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

Percentage Accurate: 99.9% → 99.9%

Time: 12.5s

Alternatives: 16

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 99.9%

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

Alternative 2: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(t\_1 - y\right) - z\\ t_3 := \frac{1}{\frac{1}{t\_1 - \left(y + z\right)}}\\ \mathbf{if}\;t\_2 \leq -4000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y)))
        (t_2 (- (- t_1 y) z))
        (t_3 (/ 1.0 (/ 1.0 (- t_1 (+ y z))))))
   (if (<= t_2 -4000000000000.0)
     t_3
     (if (<= t_2 1.0) (fma (log y) x (log t)) t_3))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (t_1 - y) - z;
	double t_3 = 1.0 / (1.0 / (t_1 - (y + z)));
	double tmp;
	if (t_2 <= -4000000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 1.0) {
		tmp = fma(log(y), x, log(t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(t_1 - y) - z)
	t_3 = Float64(1.0 / Float64(1.0 / Float64(t_1 - Float64(y + z))))
	tmp = 0.0
	if (t_2 <= -4000000000000.0)
		tmp = t_3;
	elseif (t_2 <= 1.0)
		tmp = fma(log(y), x, log(t));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 / N[(1.0 / N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4000000000000.0], t$95$3, If[LessEqual[t$95$2, 1.0], N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -4e12 or 1 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) 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 99.4

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

   7. Simplified 99.4%

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

   if -4e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 98.7

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

   5. Simplified 98.7%

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

      1. *-commutative N/A

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

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

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

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

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

      4. log-lowering-log.f64 98.7

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

   7. Applied egg-rr 98.7%

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

Alternative 3: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ t_2 := \left(-z\right) - y\\ \mathbf{if}\;t\_1 \leq -4000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (* x (log y)) y) z)) (t_2 (- (- z) y)))
   (if (<= t_1 -4000000000000.0) t_2 (if (<= t_1 1.0) (log t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) - z;
	double t_2 = -z - y;
	double tmp;
	if (t_1 <= -4000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1.0) {
		tmp = log(t);
	} 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)) - y) - z
    t_2 = -z - y
    if (t_1 <= (-4000000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1.0d0) then
        tmp = log(t)
    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)) - y) - z;
	double t_2 = -z - y;
	double tmp;
	if (t_1 <= -4000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1.0) {
		tmp = Math.log(t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) - z
	t_2 = -z - y
	tmp = 0
	if t_1 <= -4000000000000.0:
		tmp = t_2
	elif t_1 <= 1.0:
		tmp = math.log(t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) - z)
	t_2 = Float64(Float64(-z) - y)
	tmp = 0.0
	if (t_1 <= -4000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 1.0)
		tmp = log(t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) - z;
	t_2 = -z - y;
	tmp = 0.0;
	if (t_1 <= -4000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 1.0)
		tmp = log(t);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[((-z) - y), $MachinePrecision]}, If[LessEqual[t$95$1, -4000000000000.0], t$95$2, If[LessEqual[t$95$1, 1.0], N[Log[t], $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -4e12 or 1 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) 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 99.4

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. sub-neg N/A

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

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

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

      5. neg-lowering-neg.f64 63.7

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

   10. Simplified 63.7%

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

   if -4e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 1

   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

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 92.6

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

   5. Simplified 92.6%

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

   6. Taylor expanded in y around 0

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

      1. log-lowering-log.f64 91.5

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

   8. Simplified 91.5%

      \[\leadsto \color{blue}{\log t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - y\right) - z \leq -4000000000000:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;\left(x \cdot \log y - y\right) - z \leq 1:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+47}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5e+17) (- (- z) y) (if (<= t_2 5e+47) (- (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 <= -5e+17) {
		tmp = -z - y;
	} else if (t_2 <= 5e+47) {
		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 <= (-5d+17)) then
        tmp = -z - y
    else if (t_2 <= 5d+47) 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 <= -5e+17) {
		tmp = -z - y;
	} else if (t_2 <= 5e+47) {
		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 <= -5e+17:
		tmp = -z - y
	elif t_2 <= 5e+47:
		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 <= -5e+17)
		tmp = Float64(Float64(-z) - y);
	elseif (t_2 <= 5e+47)
		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 <= -5e+17)
		tmp = -z - y;
	elseif (t_2 <= 5e+47)
		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, -5e+17], N[((-z) - y), $MachinePrecision], If[LessEqual[t$95$2, 5e+47], 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) < -5e17

   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 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. sub-neg N/A

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

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

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

      5. neg-lowering-neg.f64 69.0

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

   10. Simplified 69.0%

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

   if -5e17 < (-.f64 (*.f64 x (log.f64 y)) y) < 5.00000000000000022e47

   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 96.7

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around 0

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

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

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

      2. log-lowering-log.f64 96.2

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

   8. Simplified 96.2%

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

   if 5.00000000000000022e47 < (-.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 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 77.6

