Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.4% → 96.3%

Time: 7.3s

Alternatives: 12

Speedup: 0.5×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 10^{+298}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 1e+298) (* t_1 x) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+298) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 1d+298) then
        tmp = t_1 * x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+298) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 1e+298:
		tmp = t_1 * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 1e+298)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 1e+298)
		tmp = t_1 * x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+298], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 9.9999999999999996e297

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   if 9.9999999999999996e297 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 62.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. frac-2neg 62.3%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-y}{-z}} - \frac{t}{1 - z}\right) \]

      2. div-inv 62.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right) \cdot \frac{1}{-z}} - \frac{t}{1 - z}\right) \]

      3. fma-neg 62.3%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, -\frac{t}{1 - z}\right)} \]

      4. distribute-neg-frac 62.3%

         \[\leadsto x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \color{blue}{\frac{-t}{1 - z}}\right) \]

   3. Applied egg-rr 62.3%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, \frac{-t}{1 - z}\right)} \]
   4. Step-by-step derivation

      1. fma-udef 62.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{-z} + \frac{-t}{1 - z}\right)} \]

      2. +-commutative 62.3%

         \[\leadsto x \cdot \color{blue}{\left(\frac{-t}{1 - z} + \left(-y\right) \cdot \frac{1}{-z}\right)} \]

      3. distribute-lft-neg-out 62.3%

         \[\leadsto x \cdot \left(\frac{-t}{1 - z} + \color{blue}{\left(-y \cdot \frac{1}{-z}\right)}\right) \]

      4. unsub-neg 62.3%

         \[\leadsto x \cdot \color{blue}{\left(\frac{-t}{1 - z} - y \cdot \frac{1}{-z}\right)} \]

      5. neg-mul-1 62.3%

         \[\leadsto x \cdot \left(\frac{\color{blue}{-1 \cdot t}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      6. *-commutative 62.3%

         \[\leadsto x \cdot \left(\frac{\color{blue}{t \cdot -1}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      7. associate-*r/ 62.3%

         \[\leadsto x \cdot \left(\color{blue}{t \cdot \frac{-1}{1 - z}} - y \cdot \frac{1}{-z}\right) \]

      8. metadata-eval 62.3%

         \[\leadsto x \cdot \left(t \cdot \frac{\color{blue}{\frac{1}{-1}}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      9. associate-/r* 62.3%

         \[\leadsto x \cdot \left(t \cdot \color{blue}{\frac{1}{-1 \cdot \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      10. neg-mul-1 62.3%

          \[\leadsto x \cdot \left(t \cdot \frac{1}{\color{blue}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      11. associate-*r/ 62.3%

          \[\leadsto x \cdot \left(\color{blue}{\frac{t \cdot 1}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      12. *-rgt-identity 62.3%

          \[\leadsto x \cdot \left(\frac{\color{blue}{t}}{-\left(1 - z\right)} - y \cdot \frac{1}{-z}\right) \]

      13. neg-sub0 62.3%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      14. associate--r- 62.3%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} - y \cdot \frac{1}{-z}\right) \]

      15. metadata-eval 62.3%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{-1} + z} - y \cdot \frac{1}{-z}\right) \]

      16. neg-mul-1 62.3%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{1}{\color{blue}{-1 \cdot z}}\right) \]

      17. associate-/r* 62.3%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \color{blue}{\frac{\frac{1}{-1}}{z}}\right) \]

      18. metadata-eval 62.3%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{\color{blue}{-1}}{z}\right) \]

   5. Simplified 62.3%

      \[\leadsto x \cdot \color{blue}{\left(\frac{t}{-1 + z} - y \cdot \frac{-1}{z}\right)} \]

