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

Percentage Accurate: 94.5% → 95.2%

Time: 7.2s

Alternatives: 10

Speedup: 0.5×

• 20.5% 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: 94.5% 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: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 10^{+270}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 1e+270) (* t_1 x) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+270) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 1d+270) then
        tmp = t_1 * x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+270) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 1e+270:
		tmp = t_1 * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 1e+270)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 1e+270)
		tmp = t_1 * x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+270], 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))) < 1e270

   1. Initial program 97.0%

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

   if 1e270 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 65.5%

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

   2. Taylor expanded in y around inf 95.0%

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

      1. associate-/l* 63.6%

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

      2. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+270}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+227} \lor \neg \left(z \leq 4.8 \cdot 10^{+263}\right):\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.2e+92)
   (/ x (/ z t))
   (if (<= z 2.9e+44)
     (* x (- (/ y z) t))
     (if (or (<= z 9.5e+227) (not (<= z 4.8e+263)))
       (/ (* t x) z)
       (/ x (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2e+92) {
		tmp = x / (z / t);
	} else if (z <= 2.9e+44) {
		tmp = x * ((y / z) - t);
	} else if ((z <= 9.5e+227) || !(z <= 4.8e+263)) {
		tmp = (t * x) / z;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.2d+92)) then
        tmp = x / (z / t)
    else if (z <= 2.9d+44) then
        tmp = x * ((y / z) - t)
    else if ((z <= 9.5d+227) .or. (.not. (z <= 4.8d+263))) then
        tmp = (t * x) / z
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2e+92) {
		tmp = x / (z / t);
	} else if (z <= 2.9e+44) {
		tmp = x * ((y / z) - t);
	} else if ((z <= 9.5e+227) || !(z <= 4.8e+263)) {
		tmp = (t * x) / z;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.2e+92:
		tmp = x / (z / t)
	elif z <= 2.9e+44:
		tmp = x * ((y / z) - t)
	elif (z <= 9.5e+227) or not (z <= 4.8e+263):
		tmp = (t * x) / z
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.2e+92)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= 2.9e+44)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif ((z <= 9.5e+227) || !(z <= 4.8e+263))
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.2e+92)
		tmp = x / (z / t);
	elseif (z <= 2.9e+44)
		tmp = x * ((y / z) - t);
	elseif ((z <= 9.5e+227) || ~((z <= 4.8e+263)))
		tmp = (t * x) / z;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.2e+92], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+44], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9.5e+227], N[Not[LessEqual[z, 4.8e+263]], $MachinePrecision]], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.20000000000000025e92

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 94.3%

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

      2. cancel-sign-sub-inv 94.3%

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

      3. metadata-eval 94.3%

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

      4. *-lft-identity 94.3%

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

      5. +-commutative 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in t around inf 63.9%

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

   if -3.20000000000000025e92 < z < 2.9000000000000002e44

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-*r/ 84.9%

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

      3. *-commutative 84.9%

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

      4. associate-*r* 84.9%

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

      5. neg-mul-1 84.9%

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

      6. distribute-rgt-out 86.9%

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

      7. unsub-neg 86.9%

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

   4. Simplified 86.9%

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

   if 2.9000000000000002e44 < z < 9.5000000000000005e227 or 4.8000000000000001e263 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 93.9%

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

      1. associate-/l* 97.8%

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

      2. cancel-sign-sub-inv 97.8%

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

      3. metadata-eval 97.8%

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

      4. *-lft-identity 97.8%

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

      5. +-commutative 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in t around inf 68.5%

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

   if 9.5000000000000005e227 < z < 4.8000000000000001e263

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-lft-identity 99.8%

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

      5. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 88.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+227} \lor \neg \left(z \leq 4.8 \cdot 10^{+263}\right):\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e-84)
   (* y (/ x z))
   (if (<= y 4.8e-150)
     (* x (/ t (+ z -1.0)))
     (if (<= y 1.6e+54) (* x (- (/ y z) t)) (/ x (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-84) {
		tmp = y * (x / z);
	} else if (y <= 4.8e-150) {
		tmp = x * (t / (z + -1.0));
	} else if (y <= 1.6e+54) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.3d-84)) then
        tmp = y * (x / z)
    else if (y <= 4.8d-150) then
        tmp = x * (t / (z + (-1.0d0)))
    else if (y <= 1.6d+54) then
        tmp = x * ((y / z) - t)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-84) {
		tmp = y * (x / z);
	} else if (y <= 4.8e-150) {
		tmp = x * (t / (z + -1.0));
	} else if (y <= 1.6e+54) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e-84:
		tmp = y * (x / z)
	elif y <= 4.8e-150:
		tmp = x * (t / (z + -1.0))
	elif y <= 1.6e+54:
		tmp = x * ((y / z) - t)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e-84)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 4.8e-150)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	elseif (y <= 1.6e+54)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e-84)
		tmp = y * (x / z);
	elseif (y <= 4.8e-150)
		tmp = x * (t / (z + -1.0));
	elseif (y <= 1.6e+54)
		tmp = x * ((y / z) - t);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e-84], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-150], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+54], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.29999999999999984e-84