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

   5. Simplified 77.6%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 5 \cdot 10^{+47}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ 1.0 (- (* x (log y)) (+ y z))))))
   (if (<= z -8.5e+16)
     t_1
     (if (<= z 3.2e-13) (fma x (log y) (- (log t) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	double tmp;
	if (z <= -8.5e+16) {
		tmp = t_1;
	} else if (z <= 3.2e-13) {
		tmp = fma(x, log(y), (log(t) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(1.0 / Float64(Float64(x * log(y)) - Float64(y + z))))
	tmp = 0.0
	if (z <= -8.5e+16)
		tmp = t_1;
	elseif (z <= 3.2e-13)
		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[(1.0 / N[(1.0 / N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+16], t$95$1, If[LessEqual[z, 3.2e-13], 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 < -8.5e16 or 3.2e-13 < z

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   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 99.8%

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

   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%

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

   if -8.5e16 < z < 3.2e-13

   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. Add Preprocessing

Alternative 6: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* x (log y)) y) -5e+17) (- (- z) y) (- (log t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * log(y)) - y) <= -5e+17) {
		tmp = -z - y;
	} 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) <= (-5d+17)) then
        tmp = -z - y
    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) <= -5e+17) {
		tmp = -z - y;
	} else {
		tmp = Math.log(t) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * math.log(y)) - y) <= -5e+17:
		tmp = -z - y
	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) <= -5e+17)
		tmp = Float64(Float64(-z) - y);
	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) <= -5e+17)
		tmp = -z - y;
	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], -5e+17], N[((-z) - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5e17

   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 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. sub-neg N/A

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

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

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

      5. neg-lowering-neg.f64 69.0

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

   10. Simplified 69.0%

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

   if -5e17 < (-.f64 (*.f64 x (log.f64 y)) y)

   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 65.4

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y around 0

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

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

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

      2. log-lowering-log.f64 65.2

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

   8. Simplified 65.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.2e+15)
   (fma x (log y) (- (log t) z))
   (/ 1.0 (/ 1.0 (- (* x (log y)) (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.2e+15) {
		tmp = fma(x, log(y), (log(t) - z));
	} else {
		tmp = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.2e+15)
		tmp = fma(x, log(y), Float64(log(t) - z));
	else
		tmp = Float64(1.0 / Float64(1.0 / Float64(Float64(x * log(y)) - Float64(y + z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.2e+15], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(1.0 / N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2e15

   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 99.6

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

   5. Simplified 99.6%

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

   if 3.2e15 < 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 99.6

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

   7. Simplified 99.6%

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

Alternative 8: 98.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-7}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ 1.0 (- (* x (log y)) (+ y z))))))
   (if (<= x -2.6e+51) t_1 (if (<= x 4.7e-7) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	double tmp;
	if (x <= -2.6e+51) {
		tmp = t_1;
	} else if (x <= 4.7e-7) {
		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 = 1.0d0 / (1.0d0 / ((x * log(y)) - (y + z)))
    if (x <= (-2.6d+51)) then
        tmp = t_1
    else if (x <= 4.7d-7) 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 = 1.0 / (1.0 / ((x * Math.log(y)) - (y + z)));
	double tmp;
	if (x <= -2.6e+51) {
		tmp = t_1;
	} else if (x <= 4.7e-7) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / (1.0 / ((x * math.log(y)) - (y + z)))
	tmp = 0
	if x <= -2.6e+51:
		tmp = t_1
	elif x <= 4.7e-7:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(1.0 / Float64(Float64(x * log(y)) - Float64(y + z))))
	tmp = 0.0
	if (x <= -2.6e+51)
		tmp = t_1;
	elseif (x <= 4.7e-7)
		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 = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	tmp = 0.0;
	if (x <= -2.6e+51)
		tmp = t_1;
	elseif (x <= 4.7e-7)
		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[(1.0 / N[(1.0 / N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+51], t$95$1, If[LessEqual[x, 4.7e-7], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6000000000000001e51 or 4.7e-7 < x

   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 99.3

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

   7. Simplified 99.3%

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

   if -2.6000000000000001e51 < x < 4.7e-7

   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 98.9

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

   5. Simplified 98.9%

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

Alternative 9: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -z\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.4e+52)
   (fma x (log y) (- z))
   (if (<= x 1.35e+29) (- (log t) (+ y z)) (fma x (log y) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.4e+52) {
		tmp = fma(x, log(y), -z);
	} else if (x <= 1.35e+29) {
		tmp = log(t) - (y + z);
	} else {
		tmp = fma(x, log(y), -y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.4e+52)
		tmp = fma(x, log(y), Float64(-z));
	elseif (x <= 1.35e+29)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = fma(x, log(y), Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.4e+52], N[(x * N[Log[y], $MachinePrecision] + (-z)), $MachinePrecision], If[LessEqual[x, 1.35e+29], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision] + (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e52

