Rosa's DopplerBench

Percentage Accurate: 72.7% → 97.9%

Time: 8.6s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.0%

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

   1. times-frac 98.7%

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

   2. distribute-frac-neg 98.7%

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

   3. distribute-neg-frac2 98.7%

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

   4. +-commutative 98.7%

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

   5. distribute-neg-in 98.7%

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

   6. unsub-neg 98.7%

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

3. Simplified 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 89.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t1\right) \cdot \frac{\frac{v}{t1 + u}}{t1 + u}\\ \mathbf{if}\;t1 \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 2.6 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq 1.45 \cdot 10^{+112}:\\ \;\;\;\;v \cdot \frac{-t1}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{elif}\;t1 \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* (- t1) (/ (/ v (+ t1 u)) (+ t1 u)))))
   (if (<= t1 -1.2e+89)
     (/ v (- (- t1) (* u 2.0)))
     (if (<= t1 2.6e-236)
       t_1
       (if (<= t1 1.45e+112)
         (* v (/ (- t1) (* (+ t1 u) (+ t1 u))))
         (if (<= t1 2.9e+180) t_1 (/ (- v) t1)))))))

C

double code(double u, double v, double t1) {
	double t_1 = -t1 * ((v / (t1 + u)) / (t1 + u));
	double tmp;
	if (t1 <= -1.2e+89) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 2.6e-236) {
		tmp = t_1;
	} else if (t1 <= 1.45e+112) {
		tmp = v * (-t1 / ((t1 + u) * (t1 + u)));
	} else if (t1 <= 2.9e+180) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -t1 * ((v / (t1 + u)) / (t1 + u))
    if (t1 <= (-1.2d+89)) then
        tmp = v / (-t1 - (u * 2.0d0))
    else if (t1 <= 2.6d-236) then
        tmp = t_1
    else if (t1 <= 1.45d+112) then
        tmp = v * (-t1 / ((t1 + u) * (t1 + u)))
    else if (t1 <= 2.9d+180) then
        tmp = t_1
    else
        tmp = -v / t1
    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 <= -1.2e+89) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 2.6e-236) {
		tmp = t_1;
	} else if (t1 <= 1.45e+112) {
		tmp = v * (-t1 / ((t1 + u) * (t1 + u)));
	} else if (t1 <= 2.9e+180) {
		tmp = t_1;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = -t1 * ((v / (t1 + u)) / (t1 + u))
	tmp = 0
	if t1 <= -1.2e+89:
		tmp = v / (-t1 - (u * 2.0))
	elif t1 <= 2.6e-236:
		tmp = t_1
	elif t1 <= 1.45e+112:
		tmp = v * (-t1 / ((t1 + u) * (t1 + u)))
	elif t1 <= 2.9e+180:
		tmp = t_1
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(-t1) * Float64(Float64(v / Float64(t1 + u)) / Float64(t1 + u)))
	tmp = 0.0
	if (t1 <= -1.2e+89)
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	elseif (t1 <= 2.6e-236)
		tmp = t_1;
	elseif (t1 <= 1.45e+112)
		tmp = Float64(v * Float64(Float64(-t1) / Float64(Float64(t1 + u) * Float64(t1 + u))));
	elseif (t1 <= 2.9e+180)
		tmp = t_1;
	else
		tmp = Float64(Float64(-v) / t1);
	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 <= -1.2e+89)
		tmp = v / (-t1 - (u * 2.0));
	elseif (t1 <= 2.6e-236)
		tmp = t_1;
	elseif (t1 <= 1.45e+112)
		tmp = v * (-t1 / ((t1 + u) * (t1 + u)));
	elseif (t1 <= 2.9e+180)
		tmp = t_1;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[((-t1) * N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t1, -1.2e+89], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.6e-236], t$95$1, If[LessEqual[t1, 1.45e+112], N[(v * N[((-t1) / N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.9e+180], t$95$1, N[((-v) / t1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -1.20000000000000002e89

   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. associate-/l* 51.0%

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

      2. distribute-lft-neg-out 51.0%

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

      3. distribute-rgt-neg-in 51.0%

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

      4. associate-/r* 71.3%

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

      5. distribute-neg-frac2 71.3%

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

   3. Simplified 71.3%

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

      1. associate-*r/ 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. associate-*l/ 100.0%

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

      6. clear-num 100.0%

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

      7. frac-2neg 100.0%

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

      8. frac-times 100.0%

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

      9. *-un-lft-identity 100.0%

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

      10. frac-2neg 100.0%

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

      11. sub-neg 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. remove-double-neg 100.0%

