Rosa's DopplerBench

Percentage Accurate: 72.9% → 98.1%

Time: 16.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.1%

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

   1. times-frac 97.6%

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

   2. distribute-frac-neg 97.6%

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

   3. distribute-neg-frac2 97.6%

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

   4. +-commutative 97.6%

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

   5. distribute-neg-in 97.6%

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

   6. unsub-neg 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 2: 89.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-u\right) - t1\\ \mathbf{if}\;t1 \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;t1 \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{t1 + u}}{t\_1}\\ \mathbf{elif}\;t1 \leq 2.65 \cdot 10^{+142}:\\ \;\;\;\;v \cdot \frac{t1}{t\_1 \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (- (- u) t1)))
   (if (<= t1 -3.7e+191)
     (/ v (- t1))
     (if (<= t1 5.5e-242)
       (* t1 (/ (/ v (+ t1 u)) t_1))
       (if (<= t1 2.65e+142)
         (* v (/ t1 (* t_1 (+ t1 u))))
         (/ v (- (- t1) (* u 2.0))))))))

C

double code(double u, double v, double t1) {
	double t_1 = -u - t1;
	double tmp;
	if (t1 <= -3.7e+191) {
		tmp = v / -t1;
	} else if (t1 <= 5.5e-242) {
		tmp = t1 * ((v / (t1 + u)) / t_1);
	} else if (t1 <= 2.65e+142) {
		tmp = v * (t1 / (t_1 * (t1 + u)));
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -u - t1
    if (t1 <= (-3.7d+191)) then
        tmp = v / -t1
    else if (t1 <= 5.5d-242) then
        tmp = t1 * ((v / (t1 + u)) / t_1)
    else if (t1 <= 2.65d+142) then
        tmp = v * (t1 / (t_1 * (t1 + u)))
    else
        tmp = v / (-t1 - (u * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = -u - t1;
	double tmp;
	if (t1 <= -3.7e+191) {
		tmp = v / -t1;
	} else if (t1 <= 5.5e-242) {
		tmp = t1 * ((v / (t1 + u)) / t_1);
	} else if (t1 <= 2.65e+142) {
		tmp = v * (t1 / (t_1 * (t1 + u)));
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = -u - t1
	tmp = 0
	if t1 <= -3.7e+191:
		tmp = v / -t1
	elif t1 <= 5.5e-242:
		tmp = t1 * ((v / (t1 + u)) / t_1)
	elif t1 <= 2.65e+142:
		tmp = v * (t1 / (t_1 * (t1 + u)))
	else:
		tmp = v / (-t1 - (u * 2.0))
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(-u) - t1)
	tmp = 0.0
	if (t1 <= -3.7e+191)
		tmp = Float64(v / Float64(-t1));
	elseif (t1 <= 5.5e-242)
		tmp = Float64(t1 * Float64(Float64(v / Float64(t1 + u)) / t_1));
	elseif (t1 <= 2.65e+142)
		tmp = Float64(v * Float64(t1 / Float64(t_1 * Float64(t1 + u))));
	else
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = -u - t1;
	tmp = 0.0;
	if (t1 <= -3.7e+191)
		tmp = v / -t1;
	elseif (t1 <= 5.5e-242)
		tmp = t1 * ((v / (t1 + u)) / t_1);
	elseif (t1 <= 2.65e+142)
		tmp = v * (t1 / (t_1 * (t1 + u)));
	else
		tmp = v / (-t1 - (u * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[((-u) - t1), $MachinePrecision]}, If[LessEqual[t1, -3.7e+191], N[(v / (-t1)), $MachinePrecision], If[LessEqual[t1, 5.5e-242], N[(t1 * N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.65e+142], N[(v * N[(t1 / N[(t$95$1 * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -3.70000000000000019e191

   1. Initial program 51.5%

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

      1. associate-*l/ 53.1%

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

      2. *-commutative 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in t1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   if -3.70000000000000019e191 < t1 < 5.4999999999999998e-242

   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* 78.9%

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

   3. Simplified 78.9%

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

      1. associate-/r* 92.3%

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

      2. div-inv 92.2%

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

   6. Applied egg-rr 92.2%

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

      1. associate-*r/ 92.3%

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

      2. *-rgt-identity 92.3%

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

   8. Simplified 92.3%

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

   if 5.4999999999999998e-242 < t1 < 2.65e142

   1. Initial program 85.3%

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

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   if 2.65e142 < t1

   1. Initial program 36.0%

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

      1. associate-*l/ 37.7%

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

      2. *-commutative 37.7%

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

   3. Simplified 37.7%

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

      1. associate-*r/ 36.0%

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

      2. *-commutative 36.0%

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

      3. times-frac 99.9%

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

      4. frac-2neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. clear-num 99.9%

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

      10. frac-2neg 99.9%

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

      11. frac-times 94.1%

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

      12. *-un-lft-identity 94.1%

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

      13. +-commutative 94.1%

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

      14. distribute-neg-in 94.1%

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

      15. sub-neg 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in u around 0 82.1%