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 76.9%

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

   4. Simplified 76.9%

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

   if -3.29999999999999984e-84 < y < 4.8e-150

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. associate-*r* 74.4%

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

      3. neg-mul-1 74.4%

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

      4. associate-*l/ 77.6%

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

      5. *-commutative 77.6%

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

      6. neg-mul-1 77.6%

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

      7. *-commutative 77.6%

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

      8. associate-*r/ 77.5%

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

      9. metadata-eval 77.5%

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

      10. associate-/r* 77.5%

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

      11. neg-mul-1 77.5%

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

      12. associate-*r/ 77.6%

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

      13. *-rgt-identity 77.6%

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

      14. neg-sub0 77.6%

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

      15. associate--r- 77.6%

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

      16. metadata-eval 77.6%

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

   4. Simplified 77.6%

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

   if 4.8e-150 < y < 1.6e54

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-*r/ 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-*r* 72.8%

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

      5. neg-mul-1 72.8%

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

      6. distribute-rgt-out 72.8%

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

      7. unsub-neg 72.8%

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

   4. Simplified 72.8%

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

   if 1.6e54 < y

   1. Initial program 92.4%

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

   2. Taylor expanded in z around inf 86.4%

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

      1. associate-/l* 91.2%

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

      2. cancel-sign-sub-inv 91.2%

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

      3. metadata-eval 91.2%

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

      4. *-lft-identity 91.2%

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

      5. +-commutative 91.2%

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

   4. Simplified 91.2%

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

   5. Taylor expanded in t around 0 81.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15) (not (<= z 1.0)))
   (* (/ x z) (+ y t))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15) || !(z <= 1.0)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.15d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / z) * (y + t)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15) || !(z <= 1.0)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15) or not (z <= 1.0):
		tmp = (x / z) * (y + t)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15) || !(z <= 1.0))
		tmp = Float64(Float64(x / z) * Float64(y + t));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15) || ~((z <= 1.0)))
		tmp = (x / z) * (y + t);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999 or 1 < z

   1. Initial program 96.9%

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

   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* 96.5%

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

      2. associate-/r/ 88.2%

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

      3. cancel-sign-sub-inv 88.2%

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

      4. metadata-eval 88.2%

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

      5. *-lft-identity 88.2%

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

      6. +-commutative 88.2%

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

   4. Simplified 88.2%

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

   if -1.1499999999999999 < z < 1

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-*r/ 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r* 89.3%

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

      5. neg-mul-1 89.3%

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

      6. distribute-rgt-out 91.8%

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

      7. unsub-neg 91.8%

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

   4. Simplified 91.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 5: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05) (not (<= z 1.0)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05) or not (z <= 1.0):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 1.0))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05) || ~((z <= 1.0)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 1 < z

   1. Initial program 96.9%

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

   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* 96.5%

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

      2. cancel-sign-sub-inv 96.5%

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

      3. metadata-eval 96.5%

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

      4. *-lft-identity 96.5%

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

      5. +-commutative 96.5%

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

   4. Simplified 96.5%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-*r/ 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r* 89.3%

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

      5. neg-mul-1 89.3%

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

      6. distribute-rgt-out 91.8%

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

      7. unsub-neg 91.8%

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

   4. Simplified 91.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 6: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+153} \lor \neg \left(t \leq 0.0052\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e+153) (not (<= t 0.0052))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+153) || !(t <= 0.0052)) {
		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 <= (-5d+153)) .or. (.not. (t <= 0.0052d0))) 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 <= -5e+153) || !(t <= 0.0052)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e+153) or not (t <= 0.0052):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e+153) || !(t <= 0.0052))
		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 <= -5e+153) || ~((t <= 0.0052)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e+153], N[Not[LessEqual[t, 0.0052]], $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 < -5.00000000000000018e153 or 0.0051999999999999998 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 70.4%

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

      1. associate-/l* 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. metadata-eval 73.1%

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

      4. *-lft-identity 73.1%

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

      5. +-commutative 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in t around inf 60.1%