   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 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. neg-lowering-neg.f64 89.1

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

   10. Simplified 89.1%

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

   if -4.4e52 < x < 1.35e29

   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 97.7

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

   5. Simplified 97.7%

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

   if 1.35e29 < x

   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 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. neg-lowering-neg.f64 82.8

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

   10. Simplified 82.8%

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

Alternative 10: 89.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \log y, -y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+28}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (log y) (- y))))
   (if (<= x -7e+52) t_1 (if (<= x 9e+28) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, log(y), -y);
	double tmp;
	if (x <= -7e+52) {
		tmp = t_1;
	} else if (x <= 9e+28) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, log(y), Float64(-y))
	tmp = 0.0
	if (x <= -7e+52)
		tmp = t_1;
	elseif (x <= 9e+28)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision] + (-y)), $MachinePrecision]}, If[LessEqual[x, -7e+52], t$95$1, If[LessEqual[x, 9e+28], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7e52 or 8.9999999999999994e28 < x

   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 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. neg-lowering-neg.f64 81.0

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

   10. Simplified 81.0%

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

   if -7e52 < x < 8.9999999999999994e28

   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 97.7

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

   5. Simplified 97.7%

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

Alternative 11: 82.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+224}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.3e+90) t_1 (if (<= x 1.8e+224) (- (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 <= -2.3e+90) {
		tmp = t_1;
	} else if (x <= 1.8e+224) {
		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 <= (-2.3d+90)) then
        tmp = t_1
    else if (x <= 1.8d+224) 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 <= -2.3e+90) {
		tmp = t_1;
	} else if (x <= 1.8e+224) {
		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 <= -2.3e+90:
		tmp = t_1
	elif x <= 1.8e+224:
		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 <= -2.3e+90)
		tmp = t_1;
	elseif (x <= 1.8e+224)
		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 <= -2.3e+90)
		tmp = t_1;
	elseif (x <= 1.8e+224)
		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, -2.3e+90], t$95$1, If[LessEqual[x, 1.8e+224], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e90 or 1.8e224 < x

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   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 77.2

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

   5. Simplified 77.2%

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

   if -2.3e90 < x < 1.8e224

   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 84.4

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

   5. Simplified 84.4%

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

Alternative 12: 70.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) - y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 400:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- z) y)))
   (if (<= z -8.5e+16) t_1 (if (<= z 400.0) (- (log t) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z - y;
	double tmp;
	if (z <= -8.5e+16) {
		tmp = t_1;
	} else if (z <= 400.0) {
		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 = -z - y
    if (z <= (-8.5d+16)) then
        tmp = t_1
    else if (z <= 400.0d0) 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 = -z - y;
	double tmp;
	if (z <= -8.5e+16) {
		tmp = t_1;
	} else if (z <= 400.0) {
		tmp = Math.log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z - y
	tmp = 0
	if z <= -8.5e+16:
		tmp = t_1
	elif z <= 400.0:
		tmp = math.log(t) - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) - y)
	tmp = 0.0
	if (z <= -8.5e+16)
		tmp = t_1;
	elseif (z <= 400.0)
		tmp = Float64(log(t) - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z - y;
	tmp = 0.0;
	if (z <= -8.5e+16)
		tmp = t_1;
	elseif (z <= 400.0)
		tmp = log(t) - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) - y), $MachinePrecision]}, If[LessEqual[z, -8.5e+16], t$95$1, If[LessEqual[z, 400.0], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e16 or 400 < z

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   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 99.7%

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

   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 x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. sub-neg N/A

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

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

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

      5. neg-lowering-neg.f64 77.9

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

   10. Simplified 77.9%

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

   if -8.5e16 < z < 400

   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

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 56.9

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

   5. Simplified 56.9%

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

      1. +-commutative N/A

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

      2. unsub-neg N/A

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

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

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

      4. log-lowering-log.f64 56.9

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

   7. Applied egg-rr 56.9%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 400:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.3% accurate, 23.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 9.2e+46) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.2e+46) {
		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 <= 9.2d+46) 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 <= 9.2e+46) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.2e+46:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.2e+46)
		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 <= 9.2e+46)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.2e+46], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 9.2000000000000002e46

   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 37.7

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

   5. Simplified 37.7%

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

   if 9.2000000000000002e46 < 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 67.8