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

      1. *-commutative 82.1%

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

   9. Simplified 82.1%

      \[\leadsto \frac{-v}{\color{blue}{t1 + u \cdot 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;t1 \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{t1 + u}}{\left(-u\right) - t1}\\ \mathbf{elif}\;t1 \leq 2.65 \cdot 10^{+142}:\\ \;\;\;\;v \cdot \frac{t1}{\left(\left(-u\right) - t1\right) \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -6.8 \cdot 10^{+153}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 2.15 \cdot 10^{+141}:\\ \;\;\;\;v \cdot \frac{t1}{\left(\left(-u\right) - t1\right) \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -6.8e+153)
   (/ v (- u t1))
   (if (<= t1 2.15e+141)
     (* v (/ t1 (* (- (- u) t1) (+ t1 u))))
     (/ v (- (- t1) (* u 2.0))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -6.8e+153) {
		tmp = v / (u - t1);
	} else if (t1 <= 2.15e+141) {
		tmp = v * (t1 / ((-u - t1) * (t1 + u)));
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-6.8d+153)) then
        tmp = v / (u - t1)
    else if (t1 <= 2.15d+141) then
        tmp = v * (t1 / ((-u - t1) * (t1 + u)))
    else
        tmp = v / (-t1 - (u * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -6.8e+153) {
		tmp = v / (u - t1);
	} else if (t1 <= 2.15e+141) {
		tmp = v * (t1 / ((-u - t1) * (t1 + u)));
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -6.8e+153:
		tmp = v / (u - t1)
	elif t1 <= 2.15e+141:
		tmp = v * (t1 / ((-u - t1) * (t1 + u)))
	else:
		tmp = v / (-t1 - (u * 2.0))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -6.8e+153)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 2.15e+141)
		tmp = Float64(v * Float64(t1 / Float64(Float64(Float64(-u) - t1) * Float64(t1 + u))));
	else
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -6.8e+153)
		tmp = v / (u - t1);
	elseif (t1 <= 2.15e+141)
		tmp = v * (t1 / ((-u - t1) * (t1 + u)));
	else
		tmp = v / (-t1 - (u * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -6.8e+153], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.15e+141], N[(v * N[(t1 / N[(N[((-u) - t1), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -6.7999999999999995e153

   1. Initial program 45.0%

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

      1. times-frac 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t1 around inf 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-neg-frac2 92.2%

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

      3. +-commutative 92.2%

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

      4. distribute-neg-in 92.2%

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

      5. sub-neg 92.2%

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

      6. add-sqr-sqrt 37.9%

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

      7. sqrt-unprod 89.7%

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

      8. sqr-neg 89.7%

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

      9. sqrt-unprod 54.7%

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

      10. add-sqr-sqrt 92.4%

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

   7. Applied egg-rr 92.4%

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

   if -6.7999999999999995e153 < t1 < 2.1499999999999999e141

   1. Initial program 85.0%

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

      1. associate-*l/ 87.6%

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

      2. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   if 2.1499999999999999e141 < t1

   1. Initial program 36.0%

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

      1. associate-*l/ 37.7%

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

      2. *-commutative 37.7%

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

   3. Simplified 37.7%

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

      1. associate-*r/ 36.0%

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

      2. *-commutative 36.0%

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

      3. times-frac 99.9%

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

      4. frac-2neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. clear-num 99.9%

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

      10. frac-2neg 99.9%

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

      11. frac-times 94.1%

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

      12. *-un-lft-identity 94.1%

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

      13. +-commutative 94.1%

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

      14. distribute-neg-in 94.1%

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

      15. sub-neg 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in u around 0 82.1%

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

      1. *-commutative 82.1%

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

   9. Simplified 82.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -6.8 \cdot 10^{+153}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 2.15 \cdot 10^{+141}:\\ \;\;\;\;v \cdot \frac{t1}{\left(\left(-u\right) - t1\right) \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.9 \cdot 10^{+34}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 4.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -2.9e+34)
   (/ v (- u t1))
   (if (<= t1 4.1e-42) (/ (/ t1 (/ u v)) (- u)) (/ v (- (- t1) (* u 2.0))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.9e+34) {
		tmp = v / (u - t1);
	} else if (t1 <= 4.1e-42) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-2.9d+34)) then
        tmp = v / (u - t1)
    else if (t1 <= 4.1d-42) then
        tmp = (t1 / (u / v)) / -u
    else
        tmp = v / (-t1 - (u * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.9e+34) {
		tmp = v / (u - t1);
	} else if (t1 <= 4.1e-42) {
		tmp = (t1 / (u / v)) / -u;
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -2.9e+34:
		tmp = v / (u - t1)
	elif t1 <= 4.1e-42:
		tmp = (t1 / (u / v)) / -u
	else:
		tmp = v / (-t1 - (u * 2.0))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -2.9e+34)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 4.1e-42)
		tmp = Float64(Float64(t1 / Float64(u / v)) / Float64(-u));
	else
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -2.9e+34)
		tmp = v / (u - t1);
	elseif (t1 <= 4.1e-42)
		tmp = (t1 / (u / v)) / -u;
	else
		tmp = v / (-t1 - (u * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -2.9e+34], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 4.1e-42], N[(N[(t1 / N[(u / v), $MachinePrecision]), $MachinePrecision] / (-u)), $MachinePrecision], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -2.9000000000000001e34