   6. Taylor expanded in t around 0 99.8%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+298}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+237} \lor \neg \left(z \leq 3.45 \cdot 10^{+283}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+70)
   (/ x (/ z y))
   (if (<= z 6.5e+34)
     (* x (- (/ y z) t))
     (if (<= z 1.9e+130)
       (* t (/ x z))
       (if (or (<= z 2.2e+237) (not (<= z 3.45e+283)))
         (* (/ y z) x)
         (* x (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+70) {
		tmp = x / (z / y);
	} else if (z <= 6.5e+34) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.9e+130) {
		tmp = t * (x / z);
	} else if ((z <= 2.2e+237) || !(z <= 3.45e+283)) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.5d+70)) then
        tmp = x / (z / y)
    else if (z <= 6.5d+34) then
        tmp = x * ((y / z) - t)
    else if (z <= 1.9d+130) then
        tmp = t * (x / z)
    else if ((z <= 2.2d+237) .or. (.not. (z <= 3.45d+283))) then
        tmp = (y / z) * x
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+70) {
		tmp = x / (z / y);
	} else if (z <= 6.5e+34) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.9e+130) {
		tmp = t * (x / z);
	} else if ((z <= 2.2e+237) || !(z <= 3.45e+283)) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+70:
		tmp = x / (z / y)
	elif z <= 6.5e+34:
		tmp = x * ((y / z) - t)
	elif z <= 1.9e+130:
		tmp = t * (x / z)
	elif (z <= 2.2e+237) or not (z <= 3.45e+283):
		tmp = (y / z) * x
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+70)
		tmp = Float64(x / Float64(z / y));
	elseif (z <= 6.5e+34)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 1.9e+130)
		tmp = Float64(t * Float64(x / z));
	elseif ((z <= 2.2e+237) || !(z <= 3.45e+283))
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+70)
		tmp = x / (z / y);
	elseif (z <= 6.5e+34)
		tmp = x * ((y / z) - t);
	elseif (z <= 1.9e+130)
		tmp = t * (x / z);
	elseif ((z <= 2.2e+237) || ~((z <= 3.45e+283)))
		tmp = (y / z) * x;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+70], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+34], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+130], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.2e+237], N[Not[LessEqual[z, 3.45e+283]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.49999999999999988e70

   1. Initial program 97.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 83.0%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 83.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 97.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 97.7%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around inf 62.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]

   if -1.49999999999999988e70 < z < 6.50000000000000017e34

   1. Initial program 95.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 86.9%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 87.7%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 87.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 87.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 91.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 91.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 91.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]

   if 6.50000000000000017e34 < z < 1.9000000000000001e130

   1. Initial program 94.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 89.9%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 89.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 94.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - -1 \cdot t\right)} \]

      4. cancel-sign-sub-inv 99.8%

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(y + \left(--1\right) \cdot t\right)} \]

      5. metadata-eval 99.8%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{1} \cdot t\right) \]

      6. *-lft-identity 99.8%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]

   4. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + t\right)} \]

   5. Taylor expanded in y around 0 65.2%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 70.3%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   7. Simplified 70.3%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if 1.9000000000000001e130 < z < 2.2e237 or 3.44999999999999984e283 < z

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 79.4%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   3. Step-by-step derivation

      1. associate-*l/ 89.6%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   4. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   if 2.2e237 < z < 3.44999999999999984e283

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 83.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 99.9%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 83.9%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]
   6. Step-by-step derivation

      1. clear-num 83.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{t}}{x}}} \]

      2. associate-/r/ 83.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{t}} \cdot x} \]

      3. clear-num 83.9%

         \[\leadsto \color{blue}{\frac{t}{z}} \cdot x \]

   7. Applied egg-rr 83.9%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+237} \lor \neg \left(z \leq 3.45 \cdot 10^{+283}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 3: 42.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-5} \lor \neg \left(z \leq -7.2 \cdot 10^{-235}\right) \land \left(z \leq 1.62 \cdot 10^{-221} \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.6e-5)
         (and (not (<= z -7.2e-235))
              (or (<= z 1.62e-221) (not (<= z 8.2e-16)))))
   (* t (/ x z))
   (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.6e-5) || (!(z <= -7.2e-235) && ((z <= 1.62e-221) || !(z <= 8.2e-16)))) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.6d-5)) .or. (.not. (z <= (-7.2d-235))) .and. (z <= 1.62d-221) .or. (.not. (z <= 8.2d-16))) then
        tmp = t * (x / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.6e-5) || (!(z <= -7.2e-235) && ((z <= 1.62e-221) || !(z <= 8.2e-16)))) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.6e-5) or (not (z <= -7.2e-235) and ((z <= 1.62e-221) or not (z <= 8.2e-16))):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.6e-5) || (!(z <= -7.2e-235) && ((z <= 1.62e-221) || !(z <= 8.2e-16))))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.6e-5) || (~((z <= -7.2e-235)) && ((z <= 1.62e-221) || ~((z <= 8.2e-16)))))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.6e-5], And[N[Not[LessEqual[z, -7.2e-235]], $MachinePrecision], Or[LessEqual[z, 1.62e-221], N[Not[LessEqual[z, 8.2e-16]], $MachinePrecision]]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6000000000000002e-5 or -7.19999999999999998e-235 < z < 1.62e-221 or 8.20000000000000012e-16 < z

