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

Percentage Accurate: 94.4% → 98.4%

Time: 9.2s

Alternatives: 14

Speedup: 0.3×

• 21.2% 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: 98.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+273}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot t - y \cdot \left(1 - z\right)\right)}{z \cdot \left(z + -1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 2e+273)
       (* t_1 x)
       (/ (* x (- (* z t) (* y (- 1.0 z)))) (* z (+ z -1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= 2e+273) {
		tmp = t_1 * x;
	} else {
		tmp = (x * ((z * t) - (y * (1.0 - z)))) / (z * (z + -1.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= 2e+273) {
		tmp = t_1 * x;
	} else {
		tmp = (x * ((z * t) - (y * (1.0 - z)))) / (z * (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= 2e+273:
		tmp = t_1 * x
	else:
		tmp = (x * ((z * t) - (y * (1.0 - z)))) / (z * (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= 2e+273)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(x * Float64(Float64(z * t) - Float64(y * Float64(1.0 - z)))) / Float64(z * Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= 2e+273)
		tmp = t_1 * x;
	else
		tmp = (x * ((z * t) - (y * (1.0 - z)))) / (z * (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+273], N[(t$95$1 * x), $MachinePrecision], N[(N[(x * N[(N[(z * t), $MachinePrecision] - N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 58.8%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-*r/ 58.8%

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

   5. Simplified 58.8%

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

      1. clear-num 58.8%

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

      2. un-div-inv 58.8%

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

   7. Applied egg-rr 58.8%

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

      1. associate-/r/ 99.9%

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

   9. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.99999999999999989e273

   1. Initial program 98.4%

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

   if 1.99999999999999989e273 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 72.2%

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

      1. *-commutative 72.2%

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

      2. frac-sub 72.2%

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

      3. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(y \cdot \left(1 - z\right) - z \cdot t\right) \cdot x}{z \cdot \left(1 - z\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 2 \cdot 10^{+273}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot t - y \cdot \left(1 - z\right)\right)}{z \cdot \left(z + -1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+288}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 1e+288) (* t_1 x) (/ (- (* y x) (* t (* z x))) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= 1e+288) {
		tmp = t_1 * x;
	} else {
		tmp = ((y * x) - (t * (z * x))) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= 1e+288) {
		tmp = t_1 * x;
	} else {
		tmp = ((y * x) - (t * (z * x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= 1e+288:
		tmp = t_1 * x
	else:
		tmp = ((y * x) - (t * (z * x))) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= 1e+288)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(z * x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= 1e+288)
		tmp = t_1 * x;
	else
		tmp = ((y * x) - (t * (z * 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[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+288], N[(t$95$1 * x), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 58.8%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-*r/ 58.8%

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

   5. Simplified 58.8%

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

      1. clear-num 58.8%

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

      2. un-div-inv 58.8%

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

   7. Applied egg-rr 58.8%

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

      1. associate-/r/ 99.9%

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

   9. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1e288

   1. Initial program 98.4%

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

   if 1e288 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 67.3%

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

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{+288}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+292}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 4e+292) (* t_1 x) (/ (* y x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= 4e+292) {
		tmp = t_1 * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= 4e+292) {
		tmp = t_1 * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= 4e+292:
		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(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= 4e+292)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= 4e+292)
		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[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+292], N[(t$95$1 * x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 58.8%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-*r/ 58.8%

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

   5. Simplified 58.8%

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

      1. clear-num 58.8%

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

      2. un-div-inv 58.8%

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

   7. Applied egg-rr 58.8%

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

      1. associate-/r/ 99.9%

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

   9. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 4.0000000000000001e292

   1. Initial program 98.5%

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

   if 4.0000000000000001e292 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 99.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 4 \cdot 10^{+292}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{1}{\frac{-1}{t}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4400000000.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (+ (/ y z) (/ 1.0 (/ -1.0 t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) + (1.0 / (-1.0 / 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 <= (-4400000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) + (1.0d0 / ((-1.0d0) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) + (1.0 / (-1.0 / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4400000000.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) + (1.0 / (-1.0 / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4400000000.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) + Float64(1.0 / Float64(-1.0 / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4400000000.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) + (1.0 / (-1.0 / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4400000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] + N[(1.0 / N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e9 or 1 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 97.4%