   1. Initial program 60.5%

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

      1. times-frac 99.9%

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

      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 91.9%

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

      1. mul-1-neg 91.9%

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

      2. distribute-neg-frac2 91.9%

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

      3. +-commutative 91.9%

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

      4. distribute-neg-in 91.9%

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

      5. sub-neg 91.9%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 92.0%

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

      8. sqr-neg 92.0%

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

      9. sqrt-unprod 53.2%

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

      10. add-sqr-sqrt 92.2%

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

   7. Applied egg-rr 92.2%

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

   if -2.9000000000000001e34 < t1 < 4.1000000000000001e-42

   1. Initial program 83.4%

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

      1. times-frac 95.2%

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

      2. distribute-frac-neg 95.2%

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

      3. distribute-neg-frac2 95.2%

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

      4. +-commutative 95.2%

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

      5. distribute-neg-in 95.2%

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

      6. unsub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t1 around 0 81.6%

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

      1. associate-*l/ 83.3%

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

      2. frac-2neg 83.3%

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

      3. clear-num 83.3%

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

      4. un-div-inv 83.3%

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

      5. neg-sub0 83.3%

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

      6. add-sqr-sqrt 37.1%

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

      7. sqrt-unprod 56.0%

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

      8. sqr-neg 56.0%

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

      9. sqrt-unprod 21.6%

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

      10. add-sqr-sqrt 43.7%

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

      11. associate-+l- 43.7%

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

      12. neg-sub0 43.7%

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

      13. add-sqr-sqrt 22.1%

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

      14. sqrt-unprod 63.7%

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

      15. sqr-neg 63.7%

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

      16. sqrt-unprod 46.0%

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

      17. add-sqr-sqrt 83.3%

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

      18. +-commutative 83.3%

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

   7. Applied egg-rr 83.3%

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

   8. Taylor expanded in t1 around 0 83.6%

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

   if 4.1000000000000001e-42 < t1

   1. Initial program 64.9%

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

      1. associate-*l/ 67.2%

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

      2. *-commutative 67.2%

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

   3. Simplified 67.2%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. times-frac 99.9%

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

      4. frac-2neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. clear-num 99.9%

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

      10. frac-2neg 99.9%

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

      11. frac-times 93.2%

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

      12. *-un-lft-identity 93.2%

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

      13. +-commutative 93.2%

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

      14. distribute-neg-in 93.2%

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

      15. sub-neg 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in u around 0 77.0%

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

      1. *-commutative 77.0%

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

   9. Simplified 77.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.9 \cdot 10^{+34}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 4.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{t1}{\frac{u}{v}}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{-v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -2.15e+33)
   (/ v (- u t1))
   (if (<= t1 8.2e-43) (/ t1 (* u (/ u (- v)))) (/ v (- (- t1) (* u 2.0))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.15e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 8.2e-43) {
		tmp = t1 / (u * (u / -v));
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-2.15d+33)) then
        tmp = v / (u - t1)
    else if (t1 <= 8.2d-43) then
        tmp = t1 / (u * (u / -v))
    else
        tmp = v / (-t1 - (u * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.15e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 8.2e-43) {
		tmp = t1 / (u * (u / -v));
	} else {
		tmp = v / (-t1 - (u * 2.0));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -2.15e+33:
		tmp = v / (u - t1)
	elif t1 <= 8.2e-43:
		tmp = t1 / (u * (u / -v))
	else:
		tmp = v / (-t1 - (u * 2.0))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -2.15e+33)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 8.2e-43)
		tmp = Float64(t1 / Float64(u * Float64(u / Float64(-v))));
	else
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -2.15e+33)
		tmp = v / (u - t1);
	elseif (t1 <= 8.2e-43)
		tmp = t1 / (u * (u / -v));
	else
		tmp = v / (-t1 - (u * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -2.15e+33], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 8.2e-43], N[(t1 / N[(u * N[(u / (-v)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -2.15000000000000014e33

   1. Initial program 60.5%

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

      1. times-frac 99.9%

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

      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 91.9%

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

      1. mul-1-neg 91.9%

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

      2. distribute-neg-frac2 91.9%

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

      3. +-commutative 91.9%

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

      4. distribute-neg-in 91.9%

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

      5. sub-neg 91.9%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 92.0%

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

      8. sqr-neg 92.0%

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

      9. sqrt-unprod 53.2%

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

      10. add-sqr-sqrt 92.2%

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

   7. Applied egg-rr 92.2%

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

   if -2.15000000000000014e33 < t1 < 8.1999999999999996e-43

   1. Initial program 83.4%

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

      1. times-frac 95.2%

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

      2. distribute-frac-neg 95.2%

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

      3. distribute-neg-frac2 95.2%

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

      4. +-commutative 95.2%

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

      5. distribute-neg-in 95.2%

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

      6. unsub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t1 around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. clear-num 81.6%

