tmp = -(v / t1);
	} else {
		tmp = (v / (1.0 - (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 <= (-6d-13)) then
        tmp = (t1 * (v / u)) / -u
    else if (u <= 1.4d+63) then
        tmp = -(v / t1)
    else
        tmp = (v / (1.0d0 - (u / t1))) / u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -6e-13) {
		tmp = (t1 * (v / u)) / -u;
	} else if (u <= 1.4e+63) {
		tmp = -(v / t1);
	} else {
		tmp = (v / (1.0 - (u / t1))) / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -6e-13:
		tmp = (t1 * (v / u)) / -u
	elif u <= 1.4e+63:
		tmp = -(v / t1)
	else:
		tmp = (v / (1.0 - (u / t1))) / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -6e-13)
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	elseif (u <= 1.4e+63)
		tmp = Float64(-Float64(v / t1));
	else
		tmp = Float64(Float64(v / Float64(1.0 - Float64(u / t1))) / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -6e-13)
		tmp = (t1 * (v / u)) / -u;
	elseif (u <= 1.4e+63)
		tmp = -(v / t1);
	else
		tmp = (v / (1.0 - (u / t1))) / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -6e-13], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], If[LessEqual[u, 1.4e+63], (-N[(v / t1), $MachinePrecision]), N[(N[(v / N[(1.0 - N[(u / t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / u), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -5.99999999999999968e-13

   1. Initial program 77.8%

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

      1. associate-/l* 77.7%

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

      2. distribute-lft-neg-out 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

      4. associate-/r* 86.1%

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

      5. distribute-neg-frac2 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in t1 around 0 81.8%

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

   6. Taylor expanded in t1 around 0 81.7%

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

      1. associate-*r/ 86.2%

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

      2. clear-num 86.1%

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

      3. un-div-inv 86.1%

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

      4. add-sqr-sqrt 86.0%

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

      5. sqrt-unprod 75.8%

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

      6. sqr-neg 75.8%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 62.6%

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

   8. Applied egg-rr 62.6%

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

      1. add-sqr-sqrt 34.2%

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

      2. sqrt-unprod 67.0%

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

      3. sqr-neg 67.0%

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

      4. sqrt-unprod 41.3%

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

      5. add-sqr-sqrt 86.1%

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

      6. distribute-neg-frac 86.1%

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

      7. div-inv 86.1%

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

      8. clear-num 86.2%

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

   10. Applied egg-rr 86.2%

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

   if -5.99999999999999968e-13 < u < 1.39999999999999993e63

   1. Initial program 63.9%

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

      1. associate-/l* 64.4%

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

      2. distribute-lft-neg-out 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

      4. associate-/r* 76.2%

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

      5. distribute-neg-frac2 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in t1 around inf 79.9%

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

      1. associate-*r/ 79.9%

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

      2. neg-mul-1 79.9%

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

   7. Simplified 79.9%

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

   if 1.39999999999999993e63 < u

   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* 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. associate-/r* 87.7%

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

      5. distribute-neg-frac2 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t1 around 0 82.3%

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

      1. associate-*r/ 86.7%

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

      2. associate-*r/ 81.3%

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

      3. associate-*l/ 84.4%

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

      4. remove-double-neg 84.4%

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

      5. distribute-rgt-neg-out 84.4%

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

      6. neg-mul-1 84.4%

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

      7. metadata-eval 84.4%

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

      8. associate-/r* 84.4%

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

   7. Applied egg-rr 87.4%

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

      1. metadata-eval 87.4%

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

      2. distribute-neg-frac2 87.4%

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

      3. /-rgt-identity 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-/r/ 85.1%

