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

Percentage Accurate: 94.6% → 98.1%

Time: 10.4s

Alternatives: 9

Speedup: 0.3×

• 21.0% 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: 94.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+296}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 4e+296) (* t_1 x) (/ (* y x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= 4e+296) {
		tmp = t_1 * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= 4e+296) {
		tmp = t_1 * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= 4e+296:
		tmp = t_1 * x
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= 4e+296)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= 4e+296)
		tmp = t_1 * x;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+296], N[(t$95$1 * x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

      2. associate-/r* 99.8%

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

   7. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

      2. clear-num 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 3.99999999999999993e296

   1. Initial program 98.4%

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

   if 3.99999999999999993e296 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf 99.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 4 \cdot 10^{+296}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1400 \lor \neg \left(z \leq 0.0004\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1400.0) (not (<= z 0.0004)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1400.0) || !(z <= 0.0004)) {
		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 <= (-1400.0d0)) .or. (.not. (z <= 0.0004d0))) 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 <= -1400.0) || !(z <= 0.0004)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1400.0) or not (z <= 0.0004):
		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 <= -1400.0) || !(z <= 0.0004))
		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 <= -1400.0) || ~((z <= 0.0004)))
		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, -1400.0], N[Not[LessEqual[z, 0.0004]], $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 < -1400 or 4.00000000000000019e-4 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 81.7%

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

      1. associate-/l* 95.3%

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

      2. cancel-sign-sub-inv 95.3%

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

      3. metadata-eval 95.3%

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

      4. *-lft-identity 95.3%

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

      5. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -1400 < z < 4.00000000000000019e-4

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 91.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400 \lor \neg \left(z \leq 0.0004\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+134} \lor \neg \left(t \leq 5 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.25e+134) (not (<= t 5e+80)))
   (* x (/ t (+ z -1.0)))
   (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e+134) || !(t <= 5e+80)) {
		tmp = x * (t / (z + -1.0));
	} 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 <= (-1.25d+134)) .or. (.not. (t <= 5d+80))) then
        tmp = x * (t / (z + (-1.0d0)))
    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 <= -1.25e+134) || !(t <= 5e+80)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.25e+134) or not (t <= 5e+80):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.25e+134) || !(t <= 5e+80))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	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 <= -1.25e+134) || ~((t <= 5e+80)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.25e+134], N[Not[LessEqual[t, 5e+80]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999995e134 or 4.99999999999999961e80 < t

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. distribute-neg-frac2 85.2%

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

      3. neg-sub0 85.2%

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

      4. associate--r- 85.2%

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

      5. metadata-eval 85.2%

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

   5. Simplified 85.2%

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

   if -1.24999999999999995e134 < t < 4.99999999999999961e80

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 78.9%

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

      1. associate-*r/ 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+134} \lor \neg \left(t \leq 5 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+134} \lor \neg \left(t \leq 1.45 \cdot 10^{+84}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.4e+134) (not (<= t 1.45e+84)))
   (* t (/ x (+ z -1.0)))
   (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.4e+134) || !(t <= 1.45e+84)) {
		tmp = t * (x / (z + -1.0));
	} 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 <= (-6.4d+134)) .or. (.not. (t <= 1.45d+84))) then
        tmp = t * (x / (z + (-1.0d0)))
    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 <= -6.4e+134) || !(t <= 1.45e+84)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.4e+134) or not (t <= 1.45e+84):
		tmp = t * (x / (z + -1.0))
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.4e+134) || !(t <= 1.45e+84))
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	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 <= -6.4e+134) || ~((t <= 1.45e+84)))
		tmp = t * (x / (z + -1.0));
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.4e+134], N[Not[LessEqual[t, 1.45e+84]], $MachinePrecision]], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4000000000000001e134 or 1.44999999999999994e84 < t

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/l* 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

      4. distribute-neg-frac2 74.8%

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

      5. neg-sub0 74.8%

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

      6. associate--r- 74.8%

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

      7. metadata-eval 74.8%

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

   5. Simplified 74.8%

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

   if -6.4000000000000001e134 < t < 1.44999999999999994e84

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 78.9%

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

      1. associate-*r/ 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+134} \lor \neg \left(t \leq 1.45 \cdot 10^{+84}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+136} \lor \neg \left(t \leq 5.5 \cdot 10^{+150}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e+136) (not (<= t 5.5e+150))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e+136) || !(t <= 5.5e+150)) {
		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 <= (-3d+136)) .or. (.not. (t <= 5.5d+150))) 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 <= -3e+136) || !(t <= 5.5e+150)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3e+136) or not (t <= 5.5e+150):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3e+136) || !(t <= 5.5e+150))
		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 <= -3e+136) || ~((t <= 5.5e+150)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3e+136], N[Not[LessEqual[t, 5.5e+150]], $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 < -2.99999999999999979e136 or 5.50000000000000017e150 < t

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. distribute-neg-frac2 90.5%

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

      3. neg-sub0 90.5%

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

      4. associate--r- 90.5%

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

      5. metadata-eval 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around inf 62.6%

