Rosa's DopplerBench

Percentage Accurate: 73.0% → 98.2%

Time: 16.4s

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: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% 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 68.8%

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

   1. times-frac 99.6%

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

   2. distribute-frac-neg 99.6%

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

   3. distribute-neg-frac2 99.6%

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

   4. +-commutative 99.6%

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

   5. distribute-neg-in 99.6%

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

   6. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 88.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t1 \cdot \frac{v}{-\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{if}\;t1 \leq -8.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -1.9 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq 3 \cdot 10^{-163}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{elif}\;t1 \leq 2.4 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \left(\frac{u}{t1} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* t1 (/ v (- (* (+ t1 u) (+ t1 u)))))))
   (if (<= t1 -8.8e+92)
     (/ v (- u t1))
     (if (<= t1 -1.9e-124)
       t_1
       (if (<= t1 3e-163)
         (* (/ t1 (- u)) (/ v u))
         (if (<= t1 2.4e+124) t_1 (* (/ v (+ t1 u)) (+ (/ u t1) -1.0))))))))

C

double code(double u, double v, double t1) {
	double t_1 = t1 * (v / -((t1 + u) * (t1 + u)));
	double tmp;
	if (t1 <= -8.8e+92) {
		tmp = v / (u - t1);
	} else if (t1 <= -1.9e-124) {
		tmp = t_1;
	} else if (t1 <= 3e-163) {
		tmp = (t1 / -u) * (v / u);
	} else if (t1 <= 2.4e+124) {
		tmp = t_1;
	} else {
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0);
	}
	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 = t1 * (v / -((t1 + u) * (t1 + u)))
    if (t1 <= (-8.8d+92)) then
        tmp = v / (u - t1)
    else if (t1 <= (-1.9d-124)) then
        tmp = t_1
    else if (t1 <= 3d-163) then
        tmp = (t1 / -u) * (v / u)
    else if (t1 <= 2.4d+124) then
        tmp = t_1
    else
        tmp = (v / (t1 + u)) * ((u / t1) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = t1 * (v / -((t1 + u) * (t1 + u)));
	double tmp;
	if (t1 <= -8.8e+92) {
		tmp = v / (u - t1);
	} else if (t1 <= -1.9e-124) {
		tmp = t_1;
	} else if (t1 <= 3e-163) {
		tmp = (t1 / -u) * (v / u);
	} else if (t1 <= 2.4e+124) {
		tmp = t_1;
	} else {
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = t1 * (v / -((t1 + u) * (t1 + u)))
	tmp = 0
	if t1 <= -8.8e+92:
		tmp = v / (u - t1)
	elif t1 <= -1.9e-124:
		tmp = t_1
	elif t1 <= 3e-163:
		tmp = (t1 / -u) * (v / u)
	elif t1 <= 2.4e+124:
		tmp = t_1
	else:
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(t1 * Float64(v / Float64(-Float64(Float64(t1 + u) * Float64(t1 + u)))))
	tmp = 0.0
	if (t1 <= -8.8e+92)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= -1.9e-124)
		tmp = t_1;
	elseif (t1 <= 3e-163)
		tmp = Float64(Float64(t1 / Float64(-u)) * Float64(v / u));
	elseif (t1 <= 2.4e+124)
		tmp = t_1;
	else
		tmp = Float64(Float64(v / Float64(t1 + u)) * Float64(Float64(u / t1) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = t1 * (v / -((t1 + u) * (t1 + u)));
	tmp = 0.0;
	if (t1 <= -8.8e+92)
		tmp = v / (u - t1);
	elseif (t1 <= -1.9e-124)
		tmp = t_1;
	elseif (t1 <= 3e-163)
		tmp = (t1 / -u) * (v / u);
	elseif (t1 <= 2.4e+124)
		tmp = t_1;
	else
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(t1 * N[(v / (-N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -8.8e+92], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -1.9e-124], t$95$1, If[LessEqual[t1, 3e-163], N[(N[(t1 / (-u)), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.4e+124], t$95$1, N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(N[(u / t1), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -8.79999999999999969e92

   1. Initial program 56.3%

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

      1. times-frac 99.9%

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

      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 87.9%

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

      1. *-commutative 87.9%

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

      2. clear-num 86.5%

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

      3. frac-times 73.9%

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

      4. *-un-lft-identity 73.9%

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

      5. add-sqr-sqrt 38.1%

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

      6. sqrt-unprod 74.0%

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

      7. sqr-neg 74.0%

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

      8. sqrt-unprod 35.9%

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

      9. add-sqr-sqrt 74.0%

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

   7. Applied egg-rr 74.0%

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

      1. associate-/l/ 86.7%

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

      2. associate-/r/ 88.0%

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

      3. /-rgt-identity 88.0%

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

      4. times-frac 88.1%

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

      5. *-rgt-identity 88.1%

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

      6. associate-*r/ 88.1%

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

      7. times-frac 56.3%

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

      8. *-commutative 56.3%

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

      9. times-frac 88.1%

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

      10. *-inverses 88.1%

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

      11. *-lft-identity 88.1%

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

   9. Simplified 88.1%

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

   if -8.79999999999999969e92 < t1 < -1.90000000000000006e-124 or 3.0000000000000002e-163 < t1 < 2.40000000000000006e124