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

      6. distribute-neg-frac2 85.1%

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

      7. div-sub 85.1%

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

      8. *-inverses 85.1%

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

      9. sub-neg 85.1%

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

      10. metadata-eval 85.1%

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

      11. distribute-neg-in 85.1%

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

      12. metadata-eval 85.1%

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

      13. +-commutative 85.1%

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

      14. unsub-neg 85.1%

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

   9. Simplified 85.1%

      \[\leadsto \color{blue}{\frac{\frac{v}{1 - \frac{u}{t1}}}{u}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -6 \cdot 10^{-13}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;u \leq 1.4 \cdot 10^{+63}:\\ \;\;\;\;-\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{v}{1 - \frac{u}{t1}}}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.6 \cdot 10^{-13} \lor \neg \left(u \leq 5.8 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.6e-13) (not (<= u 5.8e+83)))
   (/ (* t1 (/ v u)) (- u))
   (- (/ v t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.6e-13) || !(u <= 5.8e+83)) {
		tmp = (t1 * (v / u)) / -u;
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-1.6d-13)) .or. (.not. (u <= 5.8d+83))) then
        tmp = (t1 * (v / u)) / -u
    else
        tmp = -(v / t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.6e-13) || !(u <= 5.8e+83)) {
		tmp = (t1 * (v / u)) / -u;
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.6e-13) or not (u <= 5.8e+83):
		tmp = (t1 * (v / u)) / -u
	else:
		tmp = -(v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.6e-13) || !(u <= 5.8e+83))
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	else
		tmp = Float64(-Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.6e-13) || ~((u <= 5.8e+83)))
		tmp = (t1 * (v / u)) / -u;
	else
		tmp = -(v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.6e-13], N[Not[LessEqual[u, 5.8e+83]], $MachinePrecision]], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], (-N[(v / t1), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if u < -1.6e-13 or 5.79999999999999999e83 < u

   1. Initial program 78.8%

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

      1. associate-/l* 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. associate-/r* 86.5%

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

      5. distribute-neg-frac2 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t1 around 0 82.4%

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

   6. Taylor expanded in t1 around 0 82.5%

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

      1. associate-*r/ 87.5%

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

      2. clear-num 87.5%

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

      3. un-div-inv 87.5%

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

      4. add-sqr-sqrt 60.0%

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

      5. sqrt-unprod 73.5%

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

      6. sqr-neg 73.5%

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

      7. sqrt-unprod 20.6%

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

      8. add-sqr-sqrt 64.2%

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

   8. Applied egg-rr 64.2%

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

      1. add-sqr-sqrt 35.0%

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

      2. sqrt-unprod 66.5%

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

      3. sqr-neg 66.5%

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

      4. sqrt-unprod 41.1%

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

      5. add-sqr-sqrt 87.5%

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

      6. distribute-neg-frac 87.5%

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

      7. div-inv 87.5%

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

      8. clear-num 87.5%

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

   10. Applied egg-rr 87.5%

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

   if -1.6e-13 < u < 5.79999999999999999e83

   1. Initial program 64.7%

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

      1. associate-/l* 64.8%

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

      2. distribute-lft-neg-out 64.8%

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

      3. distribute-rgt-neg-in 64.8%

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

      4. associate-/r* 76.7%

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

      5. distribute-neg-frac2 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in t1 around inf 78.7%

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

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.6 \cdot 10^{-13} \lor \neg \left(u \leq 5.8 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -5.5 \cdot 10^{-17} \lor \neg \left(u \leq 2.7 \cdot 10^{+84}\right):\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -5.5e-17) (not (<= u 2.7e+84)))
   (* t1 (/ (/ v u) (- u)))
   (- (/ v t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -5.5e-17) || !(u <= 2.7e+84)) {
		tmp = t1 * ((v / u) / -u);
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-5.5d-17)) .or. (.not. (u <= 2.7d+84))) then
        tmp = t1 * ((v / u) / -u)
    else
        tmp = -(v / t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -5.5e-17) || !(u <= 2.7e+84)) {
		tmp = t1 * ((v / u) / -u);
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -5.5e-17) or not (u <= 2.7e+84):
		tmp = t1 * ((v / u) / -u)
	else:
		tmp = -(v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -5.5e-17) || !(u <= 2.7e+84))
		tmp = Float64(t1 * Float64(Float64(v / u) / Float64(-u)));
	else
		tmp = Float64(-Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -5.5e-17) || ~((u <= 2.7e+84)))
		tmp = t1 * ((v / u) / -u);
	else
		tmp = -(v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -5.5e-17], N[Not[LessEqual[u, 2.7e+84]], $MachinePrecision]], N[(t1 * N[(N[(v / u), $MachinePrecision] / (-u)), $MachinePrecision]), $MachinePrecision], (-N[(v / t1), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if u < -5.50000000000000001e-17 or 2.7e84 < u

   1. Initial program 78.8%

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

      1. associate-/l* 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. associate-/r* 86.5%

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

      5. distribute-neg-frac2 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t1 around 0 82.4%

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

   6. Taylor expanded in t1 around 0 82.5%

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

   if -5.50000000000000001e-17 < u < 2.7e84

   1. Initial program 64.7%

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

      1. associate-/l* 64.8%

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

      2. distribute-lft-neg-out 64.8%

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

      3. distribute-rgt-neg-in 64.8%

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

      4. associate-/r* 76.7%

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

      5. distribute-neg-frac2 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in t1 around inf 78.7%