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

      15. add-sqr-sqrt 99.5%

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

      16. sqrt-unprod 20.2%

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

      17. sqr-neg 20.2%

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

      18. sqrt-unprod 0.0%

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

      19. add-sqr-sqrt 39.6%

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

      20. add-sqr-sqrt 38.1%

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

      21. sqrt-unprod 40.4%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in u around 0 95.8%

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

      1. *-commutative 95.8%

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

   9. Simplified 95.8%

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

   if -1.20000000000000002e89 < t1 < 2.6e-236 or 1.4500000000000001e112 < t1 < 2.90000000000000007e180

   1. Initial program 77.6%

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

      1. associate-/l* 79.2%

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

      2. distribute-lft-neg-out 79.2%

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

      3. distribute-rgt-neg-in 79.2%

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

      4. associate-/r* 88.5%

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

      5. distribute-neg-frac2 88.5%

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

   3. Simplified 88.5%

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

   if 2.6e-236 < t1 < 1.4500000000000001e112

   1. Initial program 88.8%

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

      1. associate-*l/ 97.5%

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

      2. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   if 2.90000000000000007e180 < t1

   1. Initial program 28.7%

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

      1. associate-/l* 30.0%

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

      2. distribute-lft-neg-out 30.0%

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

      3. distribute-rgt-neg-in 30.0%

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

      4. associate-/r* 62.1%

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

      5. distribute-neg-frac2 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t1 around inf 93.9%

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

      1. associate-*r/ 93.9%

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

      2. neg-mul-1 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 2.6 \cdot 10^{-236}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{t1 + u}}{t1 + u}\\ \mathbf{elif}\;t1 \leq 1.45 \cdot 10^{+112}:\\ \;\;\;\;v \cdot \frac{-t1}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{elif}\;t1 \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{t1 + u}}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.55 \cdot 10^{+89}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 3.4 \cdot 10^{+180}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{t1 + u}}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.55e+89)
   (/ v (- (- t1) (* u 2.0)))
   (if (<= t1 3.4e+180) (* (- t1) (/ (/ v (+ t1 u)) (+ t1 u))) (/ (- v) t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.55e+89) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 3.4e+180) {
		tmp = -t1 * ((v / (t1 + u)) / (t1 + u));
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.55d+89)) then
        tmp = v / (-t1 - (u * 2.0d0))
    else if (t1 <= 3.4d+180) then
        tmp = -t1 * ((v / (t1 + u)) / (t1 + u))
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.55e+89) {
		tmp = v / (-t1 - (u * 2.0));
	} else if (t1 <= 3.4e+180) {
		tmp = -t1 * ((v / (t1 + u)) / (t1 + u));
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.55e+89:
		tmp = v / (-t1 - (u * 2.0))
	elif t1 <= 3.4e+180:
		tmp = -t1 * ((v / (t1 + u)) / (t1 + u))
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.55e+89)
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	elseif (t1 <= 3.4e+180)
		tmp = Float64(Float64(-t1) * Float64(Float64(v / Float64(t1 + u)) / Float64(t1 + u)));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.55e+89)
		tmp = v / (-t1 - (u * 2.0));
	elseif (t1 <= 3.4e+180)
		tmp = -t1 * ((v / (t1 + u)) / (t1 + u));
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.55e+89], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 3.4e+180], N[((-t1) * N[(N[(v / N[(t1 + u), $MachinePrecision]), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.55e89

   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. associate-/l* 51.0%

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

      2. distribute-lft-neg-out 51.0%

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

      3. distribute-rgt-neg-in 51.0%

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

      4. associate-/r* 71.3%

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

      5. distribute-neg-frac2 71.3%

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

   3. Simplified 71.3%

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

      1. associate-*r/ 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. associate-*l/ 100.0%

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

      6. clear-num 100.0%

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

      7. frac-2neg 100.0%

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

      8. frac-times 100.0%

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

      9. *-un-lft-identity 100.0%

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

      10. frac-2neg 100.0%

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

      11. sub-neg 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. remove-double-neg 100.0%

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

      15. add-sqr-sqrt 99.5%

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

      16. sqrt-unprod 20.2%

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

      17. sqr-neg 20.2%

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

      18. sqrt-unprod 0.0%

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

      19. add-sqr-sqrt 39.6%

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

      20. add-sqr-sqrt 38.1%

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

      21. sqrt-unprod 40.4%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in u around 0 95.8%

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

      1. *-commutative 95.8%

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

   9. Simplified 95.8%

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

   if -1.55e89 < t1 < 3.39999999999999985e180

   1. Initial program 81.6%

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

      1. associate-/l* 83.3%

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

      2. distribute-lft-neg-out 83.3%

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

      3. distribute-rgt-neg-in 83.3%

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

      4. associate-/r* 89.4%

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

      5. distribute-neg-frac2 89.4%

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

   3. Simplified 89.4%

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

   if 3.39999999999999985e180 < t1

   1. Initial program 28.7%

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

      1. associate-/l* 30.0%

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

      2. distribute-lft-neg-out 30.0%

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

      3. distribute-rgt-neg-in 30.0%

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

      4. associate-/r* 62.1%

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

      5. distribute-neg-frac2 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t1 around inf 93.9%