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

   if -2.99999999999999979e136 < t < 5.50000000000000017e150

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. associate-*r/ 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+136} \lor \neg \left(t \leq 5.5 \cdot 10^{+150}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1400 \lor \neg \left(z \leq 170000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1400.0) (not (<= z 170000.0))) (* x (/ t z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1400.0) || !(z <= 170000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -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 <= (-1400.0d0)) .or. (.not. (z <= 170000.0d0))) then
        tmp = x * (t / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1400.0) || !(z <= 170000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1400.0) or not (z <= 170000.0):
		tmp = x * (t / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1400.0) || !(z <= 170000.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1400.0) || ~((z <= 170000.0)))
		tmp = x * (t / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1400.0], N[Not[LessEqual[z, 170000.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1400 or 1.7e5 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-neg-frac2 54.1%

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

      3. neg-sub0 54.1%

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

      4. associate--r- 54.1%

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

      5. metadata-eval 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in z around inf 53.0%

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

   if -1400 < z < 1.7e5

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 35.1%

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

      1. mul-1-neg 35.1%

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

      2. distribute-neg-frac2 35.1%

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

      3. neg-sub0 35.1%

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

      4. associate--r- 35.1%

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

      5. metadata-eval 35.1%

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

   5. Simplified 35.1%

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

   6. Taylor expanded in z around 0 33.6%

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

      1. *-commutative 33.6%

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

      2. neg-mul-1 33.6%

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

      3. distribute-rgt-neg-in 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400 \lor \neg \left(z \leq 170000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1400 \lor \neg \left(z \leq 42000\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1400.0) (not (<= z 42000.0))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1400.0) || !(z <= 42000.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -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 <= (-1400.0d0)) .or. (.not. (z <= 42000.0d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1400.0) || !(z <= 42000.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1400.0) or not (z <= 42000.0):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1400.0) || !(z <= 42000.0))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1400.0) || ~((z <= 42000.0)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1400.0], N[Not[LessEqual[z, 42000.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1400 or 42000 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-neg-frac2 54.1%

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

      3. neg-sub0 54.1%

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

      4. associate--r- 54.1%

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

      5. metadata-eval 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in z around inf 44.5%

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

      1. associate-/l* 47.5%

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

   8. Simplified 47.5%

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

   if -1400 < z < 42000

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 35.1%

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

      1. mul-1-neg 35.1%

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

      2. distribute-neg-frac2 35.1%

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

      3. neg-sub0 35.1%

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

      4. associate--r- 35.1%

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

      5. metadata-eval 35.1%

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

   5. Simplified 35.1%

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

   6. Taylor expanded in z around 0 33.6%

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

      1. *-commutative 33.6%

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

      2. neg-mul-1 33.6%

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

      3. distribute-rgt-neg-in 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400 \lor \neg \left(z \leq 42000\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 22.4% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

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 * -t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in y around 0 43.9%

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

   1. mul-1-neg 43.9%

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

   2. distribute-neg-frac2 43.9%

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

   3. neg-sub0 43.9%

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

   4. associate--r- 43.9%

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

   5. metadata-eval 43.9%

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

5. Simplified 43.9%

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

6. Taylor expanded in z around 0 22.5%

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

   1. *-commutative 22.5%

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

   2. neg-mul-1 22.5%

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

   3. distribute-rgt-neg-in 22.5%

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

8. Simplified 22.5%

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

Alternative 9: 9.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ t \cdot x \end{array} \]

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 * 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. Add Preprocessing

3. Taylor expanded in y around 0 43.9%

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

   1. mul-1-neg 43.9%

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

   2. distribute-neg-frac2 43.9%

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

   3. neg-sub0 43.9%

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

   4. associate--r- 43.9%

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

   5. metadata-eval 43.9%

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

5. Simplified 43.9%

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

6. Taylor expanded in z around 0 22.5%

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

   1. *-commutative 22.5%

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

   2. neg-mul-1 22.5%

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

   3. distribute-rgt-neg-in 22.5%

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

8. Simplified 22.5%

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

   1. neg-sub0 22.5%

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

   2. sub-neg 22.5%

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

   3. add-sqr-sqrt 12.4%

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

   4. sqrt-unprod 14.3%

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

   5. sqr-neg 14.3%

      \[\leadsto x \cdot \left(0 + \sqrt{\color{blue}{t \cdot t}}\right) \]

   6. sqrt-unprod 3.2%

      \[\leadsto x \cdot \left(0 + \color{blue}{\sqrt{t} \cdot \sqrt{t}}\right) \]

   7. add-sqr-sqrt 8.6%

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

10. Applied egg-rr 8.6%

    \[\leadsto x \cdot \color{blue}{\left(0 + t\right)} \]
11. Step-by-step derivation

    1. +-lft-identity 8.6%

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

12. Simplified 8.6%

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

13. Final simplification 8.6%

    \[\leadsto t \cdot x \]
14. Add Preprocessing

Developer Target 1: 95.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

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