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

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -5.5 \cdot 10^{-17} \lor \neg \left(u \leq 2.7 \cdot 10^{+84}\right):\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;u \leq 1.45 \cdot 10^{+64}:\\ \;\;\;\;-\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -2.6e-12)
   (/ (* t1 (/ v u)) (- u))
   (if (<= u 1.45e+64) (- (/ v t1)) (/ (/ t1 (/ u v)) (- u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2.6e-12) {
		tmp = (t1 * (v / u)) / -u;
	} else if (u <= 1.45e+64) {
		tmp = -(v / t1);
	} else {
		tmp = (t1 / (u / v)) / -u;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (u <= (-2.6d-12)) then
        tmp = (t1 * (v / u)) / -u
    else if (u <= 1.45d+64) then
        tmp = -(v / t1)
    else
        tmp = (t1 / (u / v)) / -u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2.6e-12) {
		tmp = (t1 * (v / u)) / -u;
	} else if (u <= 1.45e+64) {
		tmp = -(v / t1);
	} else {
		tmp = (t1 / (u / v)) / -u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -2.6e-12:
		tmp = (t1 * (v / u)) / -u
	elif u <= 1.45e+64:
		tmp = -(v / t1)
	else:
		tmp = (t1 / (u / v)) / -u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -2.6e-12)
		tmp = Float64(Float64(t1 * Float64(v / u)) / Float64(-u));
	elseif (u <= 1.45e+64)
		tmp = Float64(-Float64(v / t1));
	else
		tmp = Float64(Float64(t1 / Float64(u / v)) / Float64(-u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -2.6e-12)
		tmp = (t1 * (v / u)) / -u;
	elseif (u <= 1.45e+64)
		tmp = -(v / t1);
	else
		tmp = (t1 / (u / v)) / -u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -2.6e-12], N[(N[(t1 * N[(v / u), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], If[LessEqual[u, 1.45e+64], (-N[(v / t1), $MachinePrecision]), N[(N[(t1 / N[(u / v), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -2.59999999999999983e-12

   1. Initial program 77.8%

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

      1. associate-/l* 77.7%

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

      2. distribute-lft-neg-out 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

      4. associate-/r* 86.1%

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

      5. distribute-neg-frac2 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in t1 around 0 81.8%

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

   6. Taylor expanded in t1 around 0 81.7%

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

      1. associate-*r/ 86.2%

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

      2. clear-num 86.1%

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

      3. un-div-inv 86.1%

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

      4. add-sqr-sqrt 86.0%

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

      5. sqrt-unprod 75.8%

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

      6. sqr-neg 75.8%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 62.6%

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

   8. Applied egg-rr 62.6%

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

      1. add-sqr-sqrt 34.2%

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

      2. sqrt-unprod 67.0%

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

      3. sqr-neg 67.0%

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

      4. sqrt-unprod 41.3%

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

      5. add-sqr-sqrt 86.1%

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

      6. distribute-neg-frac 86.1%

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

      7. div-inv 86.1%

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

      8. clear-num 86.2%

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

   10. Applied egg-rr 86.2%

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

   if -2.59999999999999983e-12 < u < 1.44999999999999997e64

   1. Initial program 63.9%

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

      1. associate-/l* 64.4%

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

      2. distribute-lft-neg-out 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

      4. associate-/r* 76.2%

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

      5. distribute-neg-frac2 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in t1 around inf 79.9%

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

      1. associate-*r/ 79.9%

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

      2. neg-mul-1 79.9%

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

   7. Simplified 79.9%

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

   if 1.44999999999999997e64 < u

   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* 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. associate-/r* 87.7%

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

      5. distribute-neg-frac2 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t1 around 0 82.3%

