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

Percentage Accurate: 94.0% → 95.4%

Time: 6.6s

Alternatives: 11

Speedup: 0.5×

• 20.6% 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: 94.0% 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: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 10^{+265}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} - t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 1e+265) (* t_1 x) (- (/ (* y x) z) (* t x)))))

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+265) {
		tmp = t_1 * x;
	} else {
		tmp = ((y * x) / z) - (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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 1d+265) then
        tmp = t_1 * x
    else
        tmp = ((y * x) / z) - (t * x)
    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+265) {
		tmp = t_1 * x;
	} else {
		tmp = ((y * x) / z) - (t * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 1e+265:
		tmp = t_1 * x
	else:
		tmp = ((y * x) / z) - (t * x)
	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+265)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(Float64(y * x) / z) - Float64(t * x));
	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+265)
		tmp = t_1 * x;
	else
		tmp = ((y * x) / z) - (t * x);
	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+265], N[(t$95$1 * x), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 1.00000000000000007e265

   1. Initial program 99.0%

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

   if 1.00000000000000007e265 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 73.1%

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

   2. Taylor expanded in z around 0 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+265}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} - t \cdot x\\ \end{array} \]

Alternative 2: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 2e+294) (* 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 <= 2e+294) {
		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 <= 2d+294) 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 <= 2e+294) {
		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 <= 2e+294:
		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 <= 2e+294)
		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 <= 2e+294)
		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, 2e+294], 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))) < 2.00000000000000013e294

   1. Initial program 99.0%

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

   if 2.00000000000000013e294 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 64.3%

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

   2. Taylor expanded in y around inf 99.9%

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

      1. associate-/l* 64.3%

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

   4. Simplified 64.3%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4100000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+239} \lor \neg \left(z \leq 6.8 \cdot 10^{+292}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= z -4.9e+17)
     t_1
     (if (<= z 4100000000.0)
       (* x (- (/ y z) t))
       (if (or (<= z 1.65e+239) (not (<= z 6.8e+292))) (* x (/ t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / y);
	double tmp;
	if (z <= -4.9e+17) {
		tmp = t_1;
	} else if (z <= 4100000000.0) {
		tmp = x * ((y / z) - t);
	} else if ((z <= 1.65e+239) || !(z <= 6.8e+292)) {
		tmp = x * (t / 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) :: tmp
    t_1 = x / (z / y)
    if (z <= (-4.9d+17)) then
        tmp = t_1
    else if (z <= 4100000000.0d0) then
        tmp = x * ((y / z) - t)
    else if ((z <= 1.65d+239) .or. (.not. (z <= 6.8d+292))) then
        tmp = x * (t / 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 / (z / y);
	double tmp;
	if (z <= -4.9e+17) {
		tmp = t_1;
	} else if (z <= 4100000000.0) {
		tmp = x * ((y / z) - t);
	} else if ((z <= 1.65e+239) || !(z <= 6.8e+292)) {
		tmp = x * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / y)
	tmp = 0
	if z <= -4.9e+17:
		tmp = t_1
	elif z <= 4100000000.0:
		tmp = x * ((y / z) - t)
	elif (z <= 1.65e+239) or not (z <= 6.8e+292):
		tmp = x * (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (z <= -4.9e+17)
		tmp = t_1;
	elseif (z <= 4100000000.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif ((z <= 1.65e+239) || !(z <= 6.8e+292))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / y);
	tmp = 0.0;
	if (z <= -4.9e+17)
		tmp = t_1;
	elseif (z <= 4100000000.0)
		tmp = x * ((y / z) - t);
	elseif ((z <= 1.65e+239) || ~((z <= 6.8e+292)))
		tmp = x * (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+17], t$95$1, If[LessEqual[z, 4100000000.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.65e+239], N[Not[LessEqual[z, 6.8e+292]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9e17 or 1.6499999999999999e239 < z < 6.8000000000000003e292