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

      1. associate-*r/ 93.9%

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

      2. neg-mul-1 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.55 \cdot 10^{+89}:\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{elif}\;t1 \leq 3.4 \cdot 10^{+180}:\\ \;\;\;\;\left(-t1\right) \cdot \frac{\frac{v}{t1 + u}}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.7 \cdot 10^{-63} \lor \neg \left(t1 \leq 1.16 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1}{\left(-u\right) - t1} \cdot \frac{v}{u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -1.7e-63) (not (<= t1 1.16e-157)))
   (/ v (- (- t1) (* u 2.0)))
   (* (/ t1 (- (- u) t1)) (/ v u))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.7e-63) || !(t1 <= 1.16e-157)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (t1 / (-u - t1)) * (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 <= (-1.7d-63)) .or. (.not. (t1 <= 1.16d-157))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (t1 / (-u - t1)) * (v / u)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -1.7e-63) || !(t1 <= 1.16e-157)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (t1 / (-u - t1)) * (v / u);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -1.7e-63) or not (t1 <= 1.16e-157):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (t1 / (-u - t1)) * (v / u)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -1.7e-63) || !(t1 <= 1.16e-157))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(t1 / Float64(Float64(-u) - t1)) * Float64(v / u));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -1.7e-63) || ~((t1 <= 1.16e-157)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (t1 / (-u - t1)) * (v / u);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -1.7e-63], N[Not[LessEqual[t1, 1.16e-157]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t1 / N[((-u) - t1), $MachinePrecision]), $MachinePrecision] * N[(v / u), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -1.69999999999999999e-63 or 1.15999999999999992e-157 < t1

   1. Initial program 66.0%

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

      1. associate-/l* 67.2%

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

      2. distribute-lft-neg-out 67.2%

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

      3. distribute-rgt-neg-in 67.2%

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

      4. associate-/r* 81.2%

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

      5. distribute-neg-frac2 81.2%

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

   3. Simplified 81.2%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. clear-num 99.9%

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

      7. frac-2neg 99.9%

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

      8. frac-times 96.6%

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

      9. *-un-lft-identity 96.6%

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

      10. frac-2neg 96.6%

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

      11. sub-neg 96.6%

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

      12. distribute-neg-in 96.6%

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

      13. +-commutative 96.6%

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

      14. remove-double-neg 96.6%

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

      15. add-sqr-sqrt 51.9%

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

      16. sqrt-unprod 33.8%

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

      17. sqr-neg 33.8%

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

      18. sqrt-unprod 14.3%

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

      19. add-sqr-sqrt 32.7%

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

      20. add-sqr-sqrt 21.2%

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

      21. sqrt-unprod 54.1%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in u around 0 83.5%

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

      1. *-commutative 83.5%

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

   9. Simplified 83.5%

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

   if -1.69999999999999999e-63 < t1 < 1.15999999999999992e-157

   1. Initial program 79.3%

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

      1. times-frac 96.0%

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

      2. distribute-frac-neg 96.0%

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

      3. distribute-neg-frac2 96.0%

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

      4. +-commutative 96.0%

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

      5. distribute-neg-in 96.0%

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

      6. unsub-neg 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t1 around 0 85.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.7 \cdot 10^{-63} \lor \neg \left(t1 \leq 1.16 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t1}{\left(-u\right) - t1} \cdot \frac{v}{u}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -6.1 \cdot 10^{-65} \lor \neg \left(t1 \leq 1.3 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{\frac{-v}{u}}{t1 + u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -6.1e-65) (not (<= t1 1.3e-157)))
   (/ v (- (- t1) (* u 2.0)))
   (* t1 (/ (/ (- v) u) (+ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -6.1e-65) || !(t1 <= 1.3e-157)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * ((-v / u) / (t1 + u));
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-6.1d-65)) .or. (.not. (t1 <= 1.3d-157))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = t1 * ((-v / u) / (t1 + u))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -6.1e-65) || !(t1 <= 1.3e-157)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = t1 * ((-v / u) / (t1 + u));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -6.1e-65) or not (t1 <= 1.3e-157):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = t1 * ((-v / u) / (t1 + u))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -6.1e-65) || !(t1 <= 1.3e-157))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(t1 * Float64(Float64(Float64(-v) / u) / Float64(t1 + u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -6.1e-65) || ~((t1 <= 1.3e-157)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = t1 * ((-v / u) / (t1 + u));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -6.1e-65], N[Not[LessEqual[t1, 1.3e-157]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t1 * N[(N[((-v) / u), $MachinePrecision] / N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -6.10000000000000014e-65 or 1.29999999999999994e-157 < t1