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

   6. Taylor expanded in t1 around 0 79.7%

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

      1. associate-*r/ 85.0%

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

      2. frac-2neg 85.0%

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

      3. clear-num 85.0%

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

      4. un-div-inv 85.0%

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

      5. remove-double-neg 85.0%

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

   8. Applied egg-rr 85.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{t1 \cdot \frac{v}{u}}{-u}\\ \mathbf{elif}\;u \leq 1.45 \cdot 10^{+64}:\\ \;\;\;\;-\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.4 \cdot 10^{+99} \lor \neg \left(u \leq 5 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.4e+99) (not (<= u 5e+84)))
   (/ t1 (* u (/ u v)))
   (- (/ v t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.4e+99) || !(u <= 5e+84)) {
		tmp = t1 / (u * (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 <= (-1.4d+99)) .or. (.not. (u <= 5d+84))) then
        tmp = t1 / (u * (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 <= -1.4e+99) || !(u <= 5e+84)) {
		tmp = t1 / (u * (u / v));
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.4e+99) or not (u <= 5e+84):
		tmp = t1 / (u * (u / v))
	else:
		tmp = -(v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.4e+99) || !(u <= 5e+84))
		tmp = Float64(t1 / Float64(u * Float64(u / v)));
	else
		tmp = Float64(-Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.4e+99) || ~((u <= 5e+84)))
		tmp = t1 / (u * (u / v));
	else
		tmp = -(v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.4e+99], N[Not[LessEqual[u, 5e+84]], $MachinePrecision]], N[(t1 / N[(u * N[(u / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(v / t1), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if u < -1.4e99 or 5.0000000000000001e84 < u

   1. Initial program 79.9%

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

      1. associate-/l* 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. associate-/r* 88.3%

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

      5. distribute-neg-frac2 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t1 around 0 86.0%

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

   6. Taylor expanded in t1 around 0 86.1%

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

      1. clear-num 86.0%

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

      2. un-div-inv 86.0%

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

      3. div-inv 86.0%

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

      4. clear-num 86.0%

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

      5. add-sqr-sqrt 55.9%

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

      6. sqrt-unprod 75.5%

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

      7. sqr-neg 75.5%

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

      8. sqrt-unprod 24.3%

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

      9. add-sqr-sqrt 71.6%

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

   8. Applied egg-rr 71.6%

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

   if -1.4e99 < u < 5.0000000000000001e84

   1. Initial program 65.7%

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

      1. associate-/l* 65.5%

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

      2. distribute-lft-neg-out 65.5%

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

      3. distribute-rgt-neg-in 65.5%

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

      4. associate-/r* 76.7%

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

      5. distribute-neg-frac2 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in t1 around inf 74.4%

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

      1. associate-*r/ 74.4%

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

      2. neg-mul-1 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.4 \cdot 10^{+99} \lor \neg \left(u \leq 5 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+99} \lor \neg \left(u \leq 1.36 \cdot 10^{+84}\right):\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.1e+99) (not (<= u 1.36e+84)))
   (* t1 (/ (/ v u) u))
   (- (/ v t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.1e+99) || !(u <= 1.36e+84)) {
		tmp = t1 * ((v / u) / u);
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-2.1d+99)) .or. (.not. (u <= 1.36d+84))) then
        tmp = t1 * ((v / u) / u)
    else
        tmp = -(v / t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.1e+99) || !(u <= 1.36e+84)) {
		tmp = t1 * ((v / u) / u);
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.1e+99) or not (u <= 1.36e+84):
		tmp = t1 * ((v / u) / u)
	else:
		tmp = -(v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.1e+99) || !(u <= 1.36e+84))
		tmp = Float64(t1 * Float64(Float64(v / u) / u));
	else
		tmp = Float64(-Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.1e+99) || ~((u <= 1.36e+84)))
		tmp = t1 * ((v / u) / u);
	else
		tmp = -(v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.1e+99], N[Not[LessEqual[u, 1.36e+84]], $MachinePrecision]], N[(t1 * N[(N[(v / u), $MachinePrecision] / u), $MachinePrecision]), $MachinePrecision], (-N[(v / t1), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if u < -2.1000000000000001e99 or 1.3599999999999999e84 < u

   1. Initial program 79.9%

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

      1. associate-/l* 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. associate-/r* 88.3%

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

      5. distribute-neg-frac2 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t1 around 0 86.0%

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

   6. Taylor expanded in t1 around 0 86.1%

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

      1. associate-*r/ 92.0%

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

      2. clear-num 92.0%

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

      3. un-div-inv 91.9%

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

      4. add-sqr-sqrt 59.6%

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

      5. sqrt-unprod 75.5%

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

      6. sqr-neg 75.5%

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

      7. sqrt-unprod 24.2%

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

      8. add-sqr-sqrt 70.5%

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

   8. Applied egg-rr 70.5%

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

      1. div-inv 70.5%

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

      2. clear-num 70.5%

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

      3. associate-/l* 71.6%

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

   10. Applied egg-rr 71.6%

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

   if -2.1000000000000001e99 < u < 1.3599999999999999e84

   1. Initial program 65.7%

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

      1. associate-/l* 65.5%

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

      2. distribute-lft-neg-out 65.5%

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

      3. distribute-rgt-neg-in 65.5%

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

      4. associate-/r* 76.7%

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

      5. distribute-neg-frac2 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in t1 around inf 74.4%

