Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 11.3s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(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 * log(y)) - y) - z) + log(t)
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * math.log(y)) - y) - z) + math.log(t)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(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 * log(y)) - y) - z) + log(t)
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * math.log(y)) - y) - z) + math.log(t)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(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 * log(y)) - y) - z) + log(t)
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * math.log(y)) - y) - z) + math.log(t)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5.3 \cdot 10^{+296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5.3e+296)
     t_1
     (if (<= t_2 -2000.0) (- (- y) z) (if (<= t_2 5e+87) (- (log t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -5.3e+296) {
		tmp = t_1;
	} else if (t_2 <= -2000.0) {
		tmp = -y - z;
	} else if (t_2 <= 5e+87) {
		tmp = log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-5.3d+296)) then
        tmp = t_1
    else if (t_2 <= (-2000.0d0)) then
        tmp = -y - z
    else if (t_2 <= 5d+87) then
        tmp = log(t) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -5.3e+296) {
		tmp = t_1;
	} else if (t_2 <= -2000.0) {
		tmp = -y - z;
	} else if (t_2 <= 5e+87) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -5.3e+296:
		tmp = t_1
	elif t_2 <= -2000.0:
		tmp = -y - z
	elif t_2 <= 5e+87:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -5.3e+296)
		tmp = t_1;
	elseif (t_2 <= -2000.0)
		tmp = Float64(Float64(-y) - z);
	elseif (t_2 <= 5e+87)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -5.3e+296)
		tmp = t_1;
	elseif (t_2 <= -2000.0)
		tmp = -y - z;
	elseif (t_2 <= 5e+87)
		tmp = log(t) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -5.3e+296], t$95$1, If[LessEqual[t$95$2, -2000.0], N[((-y) - z), $MachinePrecision], If[LessEqual[t$95$2, 5e+87], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5.3000000000000004e296 or 4.9999999999999998e87 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \color{blue}{x \cdot \log y} \]

      2. log-lowering-log.f64 79.5

         \[\leadsto x \cdot \color{blue}{\log y} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if -5.3000000000000004e296 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e3

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 98.2

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

   7. Simplified 98.2%

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

   8. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

         \[\leadsto \color{blue}{-1 \cdot y + -1 \cdot z} \]

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} - z \]

      6. neg-lowering-neg.f64 71.5

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

   10. Simplified 71.5%

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

   if -2e3 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999998e87

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 91.3

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

   5. Simplified 91.3%

      \[\leadsto \color{blue}{\left(-z\right)} + \log t \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto \color{blue}{\log t - z} \]

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

         \[\leadsto \color{blue}{\log t - z} \]

      4. log-lowering-log.f64 91.3

         \[\leadsto \color{blue}{\log t} - z \]

   7. Applied egg-rr 91.3%

      \[\leadsto \color{blue}{\log t - z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ \mathbf{if}\;t\_1 \leq -2000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-9}:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (* x (log y)) y) z)))
   (if (<= t_1 -2000.0) (- (- y) z) (if (<= t_1 4e-9) (log t) (- z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) - z;
	double tmp;
	if (t_1 <= -2000.0) {
		tmp = -y - z;
	} else if (t_1 <= 4e-9) {
		tmp = log(t);
	} else {
		tmp = -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 = ((x * log(y)) - y) - z
    if (t_1 <= (-2000.0d0)) then
        tmp = -y - z
    else if (t_1 <= 4d-9) then
        tmp = log(t)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x * Math.log(y)) - y) - z;
	double tmp;
	if (t_1 <= -2000.0) {
		tmp = -y - z;
	} else if (t_1 <= 4e-9) {
		tmp = Math.log(t);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) - z
	tmp = 0
	if t_1 <= -2000.0:
		tmp = -y - z
	elif t_1 <= 4e-9:
		tmp = math.log(t)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) - z)
	tmp = 0.0
	if (t_1 <= -2000.0)
		tmp = Float64(Float64(-y) - z);
	elseif (t_1 <= 4e-9)
		tmp = log(t);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) - z;
	tmp = 0.0;
	if (t_1 <= -2000.0)
		tmp = -y - z;
	elseif (t_1 <= 4e-9)
		tmp = log(t);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$1, -2000.0], N[((-y) - z), $MachinePrecision], If[LessEqual[t$95$1, 4e-9], N[Log[t], $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -2e3