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

      3. frac-2neg 81.6%

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

      4. frac-times 82.4%

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

      5. *-un-lft-identity 82.4%

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

      6. neg-sub0 82.4%

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

      7. add-sqr-sqrt 36.4%

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

      8. sqrt-unprod 55.2%

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

      9. sqr-neg 55.2%

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

      10. sqrt-unprod 21.6%

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

      11. add-sqr-sqrt 43.6%

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

      12. associate-+l- 43.6%

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

      13. neg-sub0 43.6%

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

      14. add-sqr-sqrt 22.0%

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

      15. sqrt-unprod 65.0%

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

      16. sqr-neg 65.0%

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

      17. sqrt-unprod 46.0%

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

      18. add-sqr-sqrt 82.4%

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

      19. +-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in t1 around 0 82.7%

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

   if 8.1999999999999996e-43 < t1

   1. Initial program 64.9%

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

      1. associate-*l/ 67.2%

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

      2. *-commutative 67.2%

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

   3. Simplified 67.2%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. times-frac 99.9%

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

      4. frac-2neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. clear-num 99.9%

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

      10. frac-2neg 99.9%

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

      11. frac-times 93.2%

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

      12. *-un-lft-identity 93.2%

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

      13. +-commutative 93.2%

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

      14. distribute-neg-in 93.2%

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

      15. sub-neg 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in u around 0 77.0%

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

      1. *-commutative 77.0%

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

   9. Simplified 77.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -2.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{-v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{-v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.9e+33)
   (/ v (- u t1))
   (if (<= t1 7.2e-42) (/ t1 (* u (/ u (- v)))) (/ (- v) (+ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.9e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 7.2e-42) {
		tmp = t1 / (u * (u / -v));
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.9d+33)) then
        tmp = v / (u - t1)
    else if (t1 <= 7.2d-42) then
        tmp = t1 / (u * (u / -v))
    else
        tmp = -v / (t1 + u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.9e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 7.2e-42) {
		tmp = t1 / (u * (u / -v));
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.9e+33:
		tmp = v / (u - t1)
	elif t1 <= 7.2e-42:
		tmp = t1 / (u * (u / -v))
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.9e+33)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 7.2e-42)
		tmp = Float64(t1 / Float64(u * Float64(u / Float64(-v))));
	else
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.9e+33)
		tmp = v / (u - t1);
	elseif (t1 <= 7.2e-42)
		tmp = t1 / (u * (u / -v));
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.9e+33], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 7.2e-42], N[(t1 / N[(u * N[(u / (-v)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.90000000000000001e33

   1. Initial program 60.5%

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

      1. times-frac 99.9%

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

      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 91.9%

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

      1. mul-1-neg 91.9%

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

      2. distribute-neg-frac2 91.9%

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

      3. +-commutative 91.9%

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

      4. distribute-neg-in 91.9%

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

      5. sub-neg 91.9%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 92.0%

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

      8. sqr-neg 92.0%

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

      9. sqrt-unprod 53.2%

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

      10. add-sqr-sqrt 92.2%

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

   7. Applied egg-rr 92.2%

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

   if -1.90000000000000001e33 < t1 < 7.2000000000000004e-42

   1. Initial program 83.4%

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

      1. times-frac 95.2%

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

      2. distribute-frac-neg 95.2%

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

      3. distribute-neg-frac2 95.2%

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

      4. +-commutative 95.2%

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

      5. distribute-neg-in 95.2%

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

      6. unsub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t1 around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. clear-num 81.6%

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

      3. frac-2neg 81.6%

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

      4. frac-times 82.4%

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

      5. *-un-lft-identity 82.4%

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

      6. neg-sub0 82.4%

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

      7. add-sqr-sqrt 36.4%

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

      8. sqrt-unprod 55.2%

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

      9. sqr-neg 55.2%

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

      10. sqrt-unprod 21.6%

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

      11. add-sqr-sqrt 43.6%

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

      12. associate-+l- 43.6%

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

      13. neg-sub0 43.6%

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

      14. add-sqr-sqrt 22.0%

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

      15. sqrt-unprod 65.0%

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

      16. sqr-neg 65.0%

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

      17. sqrt-unprod 46.0%

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

      18. add-sqr-sqrt 82.4%

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

      19. +-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in t1 around 0 82.7%

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

   if 7.2000000000000004e-42 < t1

   1. Initial program 64.9%

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

      1. times-frac 99.9%

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

      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 76.3%

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

      1. clear-num 76.2%

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

      2. un-div-inv 76.2%

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

   7. Applied egg-rr 76.2%

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

      1. associate-/r/ 76.1%

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

   9. Simplified 76.1%

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

   10. Taylor expanded in v around 0 76.3%

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

       1. mul-1-neg 76.3%

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

       2. distribute-frac-neg 76.3%

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

   12. Simplified 76.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{-v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 9.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.65e+33)
   (/ v (- u t1))
   (if (<= t1 9.4e-42) (* (/ t1 (- u)) (/ v u)) (/ (- v) (+ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.65e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 9.4e-42) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.65d+33)) then
        tmp = v / (u - t1)
    else if (t1 <= 9.4d-42) then
        tmp = (t1 / -u) * (v / u)
    else
        tmp = -v / (t1 + u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.65e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 9.4e-42) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.65e+33:
		tmp = v / (u - t1)
	elif t1 <= 9.4e-42:
		tmp = (t1 / -u) * (v / u)
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.65e+33)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 9.4e-42)
		tmp = Float64(Float64(t1 / Float64(-u)) * Float64(v / u));
	else
		tmp = Float64(Float64(-v) / Float64(t1 + u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.65e+33)
		tmp = v / (u - t1);
	elseif (t1 <= 9.4e-42)
		tmp = (t1 / -u) * (v / u);
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.65e+33], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 9.4e-42], N[(N[(t1 / (-u)), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.64999999999999988e33