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

      1. associate-*r/ 74.4%

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

      2. neg-mul-1 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.1 \cdot 10^{+99} \lor \neg \left(u \leq 1.36 \cdot 10^{+84}\right):\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.2 \cdot 10^{+99} \lor \neg \left(u \leq 2.1 \cdot 10^{+196}\right):\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.2e+99) (not (<= u 2.1e+196))) (/ 1.0 (/ u v)) (- (/ v t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.2e+99) || !(u <= 2.1e+196)) {
		tmp = 1.0 / (u / v);
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-2.2d+99)) .or. (.not. (u <= 2.1d+196))) then
        tmp = 1.0d0 / (u / v)
    else
        tmp = -(v / t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.2e+99) || !(u <= 2.1e+196)) {
		tmp = 1.0 / (u / v);
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.2e+99) or not (u <= 2.1e+196):
		tmp = 1.0 / (u / v)
	else:
		tmp = -(v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.2e+99) || !(u <= 2.1e+196))
		tmp = Float64(1.0 / Float64(u / v));
	else
		tmp = Float64(-Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.2e+99) || ~((u <= 2.1e+196)))
		tmp = 1.0 / (u / v);
	else
		tmp = -(v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.2e+99], N[Not[LessEqual[u, 2.1e+196]], $MachinePrecision]], N[(1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision], (-N[(v / t1), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if u < -2.19999999999999978e99 or 2.10000000000000015e196 < u

   1. Initial program 78.4%

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

      1. associate-/l* 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. associate-/r* 87.0%

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

      5. distribute-neg-frac2 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in t1 around 0 85.8%

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

   6. Taylor expanded in t1 around inf 43.4%

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

      1. associate-*r/ 43.4%

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

      2. mul-1-neg 43.4%

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

   8. Simplified 43.4%

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

      1. add-sqr-sqrt 21.9%

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

      2. sqrt-unprod 42.9%

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

      3. sqr-neg 42.9%

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

      4. sqrt-unprod 21.4%

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

      5. add-sqr-sqrt 43.3%

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

      6. clear-num 45.2%

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

      7. inv-pow 45.2%

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

   10. Applied egg-rr 45.2%

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

       1. unpow-1 45.2%

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

   12. Simplified 45.2%

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

   if -2.19999999999999978e99 < u < 2.10000000000000015e196

   1. Initial program 67.7%

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

      1. associate-/l* 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. associate-/r* 78.5%

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

      5. distribute-neg-frac2 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t1 around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   7. Simplified 68.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.2 \cdot 10^{+99} \lor \neg \left(u \leq 2.1 \cdot 10^{+196}\right):\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.5 \cdot 10^{+99} \lor \neg \left(u \leq 2.8 \cdot 10^{+196}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.5e+99) (not (<= u 2.8e+196))) (/ v u) (- (/ v t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.5e+99) || !(u <= 2.8e+196)) {
		tmp = v / u;
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-2.5d+99)) .or. (.not. (u <= 2.8d+196))) then
        tmp = v / u
    else
        tmp = -(v / t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.5e+99) || !(u <= 2.8e+196)) {
		tmp = v / u;
	} else {
		tmp = -(v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.5e+99) or not (u <= 2.8e+196):
		tmp = v / u
	else:
		tmp = -(v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.5e+99) || !(u <= 2.8e+196))
		tmp = Float64(v / u);
	else
		tmp = Float64(-Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.5e+99) || ~((u <= 2.8e+196)))
		tmp = v / u;
	else
		tmp = -(v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.5e+99], N[Not[LessEqual[u, 2.8e+196]], $MachinePrecision]], N[(v / u), $MachinePrecision], (-N[(v / t1), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if u < -2.50000000000000004e99 or 2.8000000000000002e196 < u

   1. Initial program 78.4%

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

      1. associate-/l* 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. associate-/r* 87.0%

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

      5. distribute-neg-frac2 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in t1 around 0 85.8%

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

   6. Taylor expanded in t1 around inf 43.4%

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

      1. associate-*r/ 43.4%

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

      2. mul-1-neg 43.4%

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

   8. Simplified 43.4%

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

      1. neg-sub0 43.4%

         \[\leadsto \frac{\color{blue}{0 - v}}{u} \]

      2. sub-neg 43.4%

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

      3. add-sqr-sqrt 21.9%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}{u} \]

      4. sqrt-unprod 42.9%

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

      5. sqr-neg 42.9%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{v \cdot v}}}{u} \]