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 98.4

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

   7. Simplified 98.4%

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

   8. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

         \[\leadsto \color{blue}{-1 \cdot y + -1 \cdot z} \]

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} - z \]

      6. neg-lowering-neg.f64 71.4

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

   10. Simplified 71.4%

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

   if -2e3 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 4.00000000000000025e-9

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 96.9

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\log t} \]
   7. Step-by-step derivation

      1. log-lowering-log.f64 96.8

         \[\leadsto \color{blue}{\log t} \]

   8. Simplified 96.8%

      \[\leadsto \color{blue}{\log t} \]

   if 4.00000000000000025e-9 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. neg-lowering-neg.f64 51.0

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 51.0%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-1 + \frac{x \cdot \log y - y}{z}\right)\\ \mathbf{if}\;z \leq -215:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (+ -1.0 (/ (- (* x (log y)) y) z)))))
   (if (<= z -215.0)
     t_1
     (if (<= z 3.9e-7) (fma x (log y) (- (log t) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (-1.0 + (((x * log(y)) - y) / z));
	double tmp;
	if (z <= -215.0) {
		tmp = t_1;
	} else if (z <= 3.9e-7) {
		tmp = fma(x, log(y), (log(t) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-1.0 + Float64(Float64(Float64(x * log(y)) - y) / z)))
	tmp = 0.0
	if (z <= -215.0)
		tmp = t_1;
	elseif (z <= 3.9e-7)
		tmp = fma(x, log(y), Float64(log(t) - y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(-1.0 + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -215.0], t$95$1, If[LessEqual[z, 3.9e-7], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -215 or 3.90000000000000025e-7 < z

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.1

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

   7. Simplified 99.1%

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

   8. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. associate--r+ N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

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

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

      9. --lowering--.f64 N/A

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

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

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

      11. log-lowering-log.f64 99.3

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

   10. Simplified 99.3%

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

   if -215 < z < 3.90000000000000025e-7

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t - y\right)} \]

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

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\log y}, \log t - y\right) \]

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

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\log t - y}\right) \]

      6. log-lowering-log.f64 99.8

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\log t} - y\right) \]

   5. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -215:\\ \;\;\;\;z \cdot \left(-1 + \frac{x \cdot \log y - y}{z}\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 + \frac{x \cdot \log y - y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -2000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* x (log y)) y) -2000.0) (- (- y) z) (- (log t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * log(y)) - y) <= -2000.0) {
		tmp = -y - z;
	} else {
		tmp = log(t) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x * log(y)) - y) <= (-2000.0d0)) then
        tmp = -y - z
    else
        tmp = log(t) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * Math.log(y)) - y) <= -2000.0) {
		tmp = -y - z;
	} else {
		tmp = Math.log(t) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * math.log(y)) - y) <= -2000.0:
		tmp = -y - z
	else:
		tmp = math.log(t) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * log(y)) - y) <= -2000.0)
		tmp = Float64(Float64(-y) - z);
	else
		tmp = Float64(log(t) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * log(y)) - y) <= -2000.0)
		tmp = -y - z;
	else
		tmp = log(t) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], -2000.0], N[((-y) - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -2e3

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 98.2

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

   7. Simplified 98.2%

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

   8. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

         \[\leadsto \color{blue}{-1 \cdot y + -1 \cdot z} \]

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} - z \]

      6. neg-lowering-neg.f64 68.3

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

   10. Simplified 68.3%

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

   if -2e3 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 70.8

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

   5. Simplified 70.8%

      \[\leadsto \color{blue}{\left(-z\right)} + \log t \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto \color{blue}{\log t - z} \]

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

         \[\leadsto \color{blue}{\log t - z} \]

      4. log-lowering-log.f64 70.8

         \[\leadsto \color{blue}{\log t} - z \]