   1. Initial program 83.8%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   if -1.90000000000000006e-124 < t1 < 3.0000000000000002e-163

   1. Initial program 71.7%

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

      1. times-frac 99.2%

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

      2. distribute-frac-neg 99.2%

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

      3. distribute-neg-frac2 99.2%

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

      4. +-commutative 99.2%

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

      5. distribute-neg-in 99.2%

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

      6. unsub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t1 around 0 88.4%

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

   6. Taylor expanded in t1 around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. mul-1-neg 89.0%

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

   8. Simplified 89.0%

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

   if 2.40000000000000006e124 < t1

   1. Initial program 38.6%

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

      \[\leadsto \color{blue}{\left(\frac{u}{t1} - 1\right)} \cdot \frac{v}{t1 + u} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -1.9 \cdot 10^{-124}:\\ \;\;\;\;t1 \cdot \frac{v}{-\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{elif}\;t1 \leq 3 \cdot 10^{-163}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{elif}\;t1 \leq 2.4 \cdot 10^{+124}:\\ \;\;\;\;t1 \cdot \frac{v}{-\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \left(\frac{u}{t1} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{v}{t1 + u}\\ \mathbf{if}\;t1 \leq -3.8 \cdot 10^{+200}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 3.4 \cdot 10^{+124}:\\ \;\;\;\;t1 \cdot \frac{t\_1}{\left(-u\right) - t1}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(\frac{u}{t1} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (/ v (+ t1 u))))
   (if (<= t1 -3.8e+200)
     (/ v (- u t1))
     (if (<= t1 3.4e+124)
       (* t1 (/ t_1 (- (- u) t1)))
       (* t_1 (+ (/ u t1) -1.0))))))

C

double code(double u, double v, double t1) {
	double t_1 = v / (t1 + u);
	double tmp;
	if (t1 <= -3.8e+200) {
		tmp = v / (u - t1);
	} else if (t1 <= 3.4e+124) {
		tmp = t1 * (t_1 / (-u - t1));
	} else {
		tmp = t_1 * ((u / t1) + -1.0);
	}
	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 = v / (t1 + u)
    if (t1 <= (-3.8d+200)) then
        tmp = v / (u - t1)
    else if (t1 <= 3.4d+124) then
        tmp = t1 * (t_1 / (-u - t1))
    else
        tmp = t_1 * ((u / t1) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = v / (t1 + u);
	double tmp;
	if (t1 <= -3.8e+200) {
		tmp = v / (u - t1);
	} else if (t1 <= 3.4e+124) {
		tmp = t1 * (t_1 / (-u - t1));
	} else {
		tmp = t_1 * ((u / t1) + -1.0);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = v / (t1 + u)
	tmp = 0
	if t1 <= -3.8e+200:
		tmp = v / (u - t1)
	elif t1 <= 3.4e+124:
		tmp = t1 * (t_1 / (-u - t1))
	else:
		tmp = t_1 * ((u / t1) + -1.0)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(v / Float64(t1 + u))
	tmp = 0.0
	if (t1 <= -3.8e+200)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 3.4e+124)
		tmp = Float64(t1 * Float64(t_1 / Float64(Float64(-u) - t1)));
	else
		tmp = Float64(t_1 * Float64(Float64(u / t1) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = v / (t1 + u);
	tmp = 0.0;
	if (t1 <= -3.8e+200)
		tmp = v / (u - t1);
	elseif (t1 <= 3.4e+124)
		tmp = t1 * (t_1 / (-u - t1));
	else
		tmp = t_1 * ((u / t1) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -3.8e+200], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 3.4e+124], N[(t1 * N[(t$95$1 / N[((-u) - t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[(u / t1), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -3.79999999999999982e200