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 54.6%

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

      1. associate-/l* 63.7%

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

   4. Simplified 63.7%

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

   if -4.9e17 < z < 4.1e9

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*r/ 89.1%

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

      6. distribute-lft-out-- 92.0%

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

   4. Simplified 92.0%

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

   if 4.1e9 < z < 1.6499999999999999e239 or 6.8000000000000003e292 < z

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around inf 89.1%

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

      1. *-commutative 89.1%

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

      2. sub-neg 89.1%

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

      3. mul-1-neg 89.1%

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

      4. remove-double-neg 89.1%

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

      5. associate-*l/ 99.8%

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

      6. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 60.0%

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

      1. associate-/l* 59.7%

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

      2. associate-/r/ 68.7%

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

   9. Simplified 68.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 4100000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+239} \lor \neg \left(z \leq 6.8 \cdot 10^{+292}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;y \leq -3 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) x)))
   (if (<= y -3e-57)
     t_1
     (if (<= y -7.8e-264)
       (* t (/ x z))
       (if (<= y 1.85e-110) (* t (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double tmp;
	if (y <= -3e-57) {
		tmp = t_1;
	} else if (y <= -7.8e-264) {
		tmp = t * (x / z);
	} else if (y <= 1.85e-110) {
		tmp = t * -x;
	} 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) :: tmp
    t_1 = (y / z) * x
    if (y <= (-3d-57)) then
        tmp = t_1
    else if (y <= (-7.8d-264)) then
        tmp = t * (x / z)
    else if (y <= 1.85d-110) then
        tmp = t * -x
    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 = (y / z) * x;
	double tmp;
	if (y <= -3e-57) {
		tmp = t_1;
	} else if (y <= -7.8e-264) {
		tmp = t * (x / z);
	} else if (y <= 1.85e-110) {
		tmp = t * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * x
	tmp = 0
	if y <= -3e-57:
		tmp = t_1
	elif y <= -7.8e-264:
		tmp = t * (x / z)
	elif y <= 1.85e-110:
		tmp = t * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (y <= -3e-57)
		tmp = t_1;
	elseif (y <= -7.8e-264)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 1.85e-110)
		tmp = Float64(t * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * x;
	tmp = 0.0;
	if (y <= -3e-57)
		tmp = t_1;
	elseif (y <= -7.8e-264)
		tmp = t * (x / z);
	elseif (y <= 1.85e-110)
		tmp = t * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -3e-57], t$95$1, If[LessEqual[y, -7.8e-264], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-110], N[(t * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000001e-57 or 1.85000000000000008e-110 < y

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 79.3%

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

      1. associate-*r/ 77.8%

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

   4. Simplified 77.8%

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

   if -3.00000000000000001e-57 < y < -7.7999999999999997e-264

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. associate-/l* 79.4%

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

      2. neg-mul-1 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in y around 0 62.3%

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

      1. associate-*r/ 64.8%

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

   7. Simplified 64.8%

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

   if -7.7999999999999997e-264 < y < 1.85000000000000008e-110

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

      4. *-commutative 67.9%

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

      5. associate-*r/ 69.7%

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

      6. distribute-lft-out-- 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in y around 0 57.4%

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

      1. associate-*r* 57.4%

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

      2. mul-1-neg 57.4%

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

   7. Simplified 57.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 5: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) x)))
   (if (<= y -2.8e-46)
     t_1
     (if (<= y 9.8e-183)
       (* x (/ t z))
       (if (<= y 2.05e-110) (* t (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double tmp;
	if (y <= -2.8e-46) {
		tmp = t_1;
	} else if (y <= 9.8e-183) {
		tmp = x * (t / z);
	} else if (y <= 2.05e-110) {
		tmp = t * -x;
	} 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) :: tmp
    t_1 = (y / z) * x
    if (y <= (-2.8d-46)) then
        tmp = t_1
    else if (y <= 9.8d-183) then
        tmp = x * (t / z)
    else if (y <= 2.05d-110) then
        tmp = t * -x
    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 = (y / z) * x;
	double tmp;
	if (y <= -2.8e-46) {
		tmp = t_1;
	} else if (y <= 9.8e-183) {
		tmp = x * (t / z);
	} else if (y <= 2.05e-110) {
		tmp = t * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * x
	tmp = 0
	if y <= -2.8e-46:
		tmp = t_1
	elif y <= 9.8e-183:
		tmp = x * (t / z)
	elif y <= 2.05e-110:
		tmp = t * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (y <= -2.8e-46)
		tmp = t_1;
	elseif (y <= 9.8e-183)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 2.05e-110)
		tmp = Float64(t * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * x;
	tmp = 0.0;
	if (y <= -2.8e-46)
		tmp = t_1;
	elseif (y <= 9.8e-183)
		tmp = x * (t / z);
	elseif (y <= 2.05e-110)
		tmp = t * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -2.8e-46], t$95$1, If[LessEqual[y, 9.8e-183], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-110], N[(t * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e-46 or 2.04999999999999991e-110 < y

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. associate-*r/ 79.1%

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

   4. Simplified 79.1%

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

   if -2.7999999999999998e-46 < y < 9.799999999999999e-183

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. sub-neg 64.4%

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

      3. mul-1-neg 64.4%

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

      4. remove-double-neg 64.4%

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

      5. associate-*l/ 69.3%

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

      6. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in y around 0 58.8%

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

      1. associate-/l* 56.3%

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

      2. associate-/r/ 62.5%

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

   9. Simplified 62.5%

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

   if 9.799999999999999e-183 < y < 2.04999999999999991e-110

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. *-commutative 74.6%

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

      5. associate-*r/ 79.6%

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

      6. distribute-lft-out-- 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in y around 0 64.8%