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

      1. sub-neg 97.4%

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

      2. neg-mul-1 97.4%

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

      3. remove-double-neg 97.4%

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

      4. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   if -4.4e9 < z < 1

   1. Initial program 89.0%

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

      1. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in z around 0 88.4%

      \[\leadsto x \cdot \left(\frac{y}{z} - \frac{1}{\color{blue}{\frac{1}{t}}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{1}{\frac{-1}{t}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4400000000.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} 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 <= (-4400000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    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 <= -4400000000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4400000000.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4400000000.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	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 <= -4400000000.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4400000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e9 or 1 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 97.4%

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

      1. sub-neg 97.4%

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

      2. neg-mul-1 97.4%

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

      3. remove-double-neg 97.4%

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

      4. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   if -4.4e9 < z < 1

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

      3. div-sub 88.3%

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

      4. associate-/l* 88.4%

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

      5. *-inverses 88.4%

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

      6. *-rgt-identity 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+71} \lor \neg \left(z \leq 7000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+71) (not (<= z 7000.0))) (* x (/ t z)) (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+71) || !(z <= 7000.0)) {
		tmp = x * (t / z);
	} 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 <= (-1d+71)) .or. (.not. (z <= 7000.0d0))) then
        tmp = x * (t / z)
    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 <= -1e+71) || !(z <= 7000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+71) or not (z <= 7000.0):
		tmp = x * (t / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+71) || !(z <= 7000.0))
		tmp = Float64(x * Float64(t / z));
	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 <= -1e+71) || ~((z <= 7000.0)))
		tmp = x * (t / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+71], N[Not[LessEqual[z, 7000.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e71 or 7e3 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-/l* 67.0%

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

      4. distribute-rgt-neg-out 67.0%

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

      5. distribute-frac-neg2 67.0%

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

      6. neg-sub0 67.0%

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

      7. associate--r- 67.0%

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

      8. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in z around inf 67.0%

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

   if -1e71 < z < 7e3

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. div-sub 86.2%

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

      4. associate-/l* 86.3%

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

      5. *-inverses 86.3%

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

      6. *-rgt-identity 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+71} \lor \neg \left(z \leq 7000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e+72)
   (* x (/ t z))
   (if (<= z 5.6e-17) (* x (- (/ y z) t)) (* x (/ t (+ z -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e+72) {
		tmp = x * (t / z);
	} else if (z <= 5.6e-17) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / (z + -1.0));
	}
	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 <= (-3.1d+72)) then
        tmp = x * (t / z)
    else if (z <= 5.6d-17) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * (t / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e+72) {
		tmp = x * (t / z);
	} else if (z <= 5.6e-17) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e+72:
		tmp = x * (t / z)
	elif z <= 5.6e-17:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * (t / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e+72)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 5.6e-17)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.1e+72)
		tmp = x * (t / z);
	elseif (z <= 5.6e-17)
		tmp = x * ((y / z) - t);
	else
		tmp = x * (t / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e+72], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-17], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999988e72

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. *-commutative 50.5%

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

      3. associate-/l* 66.0%

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

      4. distribute-rgt-neg-out 66.0%

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

      5. distribute-frac-neg2 66.0%

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

      6. neg-sub0 66.0%

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

      7. associate--r- 66.0%

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

      8. metadata-eval 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in z around inf 66.0%

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

   if -3.09999999999999988e72 < z < 5.5999999999999998e-17

   1. Initial program 89.8%

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

   3. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. div-sub 86.2%

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

      4. associate-/l* 86.3%

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

      5. *-inverses 86.3%

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

      6. *-rgt-identity 86.3%

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

   5. Simplified 86.3%

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

   if 5.5999999999999998e-17 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-/l* 68.7%