      6. sqrt-unprod 21.4%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{v} \cdot \sqrt{v}}}{u} \]

      7. add-sqr-sqrt 43.3%

         \[\leadsto \frac{0 + \color{blue}{v}}{u} \]

   10. Applied egg-rr 43.3%

       \[\leadsto \frac{\color{blue}{0 + v}}{u} \]
   11. Step-by-step derivation

       1. +-lft-identity 43.3%

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

   12. Simplified 43.3%

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

   if -2.50000000000000004e99 < u < 2.8000000000000002e196

   1. Initial program 67.7%

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

      1. associate-/l* 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. associate-/r* 78.5%

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

      5. distribute-neg-frac2 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t1 around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   7. Simplified 68.4%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.5 \cdot 10^{+99} \lor \neg \left(u \leq 2.8 \cdot 10^{+196}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;-\frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{v}{-u}\\ \mathbf{elif}\;u \leq 2.05 \cdot 10^{+196}:\\ \;\;\;\;-\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -2.5e+99) (/ v (- u)) (if (<= u 2.05e+196) (- (/ v t1)) (/ v u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -2.5e+99) {
		tmp = v / -u;
	} else if (u <= 2.05e+196) {
		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 <= (-2.5d+99)) then
        tmp = v / -u
    else if (u <= 2.05d+196) 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 <= -2.5e+99) {
		tmp = v / -u;
	} else if (u <= 2.05e+196) {
		tmp = -(v / t1);
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -2.5e+99:
		tmp = v / -u
	elif u <= 2.05e+196:
		tmp = -(v / t1)
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -2.5e+99)
		tmp = Float64(v / Float64(-u));
	elseif (u <= 2.05e+196)
		tmp = Float64(-Float64(v / t1));
	else
		tmp = Float64(v / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -2.5e+99)
		tmp = v / -u;
	elseif (u <= 2.05e+196)
		tmp = -(v / t1);
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -2.5e+99], N[(v / (-u)), $MachinePrecision], If[LessEqual[u, 2.05e+196], (-N[(v / t1), $MachinePrecision]), N[(v / u), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -2.50000000000000004e99

   1. Initial program 79.2%

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

      1. associate-/l* 79.6%

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

      2. distribute-lft-neg-out 79.6%

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

      3. distribute-rgt-neg-in 79.6%

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

      4. associate-/r* 88.8%

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

      5. distribute-neg-frac2 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t1 around 0 87.2%

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

   6. Taylor expanded in t1 around inf 41.7%

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

      1. associate-*r/ 41.7%

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

      2. mul-1-neg 41.7%

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

   8. Simplified 41.7%

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

   if -2.50000000000000004e99 < u < 2.0499999999999998e196

   1. Initial program 67.7%

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

      1. associate-/l* 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. associate-/r* 78.5%

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

      5. distribute-neg-frac2 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t1 around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   7. Simplified 68.4%

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

   if 2.0499999999999998e196 < u

   1. Initial program 75.8%

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

      1. associate-/l* 76.6%

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

      2. distribute-lft-neg-out 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

      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 0 81.2%

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

   6. Taylor expanded in t1 around inf 49.1%

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

      1. associate-*r/ 49.1%

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

      2. mul-1-neg 49.1%

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

   8. Simplified 49.1%

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

      1. neg-sub0 49.1%

         \[\leadsto \frac{\color{blue}{0 - v}}{u} \]

      2. sub-neg 49.1%

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

      3. add-sqr-sqrt 38.2%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}{u} \]

      4. sqrt-unprod 48.8%

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

      5. sqr-neg 48.8%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{v \cdot v}}}{u} \]

      6. sqrt-unprod 11.2%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{v} \cdot \sqrt{v}}}{u} \]

      7. add-sqr-sqrt 50.0%

         \[\leadsto \frac{0 + \color{blue}{v}}{u} \]

   10. Applied egg-rr 50.0%

       \[\leadsto \frac{\color{blue}{0 + v}}{u} \]
   11. Step-by-step derivation

       1. +-lft-identity 50.0%

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

   12. Simplified 50.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{v}{-u}\\ \mathbf{elif}\;u \leq 2.05 \cdot 10^{+196}:\\ \;\;\;\;-\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 23.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -4.3 \cdot 10^{+82} \lor \neg \left(t1 \leq 1.05 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -4.3e+82) (not (<= t1 1.05e+141))) (/ v t1) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -4.3e+82) || !(t1 <= 1.05e+141)) {
		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 <= (-4.3d+82)) .or. (.not. (t1 <= 1.05d+141))) 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 <= -4.3e+82) || !(t1 <= 1.05e+141)) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -4.3e+82) or not (t1 <= 1.05e+141):
		tmp = v / t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -4.3e+82) || !(t1 <= 1.05e+141))
		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 <= -4.3e+82) || ~((t1 <= 1.05e+141)))
		tmp = v / t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -4.3e+82], N[Not[LessEqual[t1, 1.05e+141]], $MachinePrecision]], N[(v / t1), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -4.30000000000000015e82 or 1.0499999999999999e141 < t1