   1. Initial program 48.3%

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

      1. times-frac 99.9%

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

      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 96.0%

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

      1. *-commutative 96.0%

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

      2. clear-num 93.3%

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

      3. frac-times 65.8%

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

      4. *-un-lft-identity 65.8%

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

      5. add-sqr-sqrt 39.6%

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

      6. sqrt-unprod 65.8%

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

      7. sqr-neg 65.8%

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

      8. sqrt-unprod 26.2%

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

      9. add-sqr-sqrt 65.8%

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

   7. Applied egg-rr 65.8%

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

      1. associate-/l/ 93.7%

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

      2. associate-/r/ 96.3%

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

      3. /-rgt-identity 96.3%

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

      4. times-frac 96.3%

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

      5. *-rgt-identity 96.3%

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

      6. associate-*r/ 96.3%

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

      7. times-frac 48.3%

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

      8. *-commutative 48.3%

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

      9. times-frac 96.3%

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

      10. *-inverses 96.3%

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

      11. *-lft-identity 96.3%

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

   9. Simplified 96.3%

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

   if -3.79999999999999982e200 < t1 < 3.4e124

   1. Initial program 77.3%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

      1. associate-/r* 91.3%

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

      2. div-inv 91.1%

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

   6. Applied egg-rr 91.1%

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

      1. associate-*r/ 91.3%

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

      2. *-rgt-identity 91.3%

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

   8. Simplified 91.3%

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

   if 3.4e124 < t1

   1. Initial program 38.6%

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

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -3.8 \cdot 10^{+200}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 3.4 \cdot 10^{+124}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{t1 + u}}{\left(-u\right) - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \left(\frac{u}{t1} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8 \cdot 10^{+32}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \left(\frac{u}{t1} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -8e+32)
   (/ v (- u t1))
   (if (<= t1 5.6e-46)
     (* (/ t1 (- u)) (/ v u))
     (* (/ v (+ t1 u)) (+ (/ u t1) -1.0)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -8e+32) {
		tmp = v / (u - t1);
	} else if (t1 <= 5.6e-46) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0);
	}
	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 <= (-8d+32)) then
        tmp = v / (u - t1)
    else if (t1 <= 5.6d-46) then
        tmp = (t1 / -u) * (v / u)
    else
        tmp = (v / (t1 + u)) * ((u / t1) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -8e+32) {
		tmp = v / (u - t1);
	} else if (t1 <= 5.6e-46) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -8e+32:
		tmp = v / (u - t1)
	elif t1 <= 5.6e-46:
		tmp = (t1 / -u) * (v / u)
	else:
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -8e+32)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 5.6e-46)
		tmp = Float64(Float64(t1 / Float64(-u)) * Float64(v / u));
	else
		tmp = Float64(Float64(v / Float64(t1 + u)) * Float64(Float64(u / t1) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -8e+32)
		tmp = v / (u - t1);
	elseif (t1 <= 5.6e-46)
		tmp = (t1 / -u) * (v / u);
	else
		tmp = (v / (t1 + u)) * ((u / t1) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -8e+32], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 5.6e-46], N[(N[(t1 / (-u)), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision], N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(N[(u / t1), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -8.00000000000000043e32

   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 86.9%

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

      1. *-commutative 86.9%

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

      2. clear-num 85.8%

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

      3. frac-times 76.7%

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

      4. *-un-lft-identity 76.7%

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

      5. add-sqr-sqrt 42.7%

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

      6. sqrt-unprod 78.3%

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

      7. sqr-neg 78.3%

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

      8. sqrt-unprod 34.1%

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

      9. add-sqr-sqrt 76.7%

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

   7. Applied egg-rr 76.7%

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

      1. associate-/l/ 85.9%

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

      2. associate-/r/ 86.9%

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

      3. /-rgt-identity 86.9%

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

      4. times-frac 87.0%

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

      5. *-rgt-identity 87.0%

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

      6. associate-*r/ 87.0%

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

      7. times-frac 62.7%

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

      8. *-commutative 62.7%

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

      9. times-frac 87.0%

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

      10. *-inverses 87.0%

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

      11. *-lft-identity 87.0%

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

   9. Simplified 87.0%

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

   if -8.00000000000000043e32 < t1 < 5.5999999999999997e-46

   1. Initial program 78.8%

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

      1. times-frac 99.4%

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

      2. distribute-frac-neg 99.4%

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

      3. distribute-neg-frac2 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-neg-in 99.4%

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

      6. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t1 around 0 80.1%

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

   6. Taylor expanded in t1 around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. mul-1-neg 81.5%

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

   8. Simplified 81.5%

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

   if 5.5999999999999997e-46 < t1

   1. Initial program 53.7%

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

      1. times-frac 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t1 around inf 81.2%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8 \cdot 10^{+32}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{t1 + u} \cdot \left(\frac{u}{t1} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.5e+33)
   (/ v (- u t1))
   (if (<= t1 4.5e-46)
     (* (/ t1 (- u)) (/ v u))
     (* (/ (- t1) (+ t1 u)) (/ v t1)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.5e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 4.5e-46) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = (-t1 / (t1 + u)) * (v / t1);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.5d+33)) then
        tmp = v / (u - t1)
    else if (t1 <= 4.5d-46) then
        tmp = (t1 / -u) * (v / u)
    else
        tmp = (-t1 / (t1 + u)) * (v / t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.5e+33) {
		tmp = v / (u - t1);
	} else if (t1 <= 4.5e-46) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = (-t1 / (t1 + u)) * (v / t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.5e+33:
		tmp = v / (u - t1)
	elif t1 <= 4.5e-46:
		tmp = (t1 / -u) * (v / u)
	else:
		tmp = (-t1 / (t1 + u)) * (v / t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.5e+33)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 4.5e-46)
		tmp = Float64(Float64(t1 / Float64(-u)) * Float64(v / u));
	else
		tmp = Float64(Float64(Float64(-t1) / Float64(t1 + u)) * Float64(v / t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.5e+33)
		tmp = v / (u - t1);
	elseif (t1 <= 4.5e-46)
		tmp = (t1 / -u) * (v / u);
	else
		tmp = (-t1 / (t1 + u)) * (v / t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.5e+33], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 4.5e-46], N[(N[(t1 / (-u)), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision], N[(N[((-t1) / N[(t1 + u), $MachinePrecision]), $MachinePrecision] * N[(v / t1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.49999999999999992e33