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

      4. distribute-rgt-neg-out 68.7%

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

      5. distribute-frac-neg2 68.7%

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

      6. neg-sub0 68.7%

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

      7. associate--r- 68.7%

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

      8. metadata-eval 68.7%

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

   5. Simplified 68.7%

      \[\leadsto \color{blue}{x \cdot \frac{t}{-1 + z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+108} \lor \neg \left(t \leq 21\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.2e+108) (not (<= t 21.0))) (* x (/ t z)) (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.2e+108) || !(t <= 21.0)) {
		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 <= (-9.2d+108)) .or. (.not. (t <= 21.0d0))) 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 <= -9.2e+108) || !(t <= 21.0)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.2e+108) or not (t <= 21.0):
		tmp = x * (t / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.2e+108) || !(t <= 21.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.2e+108) || ~((t <= 21.0)))
		tmp = x * (t / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.2e+108], N[Not[LessEqual[t, 21.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.1999999999999996e108 or 21 < t

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-/l* 72.8%

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

      4. distribute-rgt-neg-out 72.8%

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

      5. distribute-frac-neg2 72.8%

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

      6. neg-sub0 72.8%

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

      7. associate--r- 72.8%

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

      8. metadata-eval 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in z around inf 54.3%

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

   if -9.1999999999999996e108 < t < 21

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 79.4%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+108} \lor \neg \left(t \leq 21\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+74} \lor \neg \left(z \leq 10200000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e+74) (not (<= z 10200000000000.0)))
   (* x (/ t z))
   (/ y (/ z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+74) || !(z <= 10200000000000.0)) {
		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 ((z <= (-4.1d+74)) .or. (.not. (z <= 10200000000000.0d0))) 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 ((z <= -4.1e+74) || !(z <= 10200000000000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e+74) or not (z <= 10200000000000.0):
		tmp = x * (t / z)
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e+74) || !(z <= 10200000000000.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e+74) || ~((z <= 10200000000000.0)))
		tmp = x * (t / z);
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e+74], N[Not[LessEqual[z, 10200000000000.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e74 or 1.02e13 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-/l* 67.0%

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

      4. distribute-rgt-neg-out 67.0%

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

      5. distribute-frac-neg2 67.0%

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

      6. neg-sub0 67.0%

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

      7. associate--r- 67.0%

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

      8. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in z around inf 67.0%

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

   if -4.1e74 < z < 1.02e13

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. associate-*r/ 64.2%

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

   5. Simplified 64.2%

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

      1. clear-num 64.2%

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

      2. un-div-inv 64.8%

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

   7. Applied egg-rr 64.8%

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

      1. associate-/r/ 70.0%

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

   9. Simplified 70.0%

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

       1. *-commutative 70.0%

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

       2. clear-num 69.9%

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

       3. un-div-inv 70.2%

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

   11. Applied egg-rr 70.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+74} \lor \neg \left(z \leq 10200000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+75} \lor \neg \left(z \leq 420000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+75) (not (<= z 420000000000.0)))
   (* x (/ t z))
   (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+75) || !(z <= 420000000000.0)) {
		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 ((z <= (-2.2d+75)) .or. (.not. (z <= 420000000000.0d0))) 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 ((z <= -2.2e+75) || !(z <= 420000000000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+75) or not (z <= 420000000000.0):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+75) || !(z <= 420000000000.0))
		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 ((z <= -2.2e+75) || ~((z <= 420000000000.0)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+75], N[Not[LessEqual[z, 420000000000.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000012e75 or 4.2e11 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-/l* 67.0%

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

      4. distribute-rgt-neg-out 67.0%

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

      5. distribute-frac-neg2 67.0%

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

      6. neg-sub0 67.0%

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

      7. associate--r- 67.0%

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

      8. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in z around inf 67.0%

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

   if -2.20000000000000012e75 < z < 4.2e11

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. associate-*r/ 64.2%

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

   5. Simplified 64.2%

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

      1. clear-num 64.2%

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

      2. un-div-inv 64.8%

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

   7. Applied egg-rr 64.8%

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

      1. associate-/r/ 70.0%

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

   9. Simplified 70.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+75} \lor \neg \left(z \leq 420000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+113} \lor \neg \left(t \leq 21\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e+113) (not (<= t 21.0))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e+113) || !(t <= 21.0)) {
		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 <= (-1.35d+113)) .or. (.not. (t <= 21.0d0))) 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 <= -1.35e+113) || !(t <= 21.0)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e+113) or not (t <= 21.0):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e+113) || !(t <= 21.0))
		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 <= -1.35e+113) || ~((t <= 21.0)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e+113], N[Not[LessEqual[t, 21.0]], $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 < -1.35000000000000006e113 or 21 < t