   1. Initial program 47.7%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   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 85.9%

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

   6. Taylor expanded in u around inf 33.4%

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

   if -4.30000000000000015e82 < t1 < 1.0499999999999999e141

   1. Initial program 81.6%

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

      1. associate-/l* 80.4%

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

      2. distribute-lft-neg-out 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. associate-/r* 86.9%

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

      5. distribute-neg-frac2 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in t1 around 0 61.5%

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

   6. Taylor expanded in t1 around inf 20.2%

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

      1. associate-*r/ 20.2%

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

      2. mul-1-neg 20.2%

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

   8. Simplified 20.2%

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

      1. neg-sub0 20.2%

         \[\leadsto \frac{\color{blue}{0 - v}}{u} \]

      2. sub-neg 20.2%

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

      3. add-sqr-sqrt 9.4%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}{u} \]

      4. sqrt-unprod 24.8%

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

      5. sqr-neg 24.8%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{v \cdot v}}}{u} \]

      6. sqrt-unprod 11.3%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{v} \cdot \sqrt{v}}}{u} \]

      7. add-sqr-sqrt 21.4%

         \[\leadsto \frac{0 + \color{blue}{v}}{u} \]

   10. Applied egg-rr 21.4%

       \[\leadsto \frac{\color{blue}{0 + v}}{u} \]
   11. Step-by-step derivation

       1. +-lft-identity 21.4%

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

   12. Simplified 21.4%

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

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -4.3 \cdot 10^{+82} \lor \neg \left(t1 \leq 1.05 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(u, v, t1)
	return Float64(Float64(Float64(-t1) * Float64(v / 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) * N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.3%

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

   1. 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* 81.3%

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

   5. distribute-neg-frac2 81.3%

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

3. Simplified 81.3%

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

   1. distribute-frac-neg2 81.3%

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

   2. distribute-rgt-neg-out 81.3%

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

   3. associate-/r* 71.3%

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

   4. distribute-lft-neg-out 71.3%

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

   5. associate-/l* 71.3%

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

   6. times-frac 98.1%

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

   7. frac-2neg 98.1%

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

   8. associate-*r/ 99.4%

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

   9. add-sqr-sqrt 51.2%

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

   10. sqrt-unprod 49.4%

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

   11. sqr-neg 49.4%

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

   12. sqrt-unprod 22.6%

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

   13. add-sqr-sqrt 39.5%

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

   14. add-sqr-sqrt 23.9%

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

   15. sqrt-unprod 57.5%

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

   16. sqr-neg 57.5%

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

   17. sqrt-prod 39.5%

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

   18. add-sqr-sqrt 99.4%

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

6. Applied egg-rr 99.4%

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

7. Taylor expanded in v around 0 83.9%

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

   1. mul-1-neg 83.9%

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

   2. associate-/l* 98.3%

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

   3. distribute-lft-neg-in 98.3%

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

9. Simplified 98.3%

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

Alternative 13: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. 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* 81.3%

