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

Percentage Accurate: 94.1% → 94.1%

Time: 10.4s

Alternatives: 8

Speedup: 1.0×

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: 94.1% 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: 94.1% 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]

Derivation

1. Initial program 96.5%

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

Alternative 2: 93.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    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 + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 95.9

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

   5. Simplified 95.9%

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

   if -1 < z < 1

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 96.3%

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

4. Final simplification 96.1%

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

Alternative 3: 74.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{+134}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -1.8e-7) t_1 (if (<= t 1e+134) (* x (/ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.8e-7) {
		tmp = t_1;
	} else if (t <= 1e+134) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z + (-1.0d0)))
    if (t <= (-1.8d-7)) then
        tmp = t_1
    else if (t <= 1d+134) then
        tmp = x * (y / 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 * (t / (z + -1.0));
	double tmp;
	if (t <= -1.8e-7) {
		tmp = t_1;
	} else if (t <= 1e+134) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -1.8e-7:
		tmp = t_1
	elif t <= 1e+134:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.8e-7)
		tmp = t_1;
	elseif (t <= 1e+134)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.8e-7)
		tmp = t_1;
	elseif (t <= 1e+134)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e-7], t$95$1, If[LessEqual[t, 1e+134], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999997e-7 or 9.99999999999999921e133 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-lowering-+.f64 82.3

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

   5. Simplified 82.3%

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

   if -1.79999999999999997e-7 < t < 9.99999999999999921e133

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 85.2

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

   5. Simplified 85.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq 10^{+134}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -1.8e+62) t_1 (if (<= z 2.05e+33) (* x (- (/ y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -1.8e+62) {
		tmp = t_1;
	} else if (z <= 2.05e+33) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (z <= (-1.8d+62)) then
        tmp = t_1
    else if (z <= 2.05d+33) then
        tmp = x * ((y / z) - t)
    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 * (t / z);
	double tmp;
	if (z <= -1.8e+62) {
		tmp = t_1;
	} else if (z <= 2.05e+33) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -1.8e+62:
		tmp = t_1
	elif z <= 2.05e+33:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -1.8e+62)
		tmp = t_1;
	elseif (z <= 2.05e+33)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -1.8e+62)
		tmp = t_1;
	elseif (z <= 2.05e+33)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+62], t$95$1, If[LessEqual[z, 2.05e+33], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e62 or 2.04999999999999997e33 < z

   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

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-lowering-+.f64 66.3

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

   5. Simplified 66.3%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 66.3%

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

   if -1.8e62 < z < 2.04999999999999997e33

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 94.5%

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

Alternative 5: 68.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -5e+115) t_1 (if (<= t 4e+151) (* x (/ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5e+115) {
		tmp = t_1;
	} else if (t <= 4e+151) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-5d+115)) then
        tmp = t_1
    else if (t <= 4d+151) then
        tmp = x * (y / 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 * (t / z);
	double tmp;
	if (t <= -5e+115) {
		tmp = t_1;
	} else if (t <= 4e+151) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -5e+115:
		tmp = t_1
	elif t <= 4e+151:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -5e+115)
		tmp = t_1;
	elseif (t <= 4e+151)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -5e+115)
		tmp = t_1;
	elseif (t <= 4e+151)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+115], t$95$1, If[LessEqual[t, 4e+151], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000008e115 or 4.00000000000000007e151 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-lowering-+.f64 87.7

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

   5. Simplified 87.7%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 67.3%

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

   if -5.00000000000000008e115 < t < 4.00000000000000007e151

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 77.6

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

   5. Simplified 77.6%

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

Alternative 6: 45.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3800000000000:\\ \;\;\;\;t \cdot \left(0 - \mathsf{fma}\left(z, x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -0.75)
     t_1
     (if (<= z 3800000000000.0) (* t (- 0.0 (fma z x x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -0.75) {
		tmp = t_1;
	} else if (z <= 3800000000000.0) {
		tmp = t * (0.0 - fma(z, x, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -0.75)
		tmp = t_1;
	elseif (z <= 3800000000000.0)
		tmp = Float64(t * Float64(0.0 - fma(z, x, x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.75], t$95$1, If[LessEqual[z, 3800000000000.0], N[(t * N[(0.0 - N[(z * x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.75 or 3.8e12 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-lowering-+.f64 63.1

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 62.7%

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

   if -0.75 < z < 3.8e12

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-lowering-+.f64 32.6

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

   5. Simplified 32.6%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. distribute-lft-out N/A

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

      5. *-lowering-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. neg-sub0 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 32.7

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

   8. Simplified 32.7%

      \[\leadsto \color{blue}{\left(0 - t\right) \cdot \mathsf{fma}\left(z, x, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3800000000000:\\ \;\;\;\;t \cdot \left(0 - \mathsf{fma}\left(z, x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3800000000000:\\ \;\;\;\;t \cdot \left(0 - \mathsf{fma}\left(z, x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= z -0.75)
     t_1
     (if (<= z 3800000000000.0) (* t (- 0.0 (fma z x x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (z <= -0.75) {
		tmp = t_1;
	} else if (z <= 3800000000000.0) {
		tmp = t * (0.0 - fma(z, x, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (z <= -0.75)
		tmp = t_1;
	elseif (z <= 3800000000000.0)
		tmp = Float64(t * Float64(0.0 - fma(z, x, x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.75], t$95$1, If[LessEqual[z, 3800000000000.0], N[(t * N[(0.0 - N[(z * x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.75 or 3.8e12 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-out-- N/A

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

      5. neg-mul-1 N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. /-lowering-/.f64 N/A

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

   5. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t + y, x, 0\right)}{z}} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-lowering-+.f64 N/A

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

      5. /-lowering-/.f64 84.1

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

   7. Applied egg-rr 84.1%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 58.4%

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

   if -0.75 < z < 3.8e12

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-lowering-+.f64 32.6

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

   5. Simplified 32.6%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. distribute-lft-out N/A

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

      5. *-lowering-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. neg-sub0 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 32.7

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

   8. Simplified 32.7%

      \[\leadsto \color{blue}{\left(0 - t\right) \cdot \mathsf{fma}\left(z, x, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3800000000000:\\ \;\;\;\;t \cdot \left(0 - \mathsf{fma}\left(z, x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 23.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(0 - t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 0.0 t)))

C

double code(double x, double y, double z, double t) {
	return x * (0.0 - 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 * (0.0d0 - t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (0.0 - t);
}

Python

def code(x, y, z, t):
	return x * (0.0 - t)

Julia

function code(x, y, z, t)
	return Float64(x * Float64(0.0 - t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (0.0 - t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(0.0 - t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. distribute-neg-frac2 N/A

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

   3. /-lowering-/.f64 N/A

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

   4. sub-neg N/A

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

   5. mul-1-neg N/A

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

   6. distribute-neg-in N/A

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

   7. metadata-eval N/A

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

   8. mul-1-neg N/A

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

   9. remove-double-neg N/A

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

   10. +-lowering-+.f64 48.3

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

5. Simplified 48.3%

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

6. Taylor expanded in z around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - t \cdot x} \]

   3. --lowering--.f64 N/A

      \[\leadsto \color{blue}{0 - t \cdot x} \]

   4. *-lowering-*.f64 21.8

      \[\leadsto 0 - \color{blue}{t \cdot x} \]

8. Simplified 21.8%

   \[\leadsto \color{blue}{0 - t \cdot x} \]

9. Final simplification 21.8%

   \[\leadsto x \cdot \left(0 - t\right) \]
10. Add Preprocessing

Developer Target 1: 94.6% 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 2024195 
(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)))))