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

      1. clear-num 59.2%

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

      2. associate-/r/ 59.9%

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

      3. clear-num 59.9%

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

   7. Applied egg-rr 59.9%

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

   if -5.00000000000000018e153 < t < 0.0051999999999999998

   1. Initial program 94.0%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. associate-*r/ 78.3%

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

   4. Simplified 78.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+153} \lor \neg \left(t \leq 0.0052\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 7: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+154} \lor \neg \left(t \leq 0.0052\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.18e+154) (not (<= t 0.0052))) (/ x (/ z t)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.18e+154) || !(t <= 0.0052)) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.18d+154)) .or. (.not. (t <= 0.0052d0))) then
        tmp = x / (z / t)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.18e+154) || !(t <= 0.0052)) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.18e+154) or not (t <= 0.0052):
		tmp = x / (z / t)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.18e+154) || !(t <= 0.0052))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.18e+154) || ~((t <= 0.0052)))
		tmp = x / (z / t);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.18e+154], N[Not[LessEqual[t, 0.0052]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.18000000000000004e154 or 0.0051999999999999998 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 70.4%

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

      1. associate-/l* 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. metadata-eval 73.1%

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

      4. *-lft-identity 73.1%

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

      5. +-commutative 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in t around inf 60.1%

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

   if -1.18000000000000004e154 < t < 0.0051999999999999998

   1. Initial program 94.0%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. associate-*r/ 78.3%

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

   4. Simplified 78.3%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+154} \lor \neg \left(t \leq 0.0052\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 8: 67.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+153} \lor \neg \left(t \leq 0.0052\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.7e+153) (not (<= t 0.0052))) (/ x (/ z t)) (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.7e+153) || !(t <= 0.0052)) {
		tmp = x / (z / t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.7d+153)) .or. (.not. (t <= 0.0052d0))) then
        tmp = x / (z / t)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.7e+153) || !(t <= 0.0052)) {
		tmp = x / (z / t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.7e+153) or not (t <= 0.0052):
		tmp = x / (z / t)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.7e+153) || !(t <= 0.0052))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.7e+153) || ~((t <= 0.0052)))
		tmp = x / (z / t);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.7e+153], N[Not[LessEqual[t, 0.0052]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.69999999999999968e153 or 0.0051999999999999998 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 70.4%

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

      1. associate-/l* 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. metadata-eval 73.1%

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

      4. *-lft-identity 73.1%

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

      5. +-commutative 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in t around inf 60.1%

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

   if -4.69999999999999968e153 < t < 0.0051999999999999998

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 76.5%

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

      1. associate-/l* 78.8%

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

      2. cancel-sign-sub-inv 78.8%

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

      3. metadata-eval 78.8%

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

      4. *-lft-identity 78.8%

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

      5. +-commutative 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in t around 0 78.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+153} \lor \neg \left(t \leq 0.0052\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 9: 63.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6e+179) (* t (- x)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e+179) {
		tmp = t * -x;
	} 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 <= (-6d+179)) then
        tmp = t * -x
    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 <= -6e+179) {
		tmp = t * -x;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6e+179:
		tmp = t * -x
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6e+179)
		tmp = Float64(t * Float64(-x));
	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 <= -6e+179)
		tmp = t * -x;
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6e+179], N[(t * (-x)), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9999999999999996e179

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. associate-*r/ 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*r* 48.2%

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

      5. neg-mul-1 48.2%

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

      6. distribute-rgt-out 51.6%

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

      7. unsub-neg 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in y around 0 42.0%

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

      1. mul-1-neg 42.0%

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

      2. distribute-lft-neg-out 42.0%

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

      3. *-commutative 42.0%

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

   7. Simplified 42.0%

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

   if -5.9999999999999996e179 < t

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 64.6%

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

      1. associate-*r/ 67.7%

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

   4. Simplified 67.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 10: 22.7% 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 94.6%

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

2. Taylor expanded in z around 0 59.8%

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

   1. +-commutative 59.8%

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

   2. associate-*r/ 61.9%

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

   3. *-commutative 61.9%

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

   4. associate-*r* 61.9%

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

   5. neg-mul-1 61.9%

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

   6. distribute-rgt-out 63.4%

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

   7. unsub-neg 63.4%

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

4. Simplified 63.4%

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

5. Taylor expanded in y around 0 22.8%

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

   1. mul-1-neg 22.8%

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

   2. distribute-lft-neg-out 22.8%

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

   3. *-commutative 22.8%

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

7. Simplified 22.8%

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

8. Final simplification 22.8%

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

Developer target: 94.9% 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 2023322 
(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)))))