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

      1. associate-*r* 64.8%

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

      2. mul-1-neg 64.8%

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

   7. Simplified 64.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 6: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -2.7e-45)
     t_1
     (if (<= y 3.7e-183) (* x (/ t z)) (if (<= y 2.8e-107) (* t (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -2.7e-45) {
		tmp = t_1;
	} else if (y <= 3.7e-183) {
		tmp = x * (t / z);
	} else if (y <= 2.8e-107) {
		tmp = t * -x;
	} 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) :: tmp
    t_1 = y * (x / z)
    if (y <= (-2.7d-45)) then
        tmp = t_1
    else if (y <= 3.7d-183) then
        tmp = x * (t / z)
    else if (y <= 2.8d-107) then
        tmp = t * -x
    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 = y * (x / z);
	double tmp;
	if (y <= -2.7e-45) {
		tmp = t_1;
	} else if (y <= 3.7e-183) {
		tmp = x * (t / z);
	} else if (y <= 2.8e-107) {
		tmp = t * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -2.7e-45:
		tmp = t_1
	elif y <= 3.7e-183:
		tmp = x * (t / z)
	elif y <= 2.8e-107:
		tmp = t * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -2.7e-45)
		tmp = t_1;
	elseif (y <= 3.7e-183)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 2.8e-107)
		tmp = Float64(t * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (y <= -2.7e-45)
		tmp = t_1;
	elseif (y <= 3.7e-183)
		tmp = x * (t / z);
	elseif (y <= 2.8e-107)
		tmp = t * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-45], t$95$1, If[LessEqual[y, 3.7e-183], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-107], N[(t * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999985e-45 or 2.7999999999999999e-107 < y

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. associate-/l* 79.1%

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

   4. Simplified 79.1%

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

      1. associate-/r/ 79.9%

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

   6. Applied egg-rr 79.9%

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

   if -2.69999999999999985e-45 < y < 3.6999999999999999e-183

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. sub-neg 64.4%

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

      3. mul-1-neg 64.4%

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

      4. remove-double-neg 64.4%

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

      5. associate-*l/ 69.3%

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

      6. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in y around 0 58.8%

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

      1. associate-/l* 56.3%

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

      2. associate-/r/ 62.5%

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

   9. Simplified 62.5%

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

   if 3.6999999999999999e-183 < y < 2.7999999999999999e-107

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. *-commutative 74.6%

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

      5. associate-*r/ 79.6%

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

      6. distribute-lft-out-- 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in y around 0 64.8%

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

      1. associate-*r* 64.8%

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

      2. mul-1-neg 64.8%

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

   7. Simplified 64.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 7: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-45)
   (* y (/ x z))
   (if (<= y 2.7e-186)
     (* x (/ t z))
     (if (<= y 3.1e-111) (* t (- x)) (/ (* y x) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-45) {
		tmp = y * (x / z);
	} else if (y <= 2.7e-186) {
		tmp = x * (t / z);
	} else if (y <= 3.1e-111) {
		tmp = t * -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) :: tmp
    if (y <= (-3.5d-45)) then
        tmp = y * (x / z)
    else if (y <= 2.7d-186) then
        tmp = x * (t / z)
    else if (y <= 3.1d-111) then
        tmp = t * -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 tmp;
	if (y <= -3.5e-45) {
		tmp = y * (x / z);
	} else if (y <= 2.7e-186) {
		tmp = x * (t / z);
	} else if (y <= 3.1e-111) {
		tmp = t * -x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-45:
		tmp = y * (x / z)
	elif y <= 2.7e-186:
		tmp = x * (t / z)
	elif y <= 3.1e-111:
		tmp = t * -x
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-45)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 2.7e-186)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 3.1e-111)
		tmp = Float64(t * Float64(-x));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.5e-45)
		tmp = y * (x / z);
	elseif (y <= 2.7e-186)
		tmp = x * (t / z);
	elseif (y <= 3.1e-111)
		tmp = t * -x;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-45], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-186], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-111], N[(t * (-x)), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.5e-45

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. associate-/l* 79.8%

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

   4. Simplified 79.8%

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

      1. associate-/r/ 80.2%

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

   6. Applied egg-rr 80.2%

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

   if -3.5e-45 < y < 2.6999999999999999e-186

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. sub-neg 64.4%

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

      3. mul-1-neg 64.4%

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

      4. remove-double-neg 64.4%

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

      5. associate-*l/ 69.3%

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

      6. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in y around 0 58.8%

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

      1. associate-/l* 56.3%

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

      2. associate-/r/ 62.5%

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

   9. Simplified 62.5%

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

   if 2.6999999999999999e-186 < y < 3.10000000000000014e-111

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. *-commutative 74.6%

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

      5. associate-*r/ 79.6%

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

      6. distribute-lft-out-- 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in y around 0 64.8%