   1. Initial program 97.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 78.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 86.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. associate-/r/ 80.3%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - -1 \cdot t\right)} \]

      4. cancel-sign-sub-inv 80.3%

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(y + \left(--1\right) \cdot t\right)} \]

      5. metadata-eval 80.3%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{1} \cdot t\right) \]

      6. *-lft-identity 80.3%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]

   4. Simplified 80.3%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + t\right)} \]

   5. Taylor expanded in y around 0 44.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 45.7%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   7. Simplified 45.7%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if -9.6000000000000002e-5 < z < -7.19999999999999998e-235 or 1.62e-221 < z < 8.20000000000000012e-16

   1. Initial program 94.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 95.2%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 91.2%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 91.2%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 91.2%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 93.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 93.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 93.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]

   5. Taylor expanded in y around 0 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      2. neg-mul-1 39.9%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot x \]

   7. Simplified 39.9%

      \[\leadsto \color{blue}{\left(-t\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-5} \lor \neg \left(z \leq -7.2 \cdot 10^{-235}\right) \land \left(z \leq 1.62 \cdot 10^{-221} \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+128} \lor \neg \left(t \leq 7 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.6e+128) (not (<= t 7e+38)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e+128) || !(t <= 7e+38)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.6d+128)) .or. (.not. (t <= 7d+38))) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e+128) || !(t <= 7e+38)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.6e+128) or not (t <= 7e+38):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.6e+128) || !(t <= 7e+38))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.6e+128) || ~((t <= 7e+38)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.6e+128], N[Not[LessEqual[t, 7e+38]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.60000000000000027e128 or 7.00000000000000003e38 < t

   1. Initial program 96.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 67.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{1 - z}} \]

      2. mul-1-neg 67.1%

         \[\leadsto \frac{\color{blue}{-t \cdot x}}{1 - z} \]

      3. *-commutative 67.1%

         \[\leadsto \frac{-\color{blue}{x \cdot t}}{1 - z} \]

      4. distribute-rgt-neg-in 67.1%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-t\right)}}{1 - z} \]

      5. associate-*r/ 74.5%

         \[\leadsto \color{blue}{x \cdot \frac{-t}{1 - z}} \]

      6. neg-mul-1 74.5%

         \[\leadsto x \cdot \frac{\color{blue}{-1 \cdot t}}{1 - z} \]

      7. *-commutative 74.5%

         \[\leadsto x \cdot \frac{\color{blue}{t \cdot -1}}{1 - z} \]

      8. associate-*r/ 74.4%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \frac{-1}{1 - z}\right)} \]

      9. metadata-eval 74.4%

         \[\leadsto x \cdot \left(t \cdot \frac{\color{blue}{\frac{1}{-1}}}{1 - z}\right) \]

      10. associate-/r* 74.4%

          \[\leadsto x \cdot \left(t \cdot \color{blue}{\frac{1}{-1 \cdot \left(1 - z\right)}}\right) \]

      11. neg-mul-1 74.4%

          \[\leadsto x \cdot \left(t \cdot \frac{1}{\color{blue}{-\left(1 - z\right)}}\right) \]

      12. associate-*r/ 74.5%

          \[\leadsto x \cdot \color{blue}{\frac{t \cdot 1}{-\left(1 - z\right)}} \]