   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 86.9%

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

      1. *-commutative 86.9%

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

      2. clear-num 85.8%

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

      3. frac-times 76.7%

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

      4. *-un-lft-identity 76.7%

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

      5. add-sqr-sqrt 42.7%

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

      6. sqrt-unprod 78.3%

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

      7. sqr-neg 78.3%

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

      8. sqrt-unprod 34.1%

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

      9. add-sqr-sqrt 76.7%

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

   7. Applied egg-rr 76.7%

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

      1. associate-/l/ 85.9%

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

      2. associate-/r/ 86.9%

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

      3. /-rgt-identity 86.9%

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

      4. times-frac 87.0%

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

      5. *-rgt-identity 87.0%

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

      6. associate-*r/ 87.0%

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

      7. times-frac 62.7%

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

      8. *-commutative 62.7%

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

      9. times-frac 87.0%

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

      10. *-inverses 87.0%

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

      11. *-lft-identity 87.0%

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

   9. Simplified 87.0%

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

   if -1.49999999999999992e33 < t1 < 4.50000000000000001e-46

   1. Initial program 78.8%

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

      1. times-frac 99.4%

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

      2. distribute-frac-neg 99.4%

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

      3. distribute-neg-frac2 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-neg-in 99.4%

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

      6. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t1 around 0 80.1%

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

   6. Taylor expanded in t1 around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. mul-1-neg 81.5%

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

   8. Simplified 81.5%

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

   if 4.50000000000000001e-46 < t1

   1. Initial program 53.7%

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

      1. times-frac 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t1 around inf 81.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8 \cdot 10^{+32}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 7.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -8e+32)
   (/ v (- u t1))
   (if (<= t1 7.5e-46) (* (/ t1 (- u)) (/ v u)) (/ (- v) (+ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -8e+32) {
		tmp = v / (u - t1);
	} else if (t1 <= 7.5e-46) {
		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 <= (-8d+32)) then
        tmp = v / (u - t1)
    else if (t1 <= 7.5d-46) 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 <= -8e+32) {
		tmp = v / (u - t1);
	} else if (t1 <= 7.5e-46) {
		tmp = (t1 / -u) * (v / u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -8e+32:
		tmp = v / (u - t1)
	elif t1 <= 7.5e-46:
		tmp = (t1 / -u) * (v / u)
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -8e+32)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 7.5e-46)
		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 <= -8e+32)
		tmp = v / (u - t1);
	elseif (t1 <= 7.5e-46)
		tmp = (t1 / -u) * (v / u);
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -8e+32], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 7.5e-46], 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 < -8.00000000000000043e32

   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 86.9%

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

      1. *-commutative 86.9%

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

      2. clear-num 85.8%

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

      3. frac-times 76.7%

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

      4. *-un-lft-identity 76.7%

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

      5. add-sqr-sqrt 42.7%

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

      6. sqrt-unprod 78.3%

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

      7. sqr-neg 78.3%

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

      8. sqrt-unprod 34.1%

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

      9. add-sqr-sqrt 76.7%

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

   7. Applied egg-rr 76.7%

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

      1. associate-/l/ 85.9%

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

      2. associate-/r/ 86.9%

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

      3. /-rgt-identity 86.9%

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

      4. times-frac 87.0%

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

      5. *-rgt-identity 87.0%

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

      6. associate-*r/ 87.0%

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

      7. times-frac 62.7%

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

      8. *-commutative 62.7%

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

      9. times-frac 87.0%

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

      10. *-inverses 87.0%

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

      11. *-lft-identity 87.0%

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

   9. Simplified 87.0%

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

   if -8.00000000000000043e32 < t1 < 7.50000000000000027e-46

   1. Initial program 78.8%

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

      1. times-frac 99.4%

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

      2. distribute-frac-neg 99.4%

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

      3. distribute-neg-frac2 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-neg-in 99.4%