   7. Applied egg-rr 70.8%

      \[\leadsto \color{blue}{\log t - z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.0068:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x \cdot \log y - z}{y} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 0.0068)
   (fma x (log y) (- (log t) z))
   (* y (+ (/ (- (* x (log y)) z) y) -1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.0068) {
		tmp = fma(x, log(y), (log(t) - z));
	} else {
		tmp = y * ((((x * log(y)) - z) / y) + -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 0.0068)
		tmp = fma(x, log(y), Float64(log(t) - z));
	else
		tmp = Float64(y * Float64(Float64(Float64(Float64(x * log(y)) - z) / y) + -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 0.0068], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.00679999999999999962

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

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

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\log y}, \log t + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. log-lowering-log.f64 99.4

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

   5. Simplified 99.4%

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

   if 0.00679999999999999962 < y

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 98.6

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

      3. associate--r+ N/A

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

      4. associate-*r/ N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

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

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

   10. Simplified 98.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.0068:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x \cdot \log y - z}{y} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\log y - \frac{y + z}{x}\right)\\ \mathbf{if}\;x \leq -16800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (log y) (/ (+ y z) x)))))
   (if (<= x -16800000000000.0) t_1 (if (<= x 1.85) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (log(y) - ((y + z) / x));
	double tmp;
	if (x <= -16800000000000.0) {
		tmp = t_1;
	} else if (x <= 1.85) {
		tmp = log(t) - (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 * (log(y) - ((y + z) / x))
    if (x <= (-16800000000000.0d0)) then
        tmp = t_1
    else if (x <= 1.85d0) then
        tmp = log(t) - (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 * (Math.log(y) - ((y + z) / x));
	double tmp;
	if (x <= -16800000000000.0) {
		tmp = t_1;
	} else if (x <= 1.85) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (math.log(y) - ((y + z) / x))
	tmp = 0
	if x <= -16800000000000.0:
		tmp = t_1
	elif x <= 1.85:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(log(y) - Float64(Float64(y + z) / x)))
	tmp = 0.0
	if (x <= -16800000000000.0)
		tmp = t_1;
	elseif (x <= 1.85)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (log(y) - ((y + z) / x));
	tmp = 0.0;
	if (x <= -16800000000000.0)
		tmp = t_1;
	elseif (x <= 1.85)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[Log[y], $MachinePrecision] - N[(N[(y + z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -16800000000000.0], t$95$1, If[LessEqual[x, 1.85], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.68e13 or 1.8500000000000001 < x

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.0

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. distribute-lft-in N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. div-sub N/A

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

      6. associate-*r/ N/A

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

      7. associate--l+ N/A

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

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

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

      9. associate--l+ N/A

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

      10. associate-*r/ N/A

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

      11. div-sub N/A

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

      12. sub-neg N/A

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

      13. mul-1-neg N/A

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

      14. distribute-lft-in N/A

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

      15. associate-*r/ N/A

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

      16. mul-1-neg N/A

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

      17. unsub-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. log-lowering-log.f64 N/A

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

   10. Simplified 99.1%

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

   if -1.68e13 < x < 1.8500000000000001

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 99.1

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

   5. Simplified 99.1%

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

Alternative 8: 88.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - z\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+85}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+96}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 z)))
   (if (<= x -3.4e+85)
     (- t_1 y)
     (if (<= x -2.45e+14) t_2 (if (<= x 3.1e+96) (- (log t) (+ y z)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -3.4e+85) {
		tmp = t_1 - y;
	} else if (x <= -2.45e+14) {
		tmp = t_2;
	} else if (x <= 3.1e+96) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_2;
	}
	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 * log(y)
    t_2 = t_1 - z
    if (x <= (-3.4d+85)) then
        tmp = t_1 - y
    else if (x <= (-2.45d+14)) then
        tmp = t_2
    else if (x <= 3.1d+96) then
        tmp = log(t) - (y + z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -3.4e+85) {
		tmp = t_1 - y;
	} else if (x <= -2.45e+14) {
		tmp = t_2;
	} else if (x <= 3.1e+96) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - z
	tmp = 0
	if x <= -3.4e+85:
		tmp = t_1 - y
	elif x <= -2.45e+14:
		tmp = t_2
	elif x <= 3.1e+96:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - z)
	tmp = 0.0
	if (x <= -3.4e+85)
		tmp = Float64(t_1 - y);
	elseif (x <= -2.45e+14)
		tmp = t_2;
	elseif (x <= 3.1e+96)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - z;
	tmp = 0.0;
	if (x <= -3.4e+85)
		tmp = t_1 - y;
	elseif (x <= -2.45e+14)
		tmp = t_2;
	elseif (x <= 3.1e+96)
		tmp = log(t) - (y + z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - z), $MachinePrecision]}, If[LessEqual[x, -3.4e+85], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, -2.45e+14], t$95$2, If[LessEqual[x, 3.1e+96], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4000000000000003e85