      13. *-rgt-identity 74.5%

          \[\leadsto x \cdot \frac{\color{blue}{t}}{-\left(1 - z\right)} \]

      14. neg-sub0 74.5%

          \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      15. associate--r- 74.5%

          \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      16. metadata-eval 74.5%

          \[\leadsto x \cdot \frac{t}{\color{blue}{-1} + z} \]

   4. Simplified 74.5%

      \[\leadsto \color{blue}{x \cdot \frac{t}{-1 + z}} \]

   if -3.60000000000000027e128 < t < 7.00000000000000003e38

   1. Initial program 95.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 80.9%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 80.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 82.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 82.9%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 82.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around inf 85.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+128} \lor \neg \left(t \leq 7 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5) (not (<= z 8.2e-16)))
   (* (/ x z) (+ y t))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5) || !(z <= 8.2e-16)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.5d0)) .or. (.not. (z <= 8.2d-16))) then
        tmp = (x / z) * (y + t)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5) || !(z <= 8.2e-16)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5) or not (z <= 8.2e-16):
		tmp = (x / z) * (y + t)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5) || !(z <= 8.2e-16))
		tmp = Float64(Float64(x / z) * Float64(y + t));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5) || ~((z <= 8.2e-16)))
		tmp = (x / z) * (y + t);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5], N[Not[LessEqual[z, 8.2e-16]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5 or 8.20000000000000012e-16 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 85.9%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 85.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 96.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. associate-/r/ 86.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - -1 \cdot t\right)} \]

      4. cancel-sign-sub-inv 86.9%

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(y + \left(--1\right) \cdot t\right)} \]

      5. metadata-eval 86.9%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{1} \cdot t\right) \]

      6. *-lft-identity 86.9%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]

   4. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + t\right)} \]

   if -1.5 < z < 8.20000000000000012e-16

   1. Initial program 94.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 90.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 90.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 90.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 94.5%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 94.5%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 94.5%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 6: 93.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5) (not (<= z 8.2e-16)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5) || !(z <= 8.2e-16)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.5d0)) .or. (.not. (z <= 8.2d-16))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5) || !(z <= 8.2e-16)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5) or not (z <= 8.2e-16):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5) || !(z <= 8.2e-16))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5) || ~((z <= 8.2e-16)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5], N[Not[LessEqual[z, 8.2e-16]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5 or 8.20000000000000012e-16 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 85.9%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 85.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 96.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 96.5%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   if -1.5 < z < 8.20000000000000012e-16

   1. Initial program 94.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 90.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 90.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 90.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 94.5%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 94.5%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 94.5%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 7: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+138} \lor \neg \left(t \leq 2.8 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e+138) (not (<= t 2.8e+102))) (* x (/ t z)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e+138) || !(t <= 2.8e+102)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.45d+138)) .or. (.not. (t <= 2.8d+102))) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e+138) || !(t <= 2.8e+102)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.45e+138) or not (t <= 2.8e+102):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.45e+138) || !(t <= 2.8e+102))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.45e+138) || ~((t <= 2.8e+102)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.45e+138], N[Not[LessEqual[t, 2.8e+102]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45000000000000005e138 or 2.80000000000000018e102 < t

   1. Initial program 95.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 58.2%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 68.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 68.9%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 59.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]
   6. Step-by-step derivation

      1. clear-num 59.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{t}}{x}}} \]

      2. associate-/r/ 59.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{t}} \cdot x} \]

      3. clear-num 59.7%

         \[\leadsto \color{blue}{\frac{t}{z}} \cdot x \]

   7. Applied egg-rr 59.7%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -1.45000000000000005e138 < t < 2.80000000000000018e102

   1. Initial program 96.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. frac-2neg 96.3%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-y}{-z}} - \frac{t}{1 - z}\right) \]

      2. div-inv 96.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right) \cdot \frac{1}{-z}} - \frac{t}{1 - z}\right) \]

      3. fma-neg 96.2%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, -\frac{t}{1 - z}\right)} \]

      4. distribute-neg-frac 96.2%

         \[\leadsto x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \color{blue}{\frac{-t}{1 - z}}\right) \]