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

   5. Simplified 67.8%

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

Alternative 14: 58.7% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 88.5

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

7. Simplified 88.5%

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

8. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. distribute-neg-in N/A

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

   3. sub-neg N/A

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

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

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

   5. neg-lowering-neg.f64 56.7

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

10. Simplified 56.7%

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

11. Final simplification 56.7%

    \[\leadsto \left(-z\right) - y \]
12. Add Preprocessing

Alternative 15: 30.4% 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 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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 30.5

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

5. Simplified 30.5%

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

Alternative 16: 2.2% accurate, 215.0× 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 y
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := y

Derivation

1. Initial program 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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 30.5

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

5. Simplified 30.5%

   \[\leadsto \color{blue}{-y} \]
6. Step-by-step derivation

   1. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - y} \]

   2. sub-neg N/A

      \[\leadsto \color{blue}{0 + \left(\mathsf{neg}\left(y\right)\right)} \]

   3. flip3-+ N/A

      \[\leadsto \color{blue}{\frac{{0}^{3} + {\left(\mathsf{neg}\left(y\right)\right)}^{3}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}} \]

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

      \[\leadsto \color{blue}{\frac{{0}^{3} + {\left(\mathsf{neg}\left(y\right)\right)}^{3}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}} \]

   5. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{0} + {\left(\mathsf{neg}\left(y\right)\right)}^{3}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   6. sqr-pow N/A

      \[\leadsto \frac{0 + \color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   7. pow-prod-down N/A

      \[\leadsto \frac{0 + \color{blue}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   8. sqr-neg N/A

      \[\leadsto \frac{0 + {\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   9. pow-prod-down N/A

      \[\leadsto \frac{0 + \color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   10. sqr-pow N/A

       \[\leadsto \frac{0 + \color{blue}{{y}^{3}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

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

       \[\leadsto \frac{\color{blue}{0 + {y}^{3}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   12. cube-mult N/A

       \[\leadsto \frac{0 + \color{blue}{y \cdot \left(y \cdot y\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   13. sqr-neg N/A

       \[\leadsto \frac{0 + y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

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

       \[\leadsto \frac{0 + \color{blue}{y \cdot \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   15. sqr-neg N/A

       \[\leadsto \frac{0 + y \cdot \color{blue}{\left(y \cdot y\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

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

       \[\leadsto \frac{0 + y \cdot \color{blue}{\left(y \cdot y\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   17. metadata-eval N/A

       \[\leadsto \frac{0 + y \cdot \left(y \cdot y\right)}{\color{blue}{0} + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

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

       \[\leadsto \frac{0 + y \cdot \left(y \cdot y\right)}{\color{blue}{0 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}} \]

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

       \[\leadsto \frac{0 + y \cdot \left(y \cdot y\right)}{0 + \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right) - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}} \]

   20. sqr-neg N/A

       \[\leadsto \frac{0 + y \cdot \left(y \cdot y\right)}{0 + \left(\color{blue}{y \cdot y} - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

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

       \[\leadsto \frac{0 + y \cdot \left(y \cdot y\right)}{0 + \left(\color{blue}{y \cdot y} - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

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

       \[\leadsto \frac{0 + y \cdot \left(y \cdot y\right)}{0 + \left(y \cdot y - \color{blue}{0 \cdot \left(\mathsf{neg}\left(y\right)\right)}\right)} \]

   23. neg-lowering-neg.f64 1.2

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

7. Applied egg-rr 1.2%

   \[\leadsto \color{blue}{\frac{0 + y \cdot \left(y \cdot y\right)}{0 + \left(y \cdot y - 0 \cdot \left(-y\right)\right)}} \]
8. Step-by-step derivation

   1. +-lft-identity N/A

      \[\leadsto \frac{\color{blue}{y \cdot \left(y \cdot y\right)}}{0 + \left(y \cdot y - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   2. cube-unmult N/A

      \[\leadsto \frac{\color{blue}{{y}^{3}}}{0 + \left(y \cdot y - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   3. +-lft-identity N/A

      \[\leadsto \frac{{y}^{3}}{\color{blue}{y \cdot y - 0 \cdot \left(\mathsf{neg}\left(y\right)\right)}} \]

   4. mul0-lft N/A

      \[\leadsto \frac{{y}^{3}}{y \cdot y - \color{blue}{0}} \]

   5. --rgt-identity N/A

      \[\leadsto \frac{{y}^{3}}{\color{blue}{y \cdot y}} \]

   6. pow2 N/A

      \[\leadsto \frac{{y}^{3}}{\color{blue}{{y}^{2}}} \]

   7. pow-div N/A

      \[\leadsto \color{blue}{{y}^{\left(3 - 2\right)}} \]

   8. metadata-eval N/A

      \[\leadsto {y}^{\color{blue}{1}} \]

   9. unpow1 2.1

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

9. Applied egg-rr 2.1%

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

Reproduce

herbie shell --seed 2024198 
(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)))