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

   5. distribute-neg-frac2 81.3%

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

3. Simplified 81.3%

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

   1. distribute-frac-neg2 81.3%

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

   2. distribute-rgt-neg-out 81.3%

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

   3. associate-/r* 71.3%

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

   4. distribute-lft-neg-out 71.3%

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

   5. associate-/l* 71.3%

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

   6. times-frac 98.1%

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

   7. frac-2neg 98.1%

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

   8. associate-*r/ 99.4%

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

   9. add-sqr-sqrt 51.2%

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

   10. sqrt-unprod 49.4%

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

   11. sqr-neg 49.4%

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

   12. sqrt-unprod 22.6%

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

   13. add-sqr-sqrt 39.5%

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

   14. add-sqr-sqrt 23.9%

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

   15. sqrt-unprod 57.5%

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

   16. sqr-neg 57.5%

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

   17. sqrt-prod 39.5%

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

   18. add-sqr-sqrt 99.4%

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

6. Applied egg-rr 99.4%

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

7. Taylor expanded in v around 0 83.9%

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

   1. mul-1-neg 83.9%

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

   2. associate-/l* 98.3%

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

   3. distribute-lft-neg-in 98.3%

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

9. Simplified 98.3%

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

    1. clear-num 97.9%

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

    2. inv-pow 97.9%

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

11. Applied egg-rr 97.9%

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

    1. unpow-1 97.9%

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

13. Simplified 97.9%

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

    1. associate-/l* 81.2%

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

    2. distribute-lft-neg-out 81.2%

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

    3. add-sqr-sqrt 42.3%

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

    4. sqrt-unprod 44.9%

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

    5. sqr-neg 44.9%

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

    6. sqrt-unprod 17.0%

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

    7. add-sqr-sqrt 39.6%

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

    8. associate-/l* 39.5%

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

    9. *-commutative 39.5%

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

    10. associate-/l* 39.5%

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

    11. clear-num 39.5%

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

    12. add-sqr-sqrt 16.9%

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

    13. sqrt-unprod 47.0%

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

    14. sqr-neg 47.0%

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

    15. sqrt-unprod 47.9%

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

    16. add-sqr-sqrt 98.1%

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

15. Applied egg-rr 98.1%

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

16. Final simplification 98.1%

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

Alternative 14: 61.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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* 81.3%

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

   5. distribute-neg-frac2 81.3%

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

3. Simplified 81.3%

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

   1. distribute-frac-neg2 81.3%

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

   2. distribute-rgt-neg-out 81.3%

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

   3. associate-/r* 71.3%

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

   4. distribute-lft-neg-out 71.3%

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

   5. associate-/l* 71.3%

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

   6. times-frac 98.1%

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

   7. frac-2neg 98.1%

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

   8. associate-*r/ 99.4%

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

   9. add-sqr-sqrt 51.2%

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

   10. sqrt-unprod 49.4%

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

   11. sqr-neg 49.4%

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

   12. sqrt-unprod 22.6%

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

   13. add-sqr-sqrt 39.5%

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

   14. add-sqr-sqrt 23.9%

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

   15. sqrt-unprod 57.5%

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

   16. sqr-neg 57.5%

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

   17. sqrt-prod 39.5%

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

   18. add-sqr-sqrt 99.4%

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

6. Applied egg-rr 99.4%

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

7. Taylor expanded in t1 around inf 61.5%

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

   1. mul-1-neg 61.5%

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

9. Simplified 61.5%

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

10. Final simplification 61.5%

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

Alternative 15: 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 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* 81.3%

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

   5. distribute-neg-frac2 81.3%

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

3. Simplified 81.3%

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

   1. distribute-frac-neg2 81.3%

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

   2. distribute-rgt-neg-out 81.3%

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

   3. associate-/r* 71.3%

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

   4. distribute-lft-neg-out 71.3%

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

   5. associate-/l* 71.3%

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

   6. times-frac 98.1%

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

   7. frac-2neg 98.1%

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

   8. associate-*r/ 99.4%

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

   9. add-sqr-sqrt 51.2%

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

   10. sqrt-unprod 49.4%

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

   11. sqr-neg 49.4%

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

   12. sqrt-unprod 22.6%

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

   13. add-sqr-sqrt 39.5%

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

   14. add-sqr-sqrt 23.9%

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

   15. sqrt-unprod 57.5%

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

   16. sqr-neg 57.5%

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

   17. sqrt-prod 39.5%

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

   18. add-sqr-sqrt 99.4%

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

6. Applied egg-rr 99.4%

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

7. Taylor expanded in t1 around inf 61.5%

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

   1. mul-1-neg 61.5%

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

9. Simplified 61.5%

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

    1. add-sqr-sqrt 29.2%

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

    2. sqrt-unprod 70.1%

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

    3. sqr-neg 70.1%

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

    4. sqrt-unprod 32.6%

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

    5. add-sqr-sqrt 61.6%

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

    6. sub-neg 61.6%

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

11. Applied egg-rr 61.6%

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

12. Final simplification 61.6%

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

Alternative 16: 14.1% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. times-frac 98.1%

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

   2. distribute-frac-neg 98.1%

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

   3. distribute-neg-frac2 98.1%

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

   4. +-commutative 98.1%

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

   5. distribute-neg-in 98.1%

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

   6. unsub-neg 98.1%

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

3. Simplified 98.1%

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

5. Taylor expanded in t1 around inf 54.5%

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

6. Taylor expanded in u around inf 13.0%

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

Reproduce

herbie shell --seed 2024131 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))