   3. Applied egg-rr 96.2%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, \frac{-t}{1 - z}\right)} \]
   4. Step-by-step derivation

      1. fma-udef 96.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{-z} + \frac{-t}{1 - z}\right)} \]

      2. +-commutative 96.2%

         \[\leadsto x \cdot \color{blue}{\left(\frac{-t}{1 - z} + \left(-y\right) \cdot \frac{1}{-z}\right)} \]

      3. distribute-lft-neg-out 96.2%

         \[\leadsto x \cdot \left(\frac{-t}{1 - z} + \color{blue}{\left(-y \cdot \frac{1}{-z}\right)}\right) \]

      4. unsub-neg 96.2%

         \[\leadsto x \cdot \color{blue}{\left(\frac{-t}{1 - z} - y \cdot \frac{1}{-z}\right)} \]

      5. neg-mul-1 96.2%

         \[\leadsto x \cdot \left(\frac{\color{blue}{-1 \cdot t}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      6. *-commutative 96.2%

         \[\leadsto x \cdot \left(\frac{\color{blue}{t \cdot -1}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      7. associate-*r/ 96.2%

         \[\leadsto x \cdot \left(\color{blue}{t \cdot \frac{-1}{1 - z}} - y \cdot \frac{1}{-z}\right) \]

      8. metadata-eval 96.2%

         \[\leadsto x \cdot \left(t \cdot \frac{\color{blue}{\frac{1}{-1}}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      9. associate-/r* 96.2%

         \[\leadsto x \cdot \left(t \cdot \color{blue}{\frac{1}{-1 \cdot \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      10. neg-mul-1 96.2%

          \[\leadsto x \cdot \left(t \cdot \frac{1}{\color{blue}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      11. associate-*r/ 96.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{t \cdot 1}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      12. *-rgt-identity 96.2%

          \[\leadsto x \cdot \left(\frac{\color{blue}{t}}{-\left(1 - z\right)} - y \cdot \frac{1}{-z}\right) \]

      13. neg-sub0 96.2%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      14. associate--r- 96.2%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} - y \cdot \frac{1}{-z}\right) \]

      15. metadata-eval 96.2%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{-1} + z} - y \cdot \frac{1}{-z}\right) \]

      16. neg-mul-1 96.2%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{1}{\color{blue}{-1 \cdot z}}\right) \]

      17. associate-/r* 96.2%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \color{blue}{\frac{\frac{1}{-1}}{z}}\right) \]

      18. metadata-eval 96.2%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{\color{blue}{-1}}{z}\right) \]

   5. Simplified 96.2%

      \[\leadsto x \cdot \color{blue}{\left(\frac{t}{-1 + z} - y \cdot \frac{-1}{z}\right)} \]

   6. Taylor expanded in t around 0 77.2%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 79.4%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   8. Simplified 79.4%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+138} \lor \neg \left(t \leq 2.8 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+137} \lor \neg \left(t \leq 3.8 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.2e+137) (not (<= t 3.8e+140))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.2e+137) || !(t <= 3.8e+140)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-9.2d+137)) .or. (.not. (t <= 3.8d+140))) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.2e+137) || !(t <= 3.8e+140)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.2e+137) or not (t <= 3.8e+140):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.2e+137) || !(t <= 3.8e+140))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.2e+137) || ~((t <= 3.8e+140)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.2e+137], N[Not[LessEqual[t, 3.8e+140]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.19999999999999997e137 or 3.8000000000000001e140 < t

   1. Initial program 95.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 57.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.0%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 61.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]
   6. Step-by-step derivation

      1. clear-num 61.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{t}}{x}}} \]

      2. associate-/r/ 61.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{t}} \cdot x} \]

      3. clear-num 61.8%

         \[\leadsto \color{blue}{\frac{t}{z}} \cdot x \]

   7. Applied egg-rr 61.8%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -9.19999999999999997e137 < t < 3.8000000000000001e140

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   3. Step-by-step derivation