   1. Initial program 66.0%

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

      1. associate-/l* 67.2%

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

      2. distribute-lft-neg-out 67.2%

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

      3. distribute-rgt-neg-in 67.2%

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

      4. associate-/r* 81.2%

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

      5. distribute-neg-frac2 81.2%

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

   3. Simplified 81.2%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. clear-num 99.9%

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

      7. frac-2neg 99.9%

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

      8. frac-times 96.6%

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

      9. *-un-lft-identity 96.6%

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

      10. frac-2neg 96.6%

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

      11. sub-neg 96.6%

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

      12. distribute-neg-in 96.6%

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

      13. +-commutative 96.6%

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

      14. remove-double-neg 96.6%

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

      15. add-sqr-sqrt 51.9%

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

      16. sqrt-unprod 33.8%

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

      17. sqr-neg 33.8%

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

      18. sqrt-unprod 14.3%

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

      19. add-sqr-sqrt 32.7%

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

      20. add-sqr-sqrt 21.2%

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

      21. sqrt-unprod 54.1%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in u around 0 83.5%

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

      1. *-commutative 83.5%

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

   9. Simplified 83.5%

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

   if -6.10000000000000014e-65 < t1 < 1.29999999999999994e-157

   1. Initial program 79.3%

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

      1. associate-/l* 83.0%

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

      2. distribute-lft-neg-out 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. associate-/r* 87.9%

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

      5. distribute-neg-frac2 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t1 around 0 82.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -6.1 \cdot 10^{-65} \lor \neg \left(t1 \leq 1.3 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t1 \cdot \frac{\frac{-v}{u}}{t1 + u}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -7.4 \cdot 10^{-155} \lor \neg \left(t1 \leq 3.5 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t1} \cdot \left(v \cdot \frac{t1}{u}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -7.4e-155) (not (<= t1 3.5e-168)))
   (/ v (- (- t1) (* u 2.0)))
   (* (/ 1.0 t1) (* v (/ t1 u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -7.4e-155) || !(t1 <= 3.5e-168)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (1.0 / t1) * (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 <= (-7.4d-155)) .or. (.not. (t1 <= 3.5d-168))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (1.0d0 / t1) * (v * (t1 / u))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -7.4e-155) || !(t1 <= 3.5e-168)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (1.0 / t1) * (v * (t1 / u));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -7.4e-155) or not (t1 <= 3.5e-168):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (1.0 / t1) * (v * (t1 / u))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -7.4e-155) || !(t1 <= 3.5e-168))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(1.0 / t1) * Float64(v * Float64(t1 / u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -7.4e-155) || ~((t1 <= 3.5e-168)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (1.0 / t1) * (v * (t1 / u));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -7.4e-155], N[Not[LessEqual[t1, 3.5e-168]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / t1), $MachinePrecision] * N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -7.4000000000000001e-155 or 3.49999999999999982e-168 < t1

   1. Initial program 67.8%

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

      1. associate-/l* 68.9%

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

      2. distribute-lft-neg-out 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. associate-/r* 82.0%

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

      5. distribute-neg-frac2 82.0%

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

   3. Simplified 82.0%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. clear-num 99.9%

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

      7. frac-2neg 99.9%

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

      8. frac-times 96.0%

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

      9. *-un-lft-identity 96.0%

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

      10. frac-2neg 96.0%

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

      11. sub-neg 96.0%

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

      12. distribute-neg-in 96.0%

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

      13. +-commutative 96.0%

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

      14. remove-double-neg 96.0%

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

      15. add-sqr-sqrt 55.1%

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

      16. sqrt-unprod 38.7%

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

      17. sqr-neg 38.7%

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

      18. sqrt-unprod 12.9%

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

      19. add-sqr-sqrt 32.8%

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

      20. add-sqr-sqrt 20.3%

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

      21. sqrt-unprod 53.2%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in u around 0 81.0%

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

      1. *-commutative 81.0%

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

   9. Simplified 81.0%

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

   if -7.4000000000000001e-155 < t1 < 3.49999999999999982e-168

   1. Initial program 77.4%

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

      1. associate-/l* 82.3%

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

      2. distribute-lft-neg-out 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

      4. associate-/r* 87.2%

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

      5. distribute-neg-frac2 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t1 around 0 84.7%