   1. Initial program 60.5%

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

      1. times-frac 99.9%

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

      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 91.9%

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

      1. mul-1-neg 91.9%

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

      2. distribute-neg-frac2 91.9%

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

      3. +-commutative 91.9%

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

      4. distribute-neg-in 91.9%

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

      5. sub-neg 91.9%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 92.0%

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

      8. sqr-neg 92.0%

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

      9. sqrt-unprod 53.2%

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

      10. add-sqr-sqrt 92.2%

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

   7. Applied egg-rr 92.2%

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

   if -1.64999999999999988e33 < t1 < 9.4000000000000001e-42

   1. Initial program 83.4%

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

      1. times-frac 95.2%

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

      2. distribute-frac-neg 95.2%

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

      3. distribute-neg-frac2 95.2%

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

      4. +-commutative 95.2%

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

      5. distribute-neg-in 95.2%

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

      6. unsub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t1 around 0 81.6%

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

   6. Taylor expanded in t1 around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. mul-1-neg 81.9%

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

   8. Simplified 81.9%

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

   if 9.4000000000000001e-42 < t1

   1. Initial program 64.9%

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

      1. times-frac 99.9%

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

      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 76.3%

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

      1. clear-num 76.2%

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

      2. un-div-inv 76.2%

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

   7. Applied egg-rr 76.2%

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

      1. associate-/r/ 76.1%

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

   9. Simplified 76.1%

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

   10. Taylor expanded in v around 0 76.3%

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

       1. mul-1-neg 76.3%

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

       2. distribute-frac-neg 76.3%

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

   12. Simplified 76.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 9.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -8.4 \cdot 10^{+58} \lor \neg \left(u \leq 1.3 \cdot 10^{+175}\right):\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -8.4e+58) (not (<= u 1.3e+175)))
   (* t1 (/ (/ v u) u))
   (/ v (- u t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -8.4e+58) || !(u <= 1.3e+175)) {
		tmp = t1 * ((v / u) / u);
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-8.4d+58)) .or. (.not. (u <= 1.3d+175))) then
        tmp = t1 * ((v / u) / u)
    else
        tmp = v / (u - t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -8.4e+58) || !(u <= 1.3e+175)) {
		tmp = t1 * ((v / u) / u);
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -8.4e+58) or not (u <= 1.3e+175):
		tmp = t1 * ((v / u) / u)
	else:
		tmp = v / (u - t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -8.4e+58) || !(u <= 1.3e+175))
		tmp = Float64(t1 * Float64(Float64(v / u) / u));
	else
		tmp = Float64(v / Float64(u - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -8.4e+58) || ~((u <= 1.3e+175)))
		tmp = t1 * ((v / u) / u);
	else
		tmp = v / (u - t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -8.4e+58], N[Not[LessEqual[u, 1.3e+175]], $MachinePrecision]], N[(t1 * N[(N[(v / u), $MachinePrecision] / u), $MachinePrecision]), $MachinePrecision], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -8.40000000000000048e58 or 1.3e175 < u

   1. Initial program 79.3%

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

      1. times-frac 97.0%

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

      2. distribute-frac-neg 97.0%

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

      3. distribute-neg-frac2 97.0%

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

      4. +-commutative 97.0%

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

      5. distribute-neg-in 97.0%

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

      6. unsub-neg 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t1 around 0 89.6%

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

      1. associate-*l/ 92.5%

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

      2. frac-2neg 92.5%

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

      3. clear-num 93.5%

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

      4. un-div-inv 93.5%

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

      5. neg-sub0 93.5%

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

      6. add-sqr-sqrt 63.3%

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

      7. sqrt-unprod 78.7%

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

      8. sqr-neg 78.7%

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

      9. sqrt-unprod 23.0%

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

      10. add-sqr-sqrt 70.7%

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

      11. associate-+l- 70.7%

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

      12. neg-sub0 70.7%

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

      13. add-sqr-sqrt 47.8%

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

      14. sqrt-unprod 70.9%

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

      15. sqr-neg 70.9%

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

      16. sqrt-unprod 30.1%

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

      17. add-sqr-sqrt 93.5%

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

      18. +-commutative 93.5%

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

   7. Applied egg-rr 93.5%

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

   8. Taylor expanded in t1 around 0 93.6%

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

      1. distribute-neg-frac 93.6%

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

      2. associate-/r* 84.7%

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

      3. clear-num 84.7%

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

      4. associate-/r/ 84.6%

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

      5. associate-/r* 84.7%

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

      6. clear-num 84.7%

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

      7. add-sqr-sqrt 48.1%

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

      8. sqrt-unprod 61.5%

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

      9. sqr-neg 61.5%

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

      10. sqrt-unprod 31.9%

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

      11. add-sqr-sqrt 70.7%

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

   10. Applied egg-rr 70.7%

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

   if -8.40000000000000048e58 < u < 1.3e175

   1. Initial program 70.0%

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

      1. times-frac 97.9%

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

      2. distribute-frac-neg 97.9%

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

      3. distribute-neg-frac2 97.9%

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

      4. +-commutative 97.9%

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

      5. distribute-neg-in 97.9%

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

      6. unsub-neg 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t1 around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. distribute-neg-frac2 65.5%