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

      1. associate-*r* 64.8%

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

      2. mul-1-neg 64.8%

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

   7. Simplified 64.8%

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

   if 3.10000000000000014e-111 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in y around inf 83.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 8: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.09\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.09)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.09)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 0.09d0))) 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 <= -1.0) || !(z <= 0.09)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.09):
		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 <= -1.0) || !(z <= 0.09))
		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 <= -1.0) || ~((z <= 0.09)))
		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, -1.0], N[Not[LessEqual[z, 0.09]], $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 < -1 or 0.089999999999999997 < z

   1. Initial program 99.7%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. sub-neg 88.1%

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

      3. mul-1-neg 88.1%

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

      4. remove-double-neg 88.1%

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

      5. associate-*l/ 99.6%

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

      6. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   if -1 < z < 0.089999999999999997

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 93.0%

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

      1. +-commutative 93.0%

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

      2. mul-1-neg 93.0%

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

      3. unsub-neg 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-*r/ 89.3%

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

      6. distribute-lft-out-- 92.3%

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

   4. Simplified 92.3%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.09\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 9: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e-45)
   (* y (/ x z))
   (if (<= y 8.5e-102) (* x (/ t (+ z -1.0))) (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-45) {
		tmp = y * (x / z);
	} else if (y <= 8.5e-102) {
		tmp = x * (t / (z + -1.0));
	} 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 (y <= (-1.1d-45)) then
        tmp = y * (x / z)
    else if (y <= 8.5d-102) then
        tmp = x * (t / (z + (-1.0d0)))
    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 (y <= -1.1e-45) {
		tmp = y * (x / z);
	} else if (y <= 8.5e-102) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e-45:
		tmp = y * (x / z)
	elif y <= 8.5e-102:
		tmp = x * (t / (z + -1.0))
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e-45)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 8.5e-102)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e-45)
		tmp = y * (x / z);
	elseif (y <= 8.5e-102)
		tmp = x * (t / (z + -1.0));
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e-45], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-102], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.09999999999999997e-45

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. associate-/l* 79.8%

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

   4. Simplified 79.8%

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

      1. associate-/r/ 80.2%

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

   6. Applied egg-rr 80.2%

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

   if -1.09999999999999997e-45 < y < 8.49999999999999973e-102

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.5%

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

      1. associate-*r/ 78.5%

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

      2. associate-*r* 78.5%

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

      3. neg-mul-1 78.5%

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

      4. associate-*l/ 83.3%

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

      5. *-commutative 83.3%

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

      6. distribute-frac-neg 83.3%

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

      7. neg-mul-1 83.3%

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

      8. metadata-eval 83.3%

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

      9. times-frac 83.3%

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

      10. *-lft-identity 83.3%

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

      11. neg-mul-1 83.3%

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

      12. neg-sub0 83.3%

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

      13. associate--r- 83.3%

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

      14. metadata-eval 83.3%

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

   4. Simplified 83.3%

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

   if 8.49999999999999973e-102 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 83.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 10: 43.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.068 \lor \neg \left(z \leq 0.09\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.068) (not (<= z 0.09))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.068) || !(z <= 0.09)) {
		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 <= (-0.068d0)) .or. (.not. (z <= 0.09d0))) 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 <= -0.068) || !(z <= 0.09)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.068) or not (z <= 0.09):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.068) || !(z <= 0.09))
		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 <= -0.068) || ~((z <= 0.09)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.068], N[Not[LessEqual[z, 0.09]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.068000000000000005 or 0.089999999999999997 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 88.3%

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

      1. associate-/l* 99.6%

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

      2. neg-mul-1 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in y around 0 49.5%

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

      1. associate-*r/ 46.3%

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

   7. Simplified 46.3%

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

   if -0.068000000000000005 < z < 0.089999999999999997

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. mul-1-neg 92.9%

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

      3. unsub-neg 92.9%

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

      4. *-commutative 92.9%

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

      5. associate-*r/ 89.2%

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

      6. distribute-lft-out-- 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in y around 0 36.2%

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

      1. associate-*r* 36.2%

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

      2. mul-1-neg 36.2%

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

   7. Simplified 36.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.068 \lor \neg \left(z \leq 0.09\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 11: 23.6% 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 66.0%

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

   1. +-commutative 66.0%

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

   2. mul-1-neg 66.0%

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

   3. unsub-neg 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-*r/ 65.5%

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

   6. distribute-lft-out-- 67.1%

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

4. Simplified 67.1%

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

5. Taylor expanded in y around 0 24.9%

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

   1. associate-*r* 24.9%

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

   2. mul-1-neg 24.9%

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

7. Simplified 24.9%

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

8. Final simplification 24.9%

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

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 2023290 
(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)))))