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

      6. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t1 around 0 80.1%

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

   6. Taylor expanded in t1 around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. mul-1-neg 81.5%

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

   8. Simplified 81.5%

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

   if 7.50000000000000027e-46 < t1

   1. Initial program 53.7%

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

      1. times-frac 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t1 around inf 81.0%

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

   6. Taylor expanded in v around 0 81.0%

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

      1. associate-*r/ 81.0%

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

      2. mul-1-neg 81.0%

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

   8. Simplified 81.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8 \cdot 10^{+32}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 7.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t1}{-u} \cdot \frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -8.2e+32)
   (/ v (- u t1))
   (if (<= t1 3.2e-46) (* t1 (/ (/ v u) (- u))) (/ (- v) (+ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -8.2e+32) {
		tmp = v / (u - t1);
	} else if (t1 <= 3.2e-46) {
		tmp = t1 * ((v / u) / -u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-8.2d+32)) then
        tmp = v / (u - t1)
    else if (t1 <= 3.2d-46) then
        tmp = t1 * ((v / u) / -u)
    else
        tmp = -v / (t1 + u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -8.2e+32) {
		tmp = v / (u - t1);
	} else if (t1 <= 3.2e-46) {
		tmp = t1 * ((v / u) / -u);
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -8.2e+32:
		tmp = v / (u - t1)
	elif t1 <= 3.2e-46:
		tmp = t1 * ((v / u) / -u)
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -8.2e+32)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 3.2e-46)
		tmp = Float64(t1 * Float64(Float64(v / u) / Float64(-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 <= -8.2e+32)
		tmp = v / (u - t1);
	elseif (t1 <= 3.2e-46)
		tmp = t1 * ((v / u) / -u);
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -8.2e+32], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 3.2e-46], N[(t1 * N[(N[(v / u), $MachinePrecision] / (-u)), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -8.19999999999999961e32

   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 86.9%

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

      1. *-commutative 86.9%

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

      2. clear-num 85.8%

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

      3. frac-times 76.7%

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

      4. *-un-lft-identity 76.7%

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

      5. add-sqr-sqrt 42.7%

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

      6. sqrt-unprod 78.3%

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

      7. sqr-neg 78.3%

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

      8. sqrt-unprod 34.1%

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

      9. add-sqr-sqrt 76.7%

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

   7. Applied egg-rr 76.7%

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

      1. associate-/l/ 85.9%

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

      2. associate-/r/ 86.9%

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

      3. /-rgt-identity 86.9%

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

      4. times-frac 87.0%

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

      5. *-rgt-identity 87.0%

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

      6. associate-*r/ 87.0%

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

      7. times-frac 62.7%

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

      8. *-commutative 62.7%

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

      9. times-frac 87.0%

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

      10. *-inverses 87.0%

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

      11. *-lft-identity 87.0%

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

   9. Simplified 87.0%

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

   if -8.19999999999999961e32 < t1 < 3.1999999999999999e-46

   1. Initial program 78.8%

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

      1. times-frac 99.4%

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

      2. distribute-frac-neg 99.4%

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

      3. distribute-neg-frac2 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-neg-in 99.4%

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

      6. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t1 around 0 80.1%

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

   6. Taylor expanded in t1 around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. mul-1-neg 81.5%

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

   8. Simplified 81.5%

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

      1. *-commutative 81.5%

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

      2. clear-num 81.5%

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

      3. frac-times 78.0%

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

      4. *-un-lft-identity 78.0%

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

      5. add-sqr-sqrt 39.9%

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

      6. sqrt-unprod 50.0%

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

      7. sqr-neg 50.0%

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

      8. sqrt-unprod 19.2%

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

      9. add-sqr-sqrt 40.0%

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

   10. Applied egg-rr 40.0%

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

       1. frac-2neg 40.0%

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

       2. distribute-rgt-neg-out 40.0%

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

       3. div-inv 40.0%

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

       4. associate-/r* 40.0%

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

       5. clear-num 40.0%

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

       6. add-sqr-sqrt 17.6%

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

       7. sqrt-unprod 54.9%

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

       8. sqr-neg 54.9%

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

       9. sqrt-unprod 38.7%

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

       10. add-sqr-sqrt 78.1%

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

   12. Applied egg-rr 78.1%

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

   if 3.1999999999999999e-46 < t1

   1. Initial program 53.7%

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

      1. times-frac 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t1 around inf 81.0%