   1. Initial program 99.6%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.4

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

   7. Simplified 99.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x \cdot \log y - y} \]
   9. Step-by-step derivation

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

         \[\leadsto \color{blue}{x \cdot \log y - y} \]

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

         \[\leadsto \color{blue}{x \cdot \log y} - y \]

      3. log-lowering-log.f64 87.9

         \[\leadsto x \cdot \color{blue}{\log y} - y \]

   10. Simplified 87.9%

       \[\leadsto \color{blue}{x \cdot \log y - y} \]

   if -3.4000000000000003e85 < x < -2.45e14 or 3.0999999999999998e96 < x

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.5

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

   7. Simplified 99.5%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

      3. log-lowering-log.f64 89.8

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

   10. Simplified 89.8%

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

   if -2.45e14 < x < 3.0999999999999998e96

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 94.6

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

   5. Simplified 94.6%

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

Alternative 9: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+29}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= x -2.4e+85) t_1 (if (<= x 1.45e+29) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (x <= -2.4e+85) {
		tmp = t_1;
	} else if (x <= 1.45e+29) {
		tmp = log(t) - (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 * log(y)) - y
    if (x <= (-2.4d+85)) then
        tmp = t_1
    else if (x <= 1.45d+29) then
        tmp = log(t) - (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 * Math.log(y)) - y;
	double tmp;
	if (x <= -2.4e+85) {
		tmp = t_1;
	} else if (x <= 1.45e+29) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if x <= -2.4e+85:
		tmp = t_1
	elif x <= 1.45e+29:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (x <= -2.4e+85)
		tmp = t_1;
	elseif (x <= 1.45e+29)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if (x <= -2.4e+85)
		tmp = t_1;
	elseif (x <= 1.45e+29)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -2.4e+85], t$95$1, If[LessEqual[x, 1.45e+29], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999997e85 or 1.45e29 < x

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.5

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x \cdot \log y - y} \]
   9. Step-by-step derivation

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

         \[\leadsto \color{blue}{x \cdot \log y - y} \]

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

         \[\leadsto \color{blue}{x \cdot \log y} - y \]

      3. log-lowering-log.f64 83.0

         \[\leadsto x \cdot \color{blue}{\log y} - y \]

   10. Simplified 83.0%

       \[\leadsto \color{blue}{x \cdot \log y - y} \]

   if -2.39999999999999997e85 < x < 1.45e29

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 93.0

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

   5. Simplified 93.0%

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

Alternative 10: 84.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -5 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -5e+136) t_1 (if (<= x 2.9e+131) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -5e+136) {
		tmp = t_1;
	} else if (x <= 2.9e+131) {
		tmp = log(t) - (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 * log(y)
    if (x <= (-5d+136)) then
        tmp = t_1
    else if (x <= 2.9d+131) then
        tmp = log(t) - (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 * Math.log(y);
	double tmp;
	if (x <= -5e+136) {
		tmp = t_1;
	} else if (x <= 2.9e+131) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -5e+136:
		tmp = t_1
	elif x <= 2.9e+131:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -5e+136)
		tmp = t_1;
	elseif (x <= 2.9e+131)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -5e+136)
		tmp = t_1;
	elseif (x <= 2.9e+131)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+136], t$95$1, If[LessEqual[x, 2.9e+131], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000002e136 or 2.9000000000000001e131 < x