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

      1. associate-*r/ 85.2%

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

      2. +-commutative 85.2%

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

      3. distribute-neg-in 85.2%

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

      4. sub-neg 85.2%

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

      5. associate-*l/ 89.2%

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

      6. *-commutative 89.2%

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

      7. clear-num 89.2%

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

      8. frac-times 84.7%

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

      9. *-un-lft-identity 84.7%

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

      10. sub-neg 84.7%

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

      11. distribute-neg-in 84.7%

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

      12. +-commutative 84.7%

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

      13. add-sqr-sqrt 47.4%

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

      14. sqrt-unprod 73.3%

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

      15. sqr-neg 73.3%

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

      16. sqrt-unprod 27.5%

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

      17. add-sqr-sqrt 53.6%

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

   7. Applied egg-rr 53.6%

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

   8. Taylor expanded in u around 0 26.4%

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

      1. *-commutative 26.4%

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

      2. associate-*r/ 26.6%

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

   10. Simplified 26.6%

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

       1. clear-num 26.6%

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

       2. associate-*r/ 26.4%

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

       3. associate-/l/ 35.7%

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

       4. *-commutative 35.7%

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

       5. clear-num 35.7%

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

       6. *-un-lft-identity 35.7%

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

       7. times-frac 54.1%

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

       8. *-commutative 54.1%

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

       9. associate-/l* 59.3%

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

   12. Applied egg-rr 59.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -7.4 \cdot 10^{-155} \lor \neg \left(t1 \leq 3.5 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t1} \cdot \left(v \cdot \frac{t1}{u}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -7.4 \cdot 10^{-155} \lor \neg \left(t1 \leq 3 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -7.4e-155) (not (<= t1 3e-168)))
   (/ v (- (- t1) (* u 2.0)))
   (/ (* v (/ t1 u)) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -7.4e-155) || !(t1 <= 3e-168)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v * (t1 / u)) / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-7.4d-155)) .or. (.not. (t1 <= 3d-168))) then
        tmp = v / (-t1 - (u * 2.0d0))
    else
        tmp = (v * (t1 / u)) / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -7.4e-155) || !(t1 <= 3e-168)) {
		tmp = v / (-t1 - (u * 2.0));
	} else {
		tmp = (v * (t1 / u)) / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -7.4e-155) or not (t1 <= 3e-168):
		tmp = v / (-t1 - (u * 2.0))
	else:
		tmp = (v * (t1 / u)) / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -7.4e-155) || !(t1 <= 3e-168))
		tmp = Float64(v / Float64(Float64(-t1) - Float64(u * 2.0)));
	else
		tmp = Float64(Float64(v * Float64(t1 / u)) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -7.4e-155) || ~((t1 <= 3e-168)))
		tmp = v / (-t1 - (u * 2.0));
	else
		tmp = (v * (t1 / u)) / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -7.4e-155], N[Not[LessEqual[t1, 3e-168]], $MachinePrecision]], N[(v / N[((-t1) - N[(u * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision] / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -7.4000000000000001e-155 or 2.99999999999999991e-168 < t1

   1. Initial program 67.8%

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

      1. associate-/l* 68.9%

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

      2. distribute-lft-neg-out 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. associate-/r* 82.0%

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

      5. distribute-neg-frac2 82.0%

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

   3. Simplified 82.0%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-*l/ 99.9%

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

      6. clear-num 99.9%

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

      7. frac-2neg 99.9%

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

      8. frac-times 96.0%

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

      9. *-un-lft-identity 96.0%

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

      10. frac-2neg 96.0%

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

      11. sub-neg 96.0%

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

      12. distribute-neg-in 96.0%

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

      13. +-commutative 96.0%

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

      14. remove-double-neg 96.0%

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

      15. add-sqr-sqrt 55.1%

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

      16. sqrt-unprod 38.7%

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

      17. sqr-neg 38.7%

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

      18. sqrt-unprod 12.9%

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

      19. add-sqr-sqrt 32.8%

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

      20. add-sqr-sqrt 20.3%

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

      21. sqrt-unprod 53.2%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in u around 0 81.0%

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

      1. *-commutative 81.0%

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

   9. Simplified 81.0%

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

   if -7.4000000000000001e-155 < t1 < 2.99999999999999991e-168

   1. Initial program 77.4%

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

      1. associate-/l* 82.3%

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

      2. distribute-lft-neg-out 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

      4. associate-/r* 87.2%

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

      5. distribute-neg-frac2 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t1 around 0 84.7%