      1. associate-*l/ 80.2%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   4. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+137} \lor \neg \left(t \leq 3.8 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 9: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+136} \lor \neg \left(t \leq 1.65 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e+136) (not (<= t 1.65e+140))) (/ x (/ z t)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+136) || !(t <= 1.65e+140)) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8.5d+136)) .or. (.not. (t <= 1.65d+140))) then
        tmp = x / (z / t)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+136) || !(t <= 1.65e+140)) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e+136) or not (t <= 1.65e+140):
		tmp = x / (z / t)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e+136) || !(t <= 1.65e+140))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e+136) || ~((t <= 1.65e+140)))
		tmp = x / (z / t);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e+136], N[Not[LessEqual[t, 1.65e+140]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999966e136 or 1.6500000000000001e140 < t

   1. Initial program 95.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 57.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.0%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 61.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]

   if -8.49999999999999966e136 < t < 1.6500000000000001e140

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   3. Step-by-step derivation

      1. associate-*l/ 80.2%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   4. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+136} \lor \neg \left(t \leq 1.65 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 10: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+137} \lor \neg \left(t \leq 5.8 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4e+137) (not (<= t 5.8e+140))) (/ x (/ z t)) (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e+137) || !(t <= 5.8e+140)) {
		tmp = x / (z / t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4d+137)) .or. (.not. (t <= 5.8d+140))) then
        tmp = x / (z / t)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e+137) || !(t <= 5.8e+140)) {
		tmp = x / (z / t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4e+137) or not (t <= 5.8e+140):
		tmp = x / (z / t)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4e+137) || !(t <= 5.8e+140))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4e+137) || ~((t <= 5.8e+140)))
		tmp = x / (z / t);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4e+137], N[Not[LessEqual[t, 5.8e+140]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000001e137 or 5.7999999999999998e140 < t

   1. Initial program 95.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 57.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.0%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 61.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]

   if -4.0000000000000001e137 < t < 5.7999999999999998e140

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 77.5%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 77.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 79.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 79.7%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+137} \lor \neg \left(t \leq 5.8 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 11: 63.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e+138)
   (* t (/ x z))
   (if (<= t 5.8e+146) (* y (/ x z)) (* t (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+138) {
		tmp = t * (x / z);
	} else if (t <= 5.8e+146) {
		tmp = y * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d+138)) then
        tmp = t * (x / z)
    else if (t <= 5.8d+146) then
        tmp = y * (x / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+138) {
		tmp = t * (x / z);
	} else if (t <= 5.8e+146) {
		tmp = y * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e+138:
		tmp = t * (x / z)
	elif t <= 5.8e+146:
		tmp = y * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e+138)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= 5.8e+146)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e+138)
		tmp = t * (x / z);
	elseif (t <= 5.8e+146)
		tmp = y * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e+138], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+146], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000005e138

   1. Initial program 94.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 79.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. associate-/r/ 67.1%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - -1 \cdot t\right)} \]

      4. cancel-sign-sub-inv 67.1%

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(y + \left(--1\right) \cdot t\right)} \]

      5. metadata-eval 67.1%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{1} \cdot t\right) \]

      6. *-lft-identity 67.1%

         \[\leadsto \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]

   4. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + t\right)} \]

   5. Taylor expanded in y around 0 61.9%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 59.6%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   7. Simplified 59.6%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if -1.50000000000000005e138 < t < 5.7999999999999997e146

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. frac-2neg 96.4%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-y}{-z}} - \frac{t}{1 - z}\right) \]

      2. div-inv 96.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right) \cdot \frac{1}{-z}} - \frac{t}{1 - z}\right) \]

      3. fma-neg 96.4%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, -\frac{t}{1 - z}\right)} \]

      4. distribute-neg-frac 96.4%

         \[\leadsto x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \color{blue}{\frac{-t}{1 - z}}\right) \]

   3. Applied egg-rr 96.4%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, \frac{-t}{1 - z}\right)} \]
   4. Step-by-step derivation

      1. fma-udef 96.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{-z} + \frac{-t}{1 - z}\right)} \]

      2. +-commutative 96.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{-t}{1 - z} + \left(-y\right) \cdot \frac{1}{-z}\right)} \]