   1. Initial program 99.6%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \color{blue}{x \cdot \log y} \]

      2. log-lowering-log.f64 76.3

         \[\leadsto x \cdot \color{blue}{\log y} \]

   5. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if -5.0000000000000002e136 < x < 2.9000000000000001e131

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 86.2

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

   5. Simplified 86.2%

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

Alternative 11: 69.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) - z\\ \mathbf{if}\;z \leq -250:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+16}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- y) z)))
   (if (<= z -250.0) t_1 (if (<= z 9.2e+16) (- (log t) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -y - z;
	double tmp;
	if (z <= -250.0) {
		tmp = t_1;
	} else if (z <= 9.2e+16) {
		tmp = log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y - z
    if (z <= (-250.0d0)) then
        tmp = t_1
    else if (z <= 9.2d+16) then
        tmp = log(t) - y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -y - z;
	double tmp;
	if (z <= -250.0) {
		tmp = t_1;
	} else if (z <= 9.2e+16) {
		tmp = Math.log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -y - z
	tmp = 0
	if z <= -250.0:
		tmp = t_1
	elif z <= 9.2e+16:
		tmp = math.log(t) - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (z <= -250.0)
		tmp = t_1;
	elseif (z <= 9.2e+16)
		tmp = Float64(log(t) - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -y - z;
	tmp = 0.0;
	if (z <= -250.0)
		tmp = t_1;
	elseif (z <= 9.2e+16)
		tmp = log(t) - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[z, -250.0], t$95$1, If[LessEqual[z, 9.2e+16], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -250 or 9.2e16 < z

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.1

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

         \[\leadsto \color{blue}{-1 \cdot y + -1 \cdot z} \]

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} - z \]

      6. neg-lowering-neg.f64 80.4

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

   10. Simplified 80.4%

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

   if -250 < z < 9.2e16

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t - y\right)} \]

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

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\log y}, \log t - y\right) \]

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

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\log t - y}\right) \]

      6. log-lowering-log.f64 99.4

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\log t} - y\right) \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t - y\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\log t - y} \]
   7. Step-by-step derivation

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

         \[\leadsto \color{blue}{\log t - y} \]

      2. log-lowering-log.f64 59.2

         \[\leadsto \color{blue}{\log t} - y \]

   8. Simplified 59.2%

      \[\leadsto \color{blue}{\log t - y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 46.7% accurate, 23.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 4e+150) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4e+150) {
		tmp = -z;
	} else {
		tmp = -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 <= 4d+150) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4e+150) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4e+150:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4e+150)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4e+150)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4e+150], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3.99999999999999992e150

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. neg-lowering-neg.f64 39.0

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{-z} \]

   if 3.99999999999999992e150 < y

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. neg-lowering-neg.f64 82.7

         \[\leadsto \color{blue}{-y} \]

   5. Simplified 82.7%

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

Alternative 13: 58.3% accurate, 35.8× speedup

Math

\[\begin{array}{l} \\ \left(-y\right) - z \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return -y - 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 = -y - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[((-y) - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
2. Add Preprocessing
3. Step-by-step derivation

   1. flip3-+ N/A

      \[\leadsto \color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}} \]

   2. clear-num N/A

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

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

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

   4. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}} \]

   5. flip3-+ N/A

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

4. Applied egg-rr 99.6%

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

5. Taylor expanded in x around inf

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

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

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

   2. log-lowering-log.f64 84.8

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

7. Simplified 84.8%

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

8. Taylor expanded in x around 0

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

   1. distribute-lft-in N/A

      \[\leadsto \color{blue}{-1 \cdot y + -1 \cdot z} \]

   2. mul-1-neg N/A

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

   3. sub-neg N/A

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

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

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

   5. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} - z \]

   6. neg-lowering-neg.f64 55.6

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

10. Simplified 55.6%

    \[\leadsto \color{blue}{\left(-y\right) - z} \]
11. Add Preprocessing

Alternative 14: 30.2% accurate, 71.7× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

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 = -y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-y)

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. neg-lowering-neg.f64 25.0

      \[\leadsto \color{blue}{-y} \]

5. Simplified 25.0%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))