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

   6. Taylor expanded in u around 0 23.1%

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

      1. associate-*r/ 23.1%

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

      2. mul-1-neg 23.1%

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

   8. Simplified 23.1%

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

      1. associate-*r/ 32.6%

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

      2. distribute-rgt-neg-in 32.6%

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

      3. *-commutative 32.6%

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

      4. *-commutative 32.6%

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

      5. associate-/r* 51.0%

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

      6. *-commutative 51.0%

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

      7. distribute-rgt-neg-in 51.0%

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

      8. add-sqr-sqrt 28.2%

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

      9. sqrt-unprod 51.0%

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

      10. sqr-neg 51.0%

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

      11. sqrt-unprod 24.6%

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

      12. add-sqr-sqrt 54.1%

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

   10. Applied egg-rr 54.1%

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

       1. *-commutative 54.1%

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

       2. associate-/l* 59.3%

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

   12. Applied egg-rr 59.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -7.4 \cdot 10^{-155} \lor \neg \left(t1 \leq 3 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{v}{\left(-t1\right) - u \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -8.8 \cdot 10^{-61} \lor \neg \left(t1 \leq 6.4 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -8.8e-61) (not (<= t1 6.4e-167)))
   (/ (- v) t1)
   (/ (* v (/ t1 u)) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.8e-61) || !(t1 <= 6.4e-167)) {
		tmp = -v / t1;
	} else {
		tmp = (v * (t1 / u)) / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-8.8d-61)) .or. (.not. (t1 <= 6.4d-167))) then
        tmp = -v / t1
    else
        tmp = (v * (t1 / u)) / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -8.8e-61) || !(t1 <= 6.4e-167)) {
		tmp = -v / t1;
	} else {
		tmp = (v * (t1 / u)) / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -8.8e-61) or not (t1 <= 6.4e-167):
		tmp = -v / t1
	else:
		tmp = (v * (t1 / u)) / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -8.8e-61) || !(t1 <= 6.4e-167))
		tmp = Float64(Float64(-v) / t1);
	else
		tmp = Float64(Float64(v * Float64(t1 / u)) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -8.8e-61) || ~((t1 <= 6.4e-167)))
		tmp = -v / t1;
	else
		tmp = (v * (t1 / u)) / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -8.8e-61], N[Not[LessEqual[t1, 6.4e-167]], $MachinePrecision]], N[((-v) / t1), $MachinePrecision], N[(N[(v * N[(t1 / u), $MachinePrecision]), $MachinePrecision] / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -8.80000000000000035e-61 or 6.4000000000000003e-167 < t1

   1. Initial program 66.0%

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

      1. associate-/l* 67.2%

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

      2. distribute-lft-neg-out 67.2%

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

      3. distribute-rgt-neg-in 67.2%

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

      4. associate-/r* 81.2%

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

      5. distribute-neg-frac2 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t1 around inf 79.0%

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

      1. associate-*r/ 79.0%

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

      2. neg-mul-1 79.0%

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

   7. Simplified 79.0%

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

   if -8.80000000000000035e-61 < t1 < 6.4000000000000003e-167

   1. Initial program 79.3%

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

      1. associate-/l* 83.0%

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

      2. distribute-lft-neg-out 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. associate-/r* 87.9%

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

      5. distribute-neg-frac2 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t1 around 0 82.3%

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

   6. Taylor expanded in u around 0 25.1%

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

      1. associate-*r/ 25.1%

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

      2. mul-1-neg 25.1%

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

   8. Simplified 25.1%

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

      1. associate-*r/ 33.4%

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

      2. distribute-rgt-neg-in 33.4%

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

      3. *-commutative 33.4%

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

      4. *-commutative 33.4%

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

      5. associate-/r* 48.2%

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

      6. *-commutative 48.2%

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

      7. distribute-rgt-neg-in 48.2%

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

      8. add-sqr-sqrt 22.9%

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

      9. sqrt-unprod 49.4%

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

      10. sqr-neg 49.4%

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

      11. sqrt-unprod 27.8%

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

      12. add-sqr-sqrt 51.6%

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

   10. Applied egg-rr 51.6%

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

       1. *-commutative 51.6%

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

       2. associate-/l* 56.8%

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

   12. Applied egg-rr 56.8%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -8.8 \cdot 10^{-61} \lor \neg \left(t1 \leq 6.4 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{v \cdot \frac{t1}{u}}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.6 \cdot 10^{+115} \lor \neg \left(u \leq 1.85 \cdot 10^{+113}\right):\\ \;\;\;\;v \cdot \frac{\frac{t1}{u}}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.6e+115) (not (<= u 1.85e+113)))
   (* v (/ (/ t1 u) t1))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.6e+115) || !(u <= 1.85e+113)) {
		tmp = v * ((t1 / u) / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-1.6d+115)) .or. (.not. (u <= 1.85d+113))) then
        tmp = v * ((t1 / u) / t1)
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.6e+115) || !(u <= 1.85e+113)) {
		tmp = v * ((t1 / u) / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.6e+115) or not (u <= 1.85e+113):
		tmp = v * ((t1 / u) / t1)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.6e+115) || !(u <= 1.85e+113))
		tmp = Float64(v * Float64(Float64(t1 / u) / t1));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.6e+115) || ~((u <= 1.85e+113)))
		tmp = v * ((t1 / u) / t1);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.6e+115], N[Not[LessEqual[u, 1.85e+113]], $MachinePrecision]], N[(v * N[(N[(t1 / u), $MachinePrecision] / t1), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.6e115 or 1.8499999999999999e113 < u