      3. distribute-lft-neg-out 96.4%

         \[\leadsto x \cdot \left(\frac{-t}{1 - z} + \color{blue}{\left(-y \cdot \frac{1}{-z}\right)}\right) \]

      4. unsub-neg 96.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{-t}{1 - z} - y \cdot \frac{1}{-z}\right)} \]

      5. neg-mul-1 96.4%

         \[\leadsto x \cdot \left(\frac{\color{blue}{-1 \cdot t}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      6. *-commutative 96.4%

         \[\leadsto x \cdot \left(\frac{\color{blue}{t \cdot -1}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      7. associate-*r/ 96.4%

         \[\leadsto x \cdot \left(\color{blue}{t \cdot \frac{-1}{1 - z}} - y \cdot \frac{1}{-z}\right) \]

      8. metadata-eval 96.4%

         \[\leadsto x \cdot \left(t \cdot \frac{\color{blue}{\frac{1}{-1}}}{1 - z} - y \cdot \frac{1}{-z}\right) \]

      9. associate-/r* 96.4%

         \[\leadsto x \cdot \left(t \cdot \color{blue}{\frac{1}{-1 \cdot \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      10. neg-mul-1 96.4%

          \[\leadsto x \cdot \left(t \cdot \frac{1}{\color{blue}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      11. associate-*r/ 96.4%

          \[\leadsto x \cdot \left(\color{blue}{\frac{t \cdot 1}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      12. *-rgt-identity 96.4%

          \[\leadsto x \cdot \left(\frac{\color{blue}{t}}{-\left(1 - z\right)} - y \cdot \frac{1}{-z}\right) \]

      13. neg-sub0 96.4%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]

      14. associate--r- 96.4%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} - y \cdot \frac{1}{-z}\right) \]

      15. metadata-eval 96.4%

          \[\leadsto x \cdot \left(\frac{t}{\color{blue}{-1} + z} - y \cdot \frac{1}{-z}\right) \]

      16. neg-mul-1 96.4%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{1}{\color{blue}{-1 \cdot z}}\right) \]

      17. associate-/r* 96.4%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \color{blue}{\frac{\frac{1}{-1}}{z}}\right) \]

      18. metadata-eval 96.4%

          \[\leadsto x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{\color{blue}{-1}}{z}\right) \]

   5. Simplified 96.4%

      \[\leadsto x \cdot \color{blue}{\left(\frac{t}{-1 + z} - y \cdot \frac{-1}{z}\right)} \]

   6. Taylor expanded in t around 0 75.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 77.3%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   8. Simplified 77.3%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   if 5.7999999999999997e146 < t

   1. Initial program 96.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 55.4%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 51.6%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 51.6%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 51.6%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 59.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 59.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 59.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]

   5. Taylor expanded in y around 0 51.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      2. neg-mul-1 51.6%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot x \]

   7. Simplified 51.6%

      \[\leadsto \color{blue}{\left(-t\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 12: 22.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(-x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- x)))

C

double code(double x, double y, double z, double t) {
	return t * -x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * -x
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * -x;
}

Python

def code(x, y, z, t):
	return t * -x

Julia

function code(x, y, z, t)
	return Float64(t * Float64(-x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * -x;
end

Wolfram

code[x_, y_, z_, t_] := N[(t * (-x)), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

2. Taylor expanded in z around 0 62.0%

   \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
3. Step-by-step derivation

   1. associate-*l/ 63.9%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

   2. associate-*r* 63.9%

      \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

   3. neg-mul-1 63.9%

      \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

   4. distribute-rgt-out 66.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

   5. unsub-neg 66.6%

      \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

4. Simplified 66.6%

   \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]

5. Taylor expanded in y around 0 24.0%

   \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
6. Step-by-step derivation

   1. associate-*r* 24.0%

      \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

   2. neg-mul-1 24.0%

      \[\leadsto \color{blue}{\left(-t\right)} \cdot x \]

7. Simplified 24.0%

   \[\leadsto \color{blue}{\left(-t\right) \cdot x} \]

8. Final simplification 24.0%

   \[\leadsto t \cdot \left(-x\right) \]

Developer target: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))