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-/l* 72.8%

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

      4. distribute-rgt-neg-out 72.8%

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

      5. distribute-frac-neg2 72.8%

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

      6. neg-sub0 72.8%

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

      7. associate--r- 72.8%

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

      8. metadata-eval 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in z around inf 54.3%

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

   if -1.35000000000000006e113 < t < 21

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. associate-*r/ 77.0%

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

   5. Simplified 77.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+113} \lor \neg \left(t \leq 21\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1.4\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4400000000.0) (not (<= z 1.4))) (* x (/ t z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000000.0) || !(z <= 1.4)) {
		tmp = x * (t / 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 <= (-4400000000.0d0)) .or. (.not. (z <= 1.4d0))) then
        tmp = x * (t / 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 <= -4400000000.0) || !(z <= 1.4)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4400000000.0) or not (z <= 1.4):
		tmp = x * (t / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4400000000.0) || !(z <= 1.4))
		tmp = Float64(x * Float64(t / 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 <= -4400000000.0) || ~((z <= 1.4)))
		tmp = x * (t / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4400000000.0], N[Not[LessEqual[z, 1.4]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e9 or 1.3999999999999999 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-/l* 64.5%

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

      4. distribute-rgt-neg-out 64.5%

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

      5. distribute-frac-neg2 64.5%

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

      6. neg-sub0 64.5%

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

      7. associate--r- 64.5%

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

      8. metadata-eval 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around inf 64.4%

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

   if -4.4e9 < z < 1.3999999999999999

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. *-commutative 33.0%

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

      3. associate-/l* 33.0%

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

      4. distribute-rgt-neg-out 33.0%

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

      5. distribute-frac-neg2 33.0%

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

      6. neg-sub0 33.0%

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

      7. associate--r- 33.0%

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

      8. metadata-eval 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. *-commutative 32.6%

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

      2. neg-mul-1 32.6%

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

      3. distribute-rgt-neg-in 32.6%

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

   8. Simplified 32.6%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1.4\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4400000000.0) (not (<= z 1.0))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000000.0) || !(z <= 1.0)) {
		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 <= (-4400000000.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -4400000000.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4400000000.0) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4400000000.0) || !(z <= 1.0))
		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 <= -4400000000.0) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4400000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e9 or 1 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-/l* 64.5%

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

      4. distribute-rgt-neg-out 64.5%

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

      5. distribute-frac-neg2 64.5%

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

      6. neg-sub0 64.5%

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

      7. associate--r- 64.5%

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

      8. metadata-eval 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around inf 56.8%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -4.4e9 < z < 1

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. *-commutative 33.0%

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

      3. associate-/l* 33.0%

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

      4. distribute-rgt-neg-out 33.0%

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

      5. distribute-frac-neg2 33.0%

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

      6. neg-sub0 33.0%

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

      7. associate--r- 33.0%

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

      8. metadata-eval 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. *-commutative 32.6%

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

      2. neg-mul-1 32.6%

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

      3. distribute-rgt-neg-in 32.6%

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

   8. Simplified 32.6%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 23.0% 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 93.2%

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

3. Taylor expanded in y around 0 44.8%

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

   1. mul-1-neg 44.8%

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

   2. *-commutative 44.8%

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

   3. associate-/l* 48.5%

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

   4. distribute-rgt-neg-out 48.5%

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

   5. distribute-frac-neg2 48.5%

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

   6. neg-sub0 48.5%

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

   7. associate--r- 48.5%

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

   8. metadata-eval 48.5%

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

5. Simplified 48.5%

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

6. Taylor expanded in z around 0 22.2%

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

   1. *-commutative 22.2%

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

   2. neg-mul-1 22.2%

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

   3. distribute-rgt-neg-in 22.2%

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

8. Simplified 22.2%

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

9. Final simplification 22.2%

   \[\leadsto t \cdot \left(-x\right) \]
10. Add Preprocessing

Developer target: 94.9% accurate, 0.2× 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 2024096 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (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)))))