   1. Initial program 76.1%

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

      1. associate-/l* 75.4%

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

      2. distribute-lft-neg-out 75.4%

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

      3. distribute-rgt-neg-in 75.4%

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

      4. associate-/r* 86.5%

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

      5. distribute-neg-frac2 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t1 around 0 86.0%

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

      1. associate-*r/ 90.5%

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

      2. +-commutative 90.5%

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

      3. distribute-neg-in 90.5%

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

      4. sub-neg 90.5%

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

      5. associate-*l/ 89.4%

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

      6. *-commutative 89.4%

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

      7. clear-num 89.3%

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

      8. frac-times 84.9%

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

      9. *-un-lft-identity 84.9%

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

      10. sub-neg 84.9%

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

      11. distribute-neg-in 84.9%

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

      12. +-commutative 84.9%

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

      13. add-sqr-sqrt 46.7%

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

      14. sqrt-unprod 70.5%

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

      15. sqr-neg 70.5%

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

      16. sqrt-unprod 32.1%

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

      17. add-sqr-sqrt 67.9%

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

   7. Applied egg-rr 67.9%

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

   8. Taylor expanded in u around 0 48.1%

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

      1. *-commutative 48.1%

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

      2. associate-*r/ 48.1%

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

   10. Simplified 48.1%

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

       1. associate-/r* 55.0%

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

       2. associate-/r/ 61.5%

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

   12. Applied egg-rr 61.5%

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

   if -1.6e115 < u < 1.8499999999999999e113

   1. Initial program 67.4%

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

      1. associate-/l* 70.5%

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

      2. distribute-lft-neg-out 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. associate-/r* 81.8%

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

      5. distribute-neg-frac2 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in t1 around inf 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   7. Simplified 75.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.6 \cdot 10^{+115} \lor \neg \left(u \leq 1.85 \cdot 10^{+113}\right):\\ \;\;\;\;v \cdot \frac{\frac{t1}{u}}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.2 \cdot 10^{+115} \lor \neg \left(u \leq 2.25 \cdot 10^{+163}\right):\\ \;\;\;\;\frac{t1}{u} \cdot \frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.2e+115) (not (<= u 2.25e+163)))
   (* (/ t1 u) (/ v t1))
   (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.2e+115) || !(u <= 2.25e+163)) {
		tmp = (t1 / u) * (v / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Fortran

real(8) function code(u, v, t1)
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-2.2d+115)) .or. (.not. (u <= 2.25d+163))) then
        tmp = (t1 / u) * (v / t1)
    else
        tmp = -v / t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.2e+115) || !(u <= 2.25e+163)) {
		tmp = (t1 / u) * (v / t1);
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.2e+115) or not (u <= 2.25e+163):
		tmp = (t1 / u) * (v / t1)
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.2e+115) || !(u <= 2.25e+163))
		tmp = Float64(Float64(t1 / u) * Float64(v / t1));
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.2e+115) || ~((u <= 2.25e+163)))
		tmp = (t1 / u) * (v / t1);
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.2e+115], N[Not[LessEqual[u, 2.25e+163]], $MachinePrecision]], N[(N[(t1 / u), $MachinePrecision] * N[(v / t1), $MachinePrecision]), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2.2e115 or 2.24999999999999994e163 < u

   1. Initial program 75.1%

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

      1. associate-/l* 75.6%

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

      2. distribute-lft-neg-out 75.6%

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

      3. distribute-rgt-neg-in 75.6%

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

      4. associate-/r* 88.5%

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

      5. distribute-neg-frac2 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t1 around 0 88.0%