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

      3. +-commutative 65.5%

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

      4. distribute-neg-in 65.5%

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

      5. sub-neg 65.5%

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

      6. add-sqr-sqrt 23.2%

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

      7. sqrt-unprod 66.1%

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

      8. sqr-neg 66.1%

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

      9. sqrt-unprod 43.5%

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

      10. add-sqr-sqrt 66.6%

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

   7. Applied egg-rr 66.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -8.4 \cdot 10^{+58} \lor \neg \left(u \leq 1.3 \cdot 10^{+175}\right):\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -9.5 \cdot 10^{+102} \lor \neg \left(u \leq 1.7 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -9.5e+102) (not (<= u 1.7e+168)))
   (* (/ v u) (/ t1 u))
   (/ v (- u t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -9.5e+102) || !(u <= 1.7e+168)) {
		tmp = (v / u) * (t1 / u);
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-9.5d+102)) .or. (.not. (u <= 1.7d+168))) then
        tmp = (v / u) * (t1 / u)
    else
        tmp = v / (u - t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -9.5e+102) || !(u <= 1.7e+168)) {
		tmp = (v / u) * (t1 / u);
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -9.5e+102) or not (u <= 1.7e+168):
		tmp = (v / u) * (t1 / u)
	else:
		tmp = v / (u - t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -9.5e+102) || !(u <= 1.7e+168))
		tmp = Float64(Float64(v / u) * Float64(t1 / u));
	else
		tmp = Float64(v / Float64(u - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -9.5e+102) || ~((u <= 1.7e+168)))
		tmp = (v / u) * (t1 / u);
	else
		tmp = v / (u - t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -9.5e+102], N[Not[LessEqual[u, 1.7e+168]], $MachinePrecision]], N[(N[(v / u), $MachinePrecision] * N[(t1 / u), $MachinePrecision]), $MachinePrecision], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -9.4999999999999992e102 or 1.70000000000000001e168 < u

   1. Initial program 77.9%

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

      1. times-frac 96.6%

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

      2. distribute-frac-neg 96.6%

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

      3. distribute-neg-frac2 96.6%

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

      4. +-commutative 96.6%

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

      5. distribute-neg-in 96.6%

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

      6. unsub-neg 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t1 around 0 90.8%

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

      1. associate-*l/ 94.2%

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

      2. frac-2neg 94.2%

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

      3. clear-num 95.1%

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

      4. un-div-inv 95.2%

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

      5. neg-sub0 95.2%

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

      6. add-sqr-sqrt 60.9%

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

      7. sqrt-unprod 78.4%

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

      8. sqr-neg 78.4%

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

      9. sqrt-unprod 26.1%

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

      10. add-sqr-sqrt 73.2%

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

      11. associate-+l- 73.2%

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

      12. neg-sub0 73.2%

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

      13. add-sqr-sqrt 47.2%

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

      14. sqrt-unprod 73.4%

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

      15. sqr-neg 73.4%

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

      16. sqrt-unprod 34.1%

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

      17. add-sqr-sqrt 95.2%

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

      18. +-commutative 95.2%

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

   7. Applied egg-rr 95.2%

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

   8. Taylor expanded in t1 around 0 95.3%

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

      1. add-sqr-sqrt 74.4%

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

      2. sqrt-unprod 84.4%

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

      3. sqr-neg 84.4%

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

      4. sqrt-unprod 56.0%

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

      5. add-sqr-sqrt 73.1%

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

      6. associate-/r* 73.3%

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

      7. *-un-lft-identity 73.3%

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

      8. times-frac 73.2%

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

      9. clear-num 71.9%

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

   10. Applied egg-rr 71.9%

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

   if -9.4999999999999992e102 < u < 1.70000000000000001e168

   1. Initial program 71.1%

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

      1. times-frac 98.0%

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

      2. distribute-frac-neg 98.0%

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

      3. distribute-neg-frac2 98.0%

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

      4. +-commutative 98.0%

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

      5. distribute-neg-in 98.0%

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

      6. unsub-neg 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t1 around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-neg-frac2 64.3%