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

   6. Taylor expanded in v around 0 81.0%

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

      1. associate-*r/ 81.0%

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

      2. mul-1-neg 81.0%

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

   8. Simplified 81.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;t1 \cdot \frac{\frac{v}{u}}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.75 \cdot 10^{+179} \lor \neg \left(u \leq 1.85 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.75e+179) (not (<= u 1.85e+128)))
   (/ t1 (* u (/ u v)))
   (/ (- v) (+ t1 u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.75e+179) || !(u <= 1.85e+128)) {
		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 ((u <= (-1.75d+179)) .or. (.not. (u <= 1.85d+128))) 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 ((u <= -1.75e+179) || !(u <= 1.85e+128)) {
		tmp = t1 / (u * (u / v));
	} else {
		tmp = -v / (t1 + u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.75e+179) or not (u <= 1.85e+128):
		tmp = t1 / (u * (u / v))
	else:
		tmp = -v / (t1 + u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.75e+179) || !(u <= 1.85e+128))
		tmp = Float64(t1 / Float64(u * Float64(u / 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 ((u <= -1.75e+179) || ~((u <= 1.85e+128)))
		tmp = t1 / (u * (u / v));
	else
		tmp = -v / (t1 + u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.75e+179], N[Not[LessEqual[u, 1.85e+128]], $MachinePrecision]], N[(t1 / N[(u * N[(u / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-v) / N[(t1 + u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.75000000000000007e179 or 1.85e128 < u

   1. Initial program 81.7%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around 0 94.1%

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

   6. Taylor expanded in t1 around 0 94.0%

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

      1. associate-*r/ 94.0%

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

      2. mul-1-neg 94.0%

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

   8. Simplified 94.0%

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

      1. *-commutative 94.0%

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

      2. clear-num 94.0%

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

      3. frac-times 87.3%

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

      4. *-un-lft-identity 87.3%

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

      5. add-sqr-sqrt 44.2%

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

      6. sqrt-unprod 66.3%

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

      7. sqr-neg 66.3%

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

      8. sqrt-unprod 37.9%

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

      9. add-sqr-sqrt 80.7%

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

   10. Applied egg-rr 80.7%

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

   if -1.75000000000000007e179 < u < 1.85e128

   1. Initial program 63.7%

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

      1. times-frac 99.6%

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

      2. distribute-frac-neg 99.6%

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

      3. distribute-neg-frac2 99.6%

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

      4. +-commutative 99.6%

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

      5. distribute-neg-in 99.6%

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

      6. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t1 around inf 66.6%

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

   6. Taylor expanded in v around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. mul-1-neg 66.1%

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

   8. Simplified 66.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.75 \cdot 10^{+179} \lor \neg \left(u \leq 1.85 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{t1}{u \cdot \frac{u}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -8.6 \cdot 10^{+194} \lor \neg \left(u \leq 2.9 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{v}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -8.6e+194) (not (<= u 2.9e+129))) (/ v (- u)) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -8.6e+194) || !(u <= 2.9e+129)) {
		tmp = v / -u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-8.6d+194)) .or. (.not. (u <= 2.9d+129))) then
        tmp = v / -u
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -8.6e+194) || !(u <= 2.9e+129)) {
		tmp = v / -u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -8.6e+194) or not (u <= 2.9e+129):
		tmp = v / -u
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -8.6e+194) || !(u <= 2.9e+129))
		tmp = Float64(v / Float64(-u));
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -8.6e+194) || ~((u <= 2.9e+129)))
		tmp = v / -u;
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -8.6e+194], N[Not[LessEqual[u, 2.9e+129]], $MachinePrecision]], N[(v / (-u)), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -8.59999999999999988e194 or 2.90000000000000003e129 < u

   1. Initial program 81.7%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around 0 96.4%

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

   6. Taylor expanded in t1 around inf 38.6%

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

      1. associate-*r/ 38.6%

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

      2. mul-1-neg 38.6%

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

   8. Simplified 38.6%

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

   if -8.59999999999999988e194 < u < 2.90000000000000003e129

   1. Initial program 64.1%

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

      1. associate-/l* 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t1 around inf 64.4%

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

      1. associate-*r/ 64.4%

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

      2. neg-mul-1 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -8.6 \cdot 10^{+194} \lor \neg \left(u \leq 2.9 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{v}{-u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.15 \cdot 10^{+192} \lor \neg \left(u \leq 8.2 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.15e+192) (not (<= u 8.2e+128))) (/ v u) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.15e+192) || !(u <= 8.2e+128)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-1.15d+192)) .or. (.not. (u <= 8.2d+128))) then
        tmp = v / u
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.15e+192) || !(u <= 8.2e+128)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.15e+192) or not (u <= 8.2e+128):
		tmp = v / u
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.15e+192) || !(u <= 8.2e+128))
		tmp = Float64(v / u);
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.15e+192) || ~((u <= 8.2e+128)))
		tmp = v / u;
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.15e+192], N[Not[LessEqual[u, 8.2e+128]], $MachinePrecision]], N[(v / u), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.15e192 or 8.20000000000000023e128 < u

   1. Initial program 80.6%

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

      1. times-frac 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around 0 96.4%