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

      1. associate-*r/ 90.9%

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

      2. +-commutative 90.9%

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

      3. distribute-neg-in 90.9%

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

      4. sub-neg 90.9%

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

      5. associate-*l/ 90.9%

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

      6. *-commutative 90.9%

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

      7. clear-num 90.8%

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

      8. frac-times 86.6%

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

      9. *-un-lft-identity 86.6%

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

      10. sub-neg 86.6%

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

      11. distribute-neg-in 86.6%

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

      12. +-commutative 86.6%

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

      13. add-sqr-sqrt 54.4%

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

      14. sqrt-unprod 75.5%

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

      15. sqr-neg 75.5%

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

      16. sqrt-unprod 30.8%

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

      17. add-sqr-sqrt 72.5%

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

   7. Applied egg-rr 72.5%

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

   8. Taylor expanded in u around 0 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*r/ 52.4%

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

   10. Simplified 52.4%

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

       1. *-un-lft-identity 52.4%

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

       2. *-commutative 52.4%

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

       3. times-frac 59.2%

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

       4. clear-num 59.2%

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

   12. Applied egg-rr 59.2%

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

   if -2.2e115 < u < 2.24999999999999994e163

   1. Initial program 68.3%

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

      1. associate-/l* 70.7%

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

      2. distribute-lft-neg-out 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

      4. associate-/r* 81.3%

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

      5. distribute-neg-frac2 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t1 around inf 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.2 \cdot 10^{+115} \lor \neg \left(u \leq 2.25 \cdot 10^{+163}\right):\\ \;\;\;\;\frac{t1}{u} \cdot \frac{v}{t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -1.15 \cdot 10^{+193} \lor \neg \left(u \leq 3 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -1.15e+193) (not (<= u 3e+164))) (/ v u) (/ (- v) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -1.15e+193) || !(u <= 3e+164)) {
		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+193)) .or. (.not. (u <= 3d+164))) 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+193) || !(u <= 3e+164)) {
		tmp = v / u;
	} else {
		tmp = -v / t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -1.15e+193) or not (u <= 3e+164):
		tmp = v / u
	else:
		tmp = -v / t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -1.15e+193) || !(u <= 3e+164))
		tmp = Float64(v / u);
	else
		tmp = Float64(Float64(-v) / t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -1.15e+193) || ~((u <= 3e+164)))
		tmp = v / u;
	else
		tmp = -v / t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -1.15e+193], N[Not[LessEqual[u, 3e+164]], $MachinePrecision]], N[(v / u), $MachinePrecision], N[((-v) / t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -1.15000000000000007e193 or 3.00000000000000001e164 < u

   1. Initial program 79.1%

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

      1. associate-/l* 79.7%

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

      2. distribute-lft-neg-out 79.7%

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

      3. distribute-rgt-neg-in 79.7%

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

      4. associate-/r* 90.3%

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

      5. distribute-neg-frac2 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t1 around 0 90.0%

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

      1. associate-*r/ 92.0%

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

      2. +-commutative 92.0%

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

      3. distribute-neg-in 92.0%

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

      4. sub-neg 92.0%

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

      5. associate-*l/ 92.0%

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

      6. *-commutative 92.0%

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

      7. clear-num 92.0%

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

      8. frac-times 88.4%

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

      9. *-un-lft-identity 88.4%

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

      10. sub-neg 88.4%

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

      11. distribute-neg-in 88.4%

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

      12. +-commutative 88.4%

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

      13. add-sqr-sqrt 47.6%

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

      14. sqrt-unprod 79.7%

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

      15. sqr-neg 79.7%

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

      16. sqrt-unprod 39.0%

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

      17. add-sqr-sqrt 79.5%

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

   7. Applied egg-rr 79.5%

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

   8. Taylor expanded in t1 around inf 61.4%

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

   if -1.15000000000000007e193 < u < 3.00000000000000001e164

   1. Initial program 67.7%

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

      1. associate-/l* 70.0%

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

      2. distribute-lft-neg-out 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

      4. associate-/r* 81.4%

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

      5. distribute-neg-frac2 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in t1 around inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. neg-mul-1 70.2%

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

   7. Simplified 70.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -1.15 \cdot 10^{+193} \lor \neg \left(u \leq 3 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 17.6% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.0%

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

   1. associate-/l* 72.0%

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

   2. distribute-lft-neg-out 72.0%

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

   3. distribute-rgt-neg-in 72.0%

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

   4. associate-/r* 83.2%

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

   5. distribute-neg-frac2 83.2%

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

3. Simplified 83.2%

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

5. Taylor expanded in t1 around 0 49.2%

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

   1. associate-*r/ 48.2%

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

   2. +-commutative 48.2%

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

   3. distribute-neg-in 48.2%

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

   4. sub-neg 48.2%

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

   5. associate-*l/ 49.2%

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

   6. *-commutative 49.2%

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

   7. clear-num 49.4%

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

   8. frac-times 49.2%

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

   9. *-un-lft-identity 49.2%

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

   10. sub-neg 49.2%

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

   11. distribute-neg-in 49.2%

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

   12. +-commutative 49.2%

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

   13. add-sqr-sqrt 29.0%

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

   14. sqrt-unprod 44.4%

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

   15. sqr-neg 44.4%

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

   16. sqrt-unprod 14.3%

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

   17. add-sqr-sqrt 32.7%

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

7. Applied egg-rr 32.7%

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

8. Taylor expanded in t1 around inf 20.4%

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

Reproduce

herbie shell --seed 2024103 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))