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

      3. +-commutative 64.3%

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

      4. distribute-neg-in 64.3%

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

      5. sub-neg 64.3%

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

      6. add-sqr-sqrt 24.3%

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

      7. sqrt-unprod 64.9%

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

      8. sqr-neg 64.9%

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

      9. sqrt-unprod 41.1%

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

      10. add-sqr-sqrt 65.3%

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

   7. Applied egg-rr 65.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -9.5 \cdot 10^{+102} \lor \neg \left(u \leq 1.7 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{v}{u} \cdot \frac{t1}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -3 \cdot 10^{+164}:\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{elif}\;u \leq 1.3 \cdot 10^{+112}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -3e+164)
   (/ 1.0 (/ u v))
   (if (<= u 1.3e+112) (/ v (- t1)) (/ (- v) u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -3e+164) {
		tmp = 1.0 / (u / v);
	} else if (u <= 1.3e+112) {
		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 <= (-3d+164)) then
        tmp = 1.0d0 / (u / v)
    else if (u <= 1.3d+112) 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 <= -3e+164) {
		tmp = 1.0 / (u / v);
	} else if (u <= 1.3e+112) {
		tmp = v / -t1;
	} else {
		tmp = -v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -3e+164:
		tmp = 1.0 / (u / v)
	elif u <= 1.3e+112:
		tmp = v / -t1
	else:
		tmp = -v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -3e+164)
		tmp = Float64(1.0 / Float64(u / v));
	elseif (u <= 1.3e+112)
		tmp = Float64(v / Float64(-t1));
	else
		tmp = Float64(Float64(-v) / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -3e+164)
		tmp = 1.0 / (u / v);
	elseif (u <= 1.3e+112)
		tmp = v / -t1;
	else
		tmp = -v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -3e+164], N[(1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 1.3e+112], N[(v / (-t1)), $MachinePrecision], N[((-v) / u), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -3.00000000000000001e164

   1. Initial program 79.5%

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

      1. times-frac 95.1%

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

      2. distribute-frac-neg 95.1%

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

      3. distribute-neg-frac2 95.1%

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

      4. +-commutative 95.1%

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

      5. distribute-neg-in 95.1%

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

      6. unsub-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t1 around inf 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

      3. add-sqr-sqrt 16.1%

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

      4. sqrt-unprod 47.1%

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

      5. sqr-neg 47.1%

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

      6. sqrt-unprod 31.5%

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

      7. add-sqr-sqrt 47.6%

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

      8. clear-num 49.4%

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

   7. Applied egg-rr 49.4%

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

   8. Taylor expanded in t1 around 0 49.4%

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

   if -3.00000000000000001e164 < u < 1.3e112

   1. Initial program 71.4%

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

      1. associate-*l/ 75.3%

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

      2. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t1 around inf 62.2%

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

      1. associate-*r/ 62.2%

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

      2. neg-mul-1 62.2%

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

   7. Simplified 62.2%

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

   if 1.3e112 < u

   1. Initial program 76.0%

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

      1. times-frac 97.3%

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

      2. distribute-frac-neg 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. +-commutative 97.3%

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

      5. distribute-neg-in 97.3%

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

      6. unsub-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t1 around inf 36.2%

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

   6. Taylor expanded in t1 around 0 33.6%

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

      1. neg-mul-1 33.6%

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

      2. distribute-neg-frac2 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -3 \cdot 10^{+164}:\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{elif}\;u \leq 1.3 \cdot 10^{+112}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -6.5 \cdot 10^{+163}:\\ \;\;\;\;\frac{v}{u}\\ \mathbf{elif}\;u \leq 1.05 \cdot 10^{+111}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -6.5e+163) (/ v u) (if (<= u 1.05e+111) (/ v (- t1)) (/ (- v) u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -6.5e+163) {
		tmp = v / u;
	} else if (u <= 1.05e+111) {
		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 <= (-6.5d+163)) then
        tmp = v / u
    else if (u <= 1.05d+111) 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 <= -6.5e+163) {
		tmp = v / u;
	} else if (u <= 1.05e+111) {
		tmp = v / -t1;
	} else {
		tmp = -v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -6.5e+163:
		tmp = v / u
	elif u <= 1.05e+111:
		tmp = v / -t1
	else:
		tmp = -v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -6.5e+163)
		tmp = Float64(v / u);
	elseif (u <= 1.05e+111)
		tmp = Float64(v / Float64(-t1));
	else
		tmp = Float64(Float64(-v) / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -6.5e+163)
		tmp = v / u;
	elseif (u <= 1.05e+111)
		tmp = v / -t1;
	else
		tmp = -v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -6.5e+163], N[(v / u), $MachinePrecision], If[LessEqual[u, 1.05e+111], N[(v / (-t1)), $MachinePrecision], N[((-v) / u), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -6.4999999999999998e163

   1. Initial program 79.5%

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

      1. times-frac 95.1%

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

      2. distribute-frac-neg 95.1%

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

      3. distribute-neg-frac2 95.1%

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

      4. +-commutative 95.1%

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

      5. distribute-neg-in 95.1%

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

      6. unsub-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t1 around inf 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