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

   6. Taylor expanded in t1 around inf 38.1%

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

      1. associate-*r/ 38.1%

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

      2. mul-1-neg 38.1%

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

   8. Simplified 38.1%

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

      1. add-sqr-sqrt 23.0%

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

      2. sqrt-unprod 37.7%

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

      3. sqr-neg 37.7%

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

      4. sqrt-unprod 15.3%

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

      5. add-sqr-sqrt 38.1%

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

      6. *-un-lft-identity 38.1%

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

   10. Applied egg-rr 38.1%

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

       1. *-lft-identity 38.1%

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

   12. Simplified 38.1%

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

   if -1.15e192 < u < 8.20000000000000023e128

   1. Initial program 64.5%

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

      1. associate-/l* 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in t1 around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. neg-mul-1 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.15 \cdot 10^{+192} \lor \neg \left(u \leq 8.2 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -7 \cdot 10^{+192}:\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{elif}\;u \leq 8 \cdot 10^{+129}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= u -7e+192)
   (/ 1.0 (/ u v))
   (if (<= u 8e+129) (/ v (- t1)) (/ v (- u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (u <= -7e+192) {
		tmp = 1.0 / (u / v);
	} else if (u <= 8e+129) {
		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 <= (-7d+192)) then
        tmp = 1.0d0 / (u / v)
    else if (u <= 8d+129) 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 <= -7e+192) {
		tmp = 1.0 / (u / v);
	} else if (u <= 8e+129) {
		tmp = v / -t1;
	} else {
		tmp = v / -u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if u <= -7e+192:
		tmp = 1.0 / (u / v)
	elif u <= 8e+129:
		tmp = v / -t1
	else:
		tmp = v / -u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (u <= -7e+192)
		tmp = Float64(1.0 / Float64(u / v));
	elseif (u <= 8e+129)
		tmp = Float64(v / Float64(-t1));
	else
		tmp = Float64(v / Float64(-u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (u <= -7e+192)
		tmp = 1.0 / (u / v);
	elseif (u <= 8e+129)
		tmp = v / -t1;
	else
		tmp = v / -u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[u, -7e+192], N[(1.0 / N[(u / v), $MachinePrecision]), $MachinePrecision], If[LessEqual[u, 8e+129], N[(v / (-t1)), $MachinePrecision], N[(v / (-u)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if u < -6.99999999999999965e192

   1. Initial program 84.3%

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

      1. times-frac 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 0 96.9%

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

   6. Taylor expanded in t1 around inf 44.1%

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

      1. associate-*r/ 44.1%

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

      2. mul-1-neg 44.1%

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

   8. Simplified 44.1%

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

      1. clear-num 45.3%

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

      2. inv-pow 45.3%

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

      3. add-sqr-sqrt 35.9%

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

      4. sqrt-unprod 45.0%

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

      5. sqr-neg 45.0%

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

      6. sqrt-unprod 9.5%

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

      7. add-sqr-sqrt 45.2%

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

   10. Applied egg-rr 45.2%

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

       1. unpow-1 45.2%

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

   12. Simplified 45.2%

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

   if -6.99999999999999965e192 < u < 8e129

   1. Initial program 64.5%

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

      1. associate-/l* 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in t1 around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. neg-mul-1 64.7%

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

   7. Simplified 64.7%

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

   if 8e129 < 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 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-neg-frac2 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t1 around 0 96.1%

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

   6. Taylor expanded in t1 around inf 33.8%

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

      1. associate-*r/ 33.8%

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

      2. mul-1-neg 33.8%

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

   8. Simplified 33.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -7 \cdot 10^{+192}:\\ \;\;\;\;\frac{1}{\frac{u}{v}}\\ \mathbf{elif}\;u \leq 8 \cdot 10^{+129}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-u}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 23.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -6 \cdot 10^{+61} \lor \neg \left(t1 \leq 2.3 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -6e+61) (not (<= t1 2.3e+130))) (/ v t1) (/ v u)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -6e+61) || !(t1 <= 2.3e+130)) {
		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 <= (-6d+61)) .or. (.not. (t1 <= 2.3d+130))) 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 <= -6e+61) || !(t1 <= 2.3e+130)) {
		tmp = v / t1;
	} else {
		tmp = v / u;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -6e+61) or not (t1 <= 2.3e+130):
		tmp = v / t1
	else:
		tmp = v / u
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -6e+61) || !(t1 <= 2.3e+130))
		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 <= -6e+61) || ~((t1 <= 2.3e+130)))
		tmp = v / t1;
	else
		tmp = v / u;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -6e+61], N[Not[LessEqual[t1, 2.3e+130]], $MachinePrecision]], N[(v / t1), $MachinePrecision], N[(v / u), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -6e61 or 2.30000000000000021e130 < t1

   1. Initial program 50.6%

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

      1. associate-/l* 51.0%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in t1 around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   7. Simplified 87.6%

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

      1. neg-sub0 87.6%

         \[\leadsto \frac{\color{blue}{0 - v}}{t1} \]

      2. sub-neg 87.6%

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

      3. add-sqr-sqrt 37.9%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}{t1} \]

      4. sqrt-unprod 51.0%

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

      5. sqr-neg 51.0%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{v \cdot v}}}{t1} \]

      6. sqrt-unprod 18.7%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{v} \cdot \sqrt{v}}}{t1} \]

      7. add-sqr-sqrt 35.8%

         \[\leadsto \frac{0 + \color{blue}{v}}{t1} \]

   9. Applied egg-rr 35.8%

      \[\leadsto \frac{\color{blue}{0 + v}}{t1} \]
   10. Step-by-step derivation

       1. +-lft-identity 35.8%

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

   11. Simplified 35.8%

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

   if -6e61 < t1 < 2.30000000000000021e130

   1. Initial program 78.3%

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

      1. times-frac 99.5%

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

      2. distribute-frac-neg 99.5%

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

      3. distribute-neg-frac2 99.5%

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

      4. +-commutative 99.5%

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

      5. distribute-neg-in 99.5%

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

      6. unsub-neg 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t1 around 0 71.2%

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

   6. Taylor expanded in t1 around inf 17.9%

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

      1. associate-*r/ 17.9%

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

      2. mul-1-neg 17.9%

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

   8. Simplified 17.9%

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

      1. add-sqr-sqrt 10.5%

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

      2. sqrt-unprod 21.9%

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

      3. sqr-neg 21.9%

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

      4. sqrt-unprod 7.4%

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

      5. add-sqr-sqrt 17.3%

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

      6. *-un-lft-identity 17.3%

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

   10. Applied egg-rr 17.3%

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

       1. *-lft-identity 17.3%

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

   12. Simplified 17.3%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -6 \cdot 10^{+61} \lor \neg \left(t1 \leq 2.3 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.8%

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

   1. times-frac 99.6%

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

   2. distribute-frac-neg 99.6%

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

   3. distribute-neg-frac2 99.6%

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

   4. +-commutative 99.6%

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

   5. distribute-neg-in 99.6%

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

   6. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t1 around inf 62.3%

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

6. Taylor expanded in v around 0 59.2%

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

   1. associate-*r/ 59.2%

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

   2. mul-1-neg 59.2%

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

8. Simplified 59.2%

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

Alternative 14: 61.1% 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 68.8%

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

   1. times-frac 99.6%

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

   2. distribute-frac-neg 99.6%

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

   3. distribute-neg-frac2 99.6%

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

   4. +-commutative 99.6%

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

   5. distribute-neg-in 99.6%

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

   6. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t1 around inf 62.3%

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

   1. *-commutative 62.3%

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

   2. clear-num 61.9%

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

   3. frac-times 50.4%

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

   4. *-un-lft-identity 50.4%

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

   5. add-sqr-sqrt 26.3%

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

   6. sqrt-unprod 56.3%

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

   7. sqr-neg 56.3%

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

   8. sqrt-unprod 24.1%

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

   9. add-sqr-sqrt 49.9%

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

7. Applied egg-rr 49.9%

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

   1. associate-/l/ 61.8%

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

   2. associate-/r/ 66.4%

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

   3. /-rgt-identity 66.4%

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

   4. times-frac 69.0%

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

   5. *-rgt-identity 69.0%

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

   6. associate-*r/ 61.8%

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

   7. times-frac 43.1%

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

   8. *-commutative 43.1%

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

   9. times-frac 58.7%

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

   10. *-inverses 58.7%

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

   11. *-lft-identity 58.7%

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

9. Simplified 58.7%

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

Alternative 15: 14.7% 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 68.8%

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

   1. associate-/l* 72.8%

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

3. Simplified 72.8%

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

5. Taylor expanded in t1 around inf 51.0%

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

   1. associate-*r/ 51.0%

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

   2. neg-mul-1 51.0%

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

7. Simplified 51.0%

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

   1. neg-sub0 51.0%

      \[\leadsto \frac{\color{blue}{0 - v}}{t1} \]

   2. sub-neg 51.0%

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

   3. add-sqr-sqrt 21.8%

      \[\leadsto \frac{0 + \color{blue}{\sqrt{-v} \cdot \sqrt{-v}}}{t1} \]

   4. sqrt-unprod 31.1%

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

   5. sqr-neg 31.1%

      \[\leadsto \frac{0 + \sqrt{\color{blue}{v \cdot v}}}{t1} \]

   6. sqrt-unprod 7.6%

      \[\leadsto \frac{0 + \color{blue}{\sqrt{v} \cdot \sqrt{v}}}{t1} \]

   7. add-sqr-sqrt 14.6%

      \[\leadsto \frac{0 + \color{blue}{v}}{t1} \]

9. Applied egg-rr 14.6%

   \[\leadsto \frac{\color{blue}{0 + v}}{t1} \]
10. Step-by-step derivation

    1. +-lft-identity 14.6%

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

11. Simplified 14.6%

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

Reproduce

herbie shell --seed 2024154 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))