      3. add-sqr-sqrt 16.1%

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

      4. sqrt-unprod 47.1%

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

      5. sqr-neg 47.1%

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

      6. sqrt-unprod 31.5%

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

      7. add-sqr-sqrt 47.6%

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

      8. clear-num 49.4%

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

   7. Applied egg-rr 49.4%

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

   8. Taylor expanded in t1 around 0 47.6%

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

   if -6.4999999999999998e163 < u < 1.04999999999999997e111

   1. Initial program 71.4%

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

      1. associate-*l/ 75.3%

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

      2. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t1 around inf 62.2%

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

      1. associate-*r/ 62.2%

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

      2. neg-mul-1 62.2%

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

   7. Simplified 62.2%

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

   if 1.04999999999999997e111 < u

   1. Initial program 76.0%

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

      1. times-frac 97.3%

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

      2. distribute-frac-neg 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. +-commutative 97.3%

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

      5. distribute-neg-in 97.3%

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

      6. unsub-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t1 around inf 36.2%

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

   6. Taylor expanded in t1 around 0 33.6%

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

      1. neg-mul-1 33.6%

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

      2. distribute-neg-frac2 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -6.5 \cdot 10^{+163}:\\ \;\;\;\;\frac{v}{u}\\ \mathbf{elif}\;u \leq 1.05 \cdot 10^{+111}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 21.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -6.3 \cdot 10^{+128}:\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -6.3e+128) (/ v t1) (/ (- v) u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -6.3e+128) {
		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 <= (-6.3d+128)) 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 <= -6.3e+128) {
		tmp = v / t1;
	} else {
		tmp = -v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -6.3e+128:
		tmp = v / t1
	else:
		tmp = -v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -6.3e+128)
		tmp = Float64(v / t1);
	else
		tmp = Float64(Float64(-v) / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -6.3e+128)
		tmp = v / t1;
	else
		tmp = -v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -6.3e+128], N[(v / t1), $MachinePrecision], N[((-v) / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -6.2999999999999999e128

   1. Initial program 52.7%

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

      1. times-frac 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t1 around inf 91.0%

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

   6. Taylor expanded in u around inf 39.3%

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

   if -6.2999999999999999e128 < t1

   1. Initial program 77.2%

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

      1. times-frac 97.1%

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

      2. distribute-frac-neg 97.1%

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

      3. distribute-neg-frac2 97.1%

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

      4. +-commutative 97.1%

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

      5. distribute-neg-in 97.1%

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

      6. unsub-neg 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t1 around inf 50.3%

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

   6. Taylor expanded in t1 around 0 15.7%

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

      1. neg-mul-1 15.7%

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

      2. distribute-neg-frac2 15.7%

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

   8. Simplified 15.7%

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

4. Final simplification 19.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -6.3 \cdot 10^{+128}:\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 20.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (if (<= t1 -2.3e+122) (/ v t1) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.3e+122) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-2.3d+122)) then
        tmp = v / t1
    else
        tmp = v / u
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -2.3e+122) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -2.3e+122:
		tmp = v / t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -2.3e+122)
		tmp = Float64(v / t1);
	else
		tmp = Float64(v / u);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -2.3e+122)
		tmp = v / t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -2.3e+122], N[(v / t1), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -2.3000000000000001e122

   1. Initial program 54.8%

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

      1. times-frac 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t1 around inf 91.4%

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

   6. Taylor expanded in u around inf 37.7%

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

   if -2.3000000000000001e122 < t1

   1. Initial program 77.0%

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

      1. times-frac 97.1%

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

      2. distribute-frac-neg 97.1%

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

      3. distribute-neg-frac2 97.1%

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

      4. +-commutative 97.1%

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

      5. distribute-neg-in 97.1%

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

      6. unsub-neg 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t1 around inf 49.8%

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

      1. associate-*r/ 49.8%

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

      2. neg-mul-1 49.8%

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

      3. add-sqr-sqrt 29.2%

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

      4. sqrt-unprod 33.3%

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

      5. sqr-neg 33.3%

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

      6. sqrt-unprod 9.5%

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

      7. add-sqr-sqrt 17.3%

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

      8. clear-num 17.5%

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

   7. Applied egg-rr 17.5%

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

   8. Taylor expanded in t1 around 0 15.8%

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

Alternative 14: 62.3% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.1%

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

   1. times-frac 97.6%

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

   2. distribute-frac-neg 97.6%

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

   3. distribute-neg-frac2 97.6%

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

   4. +-commutative 97.6%

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

   5. distribute-neg-in 97.6%

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

   6. unsub-neg 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in t1 around inf 57.2%

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

   1. mul-1-neg 57.2%

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

   2. distribute-neg-frac2 57.2%

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

   3. +-commutative 57.2%

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

   4. distribute-neg-in 57.2%

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

   5. sub-neg 57.2%

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

   6. add-sqr-sqrt 26.0%

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

   7. sqrt-unprod 66.1%

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

   8. sqr-neg 66.1%

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

   9. sqrt-unprod 32.0%

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

   10. add-sqr-sqrt 57.9%

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

7. Applied egg-rr 57.9%

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

Alternative 15: 14.8% 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 73.1%

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

   1. times-frac 97.6%

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

   2. distribute-frac-neg 97.6%

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

   3. distribute-neg-frac2 97.6%

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

   4. +-commutative 97.6%

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

   5. distribute-neg-in 97.6%

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

   6. unsub-neg 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in t1 around inf 51.0%

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

6. Taylor expanded in u around inf 11.7%

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

Reproduce

herbie shell --seed 2024157 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))