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

Percentage Accurate: 99.9% → 99.9%

Time: 12.2s

Alternatives: 13

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[Log[y], $MachinePrecision] + N[((-y) - z), $MachinePrecision]), $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. Step-by-step derivation

   1. sub-neg 99.9%

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

   2. associate--l+ 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(x, \log y, \left(-y\right) - z\right) + \log t \]
6. Add Preprocessing

Alternative 2: 84.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -20000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 200000:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)) (t_2 (- (- y) z)))
   (if (<= t_1 -1e+197)
     t_1
     (if (<= t_1 -1e+147)
       t_2
       (if (<= t_1 -2e+80)
         t_1
         (if (<= t_1 -20000.0)
           t_2
           (if (<= t_1 200000.0) (- (log t) z) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double t_2 = -y - z;
	double tmp;
	if (t_1 <= -1e+197) {
		tmp = t_1;
	} else if (t_1 <= -1e+147) {
		tmp = t_2;
	} else if (t_1 <= -2e+80) {
		tmp = t_1;
	} else if (t_1 <= -20000.0) {
		tmp = t_2;
	} else if (t_1 <= 200000.0) {
		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)) - y
    t_2 = -y - z
    if (t_1 <= (-1d+197)) then
        tmp = t_1
    else if (t_1 <= (-1d+147)) then
        tmp = t_2
    else if (t_1 <= (-2d+80)) then
        tmp = t_1
    else if (t_1 <= (-20000.0d0)) then
        tmp = t_2
    else if (t_1 <= 200000.0d0) 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)) - y;
	double t_2 = -y - z;
	double tmp;
	if (t_1 <= -1e+197) {
		tmp = t_1;
	} else if (t_1 <= -1e+147) {
		tmp = t_2;
	} else if (t_1 <= -2e+80) {
		tmp = t_1;
	} else if (t_1 <= -20000.0) {
		tmp = t_2;
	} else if (t_1 <= 200000.0) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	t_2 = -y - z
	tmp = 0
	if t_1 <= -1e+197:
		tmp = t_1
	elif t_1 <= -1e+147:
		tmp = t_2
	elif t_1 <= -2e+80:
		tmp = t_1
	elif t_1 <= -20000.0:
		tmp = t_2
	elif t_1 <= 200000.0:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	t_2 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (t_1 <= -1e+197)
		tmp = t_1;
	elseif (t_1 <= -1e+147)
		tmp = t_2;
	elseif (t_1 <= -2e+80)
		tmp = t_1;
	elseif (t_1 <= -20000.0)
		tmp = t_2;
	elseif (t_1 <= 200000.0)
		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)) - y;
	t_2 = -y - z;
	tmp = 0.0;
	if (t_1 <= -1e+197)
		tmp = t_1;
	elseif (t_1 <= -1e+147)
		tmp = t_2;
	elseif (t_1 <= -2e+80)
		tmp = t_1;
	elseif (t_1 <= -20000.0)
		tmp = t_2;
	elseif (t_1 <= 200000.0)
		tmp = log(t) - 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]}, Block[{t$95$2 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+197], t$95$1, If[LessEqual[t$95$1, -1e+147], t$95$2, If[LessEqual[t$95$1, -2e+80], t$95$1, If[LessEqual[t$95$1, -20000.0], t$95$2, If[LessEqual[t$95$1, 200000.0], 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) < -9.9999999999999995e196 or -9.9999999999999998e146 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e80 or 2e5 < (-.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. Step-by-step derivation

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.0%

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

   6. Taylor expanded in z around 0 88.6%

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

   if -9.9999999999999995e196 < (-.f64 (*.f64 x (log.f64 y)) y) < -9.9999999999999998e146 or -2e80 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e4

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 95.5%

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

   6. Taylor expanded in x around 0 88.8%

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

      1. neg-mul-1 88.8%

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

      2. distribute-neg-in 88.8%

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

      3. unsub-neg 88.8%

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

   8. Simplified 88.8%

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

   if -2e4 < (-.f64 (*.f64 x (log.f64 y)) y) < 2e5

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.4%

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

      1. neg-mul-1 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -1 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -1 \cdot 10^{+147}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -20000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq 200000:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ t_3 := \left(-y\right) - z\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -20000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-70}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)) (t_3 (- (- y) z)))
   (if (<= t_2 -1e+197)
     t_2
     (if (<= t_2 -1e+147)
       t_3
       (if (<= t_2 -2e+80)
         t_2
         (if (<= t_2 -20000.0)
           t_3
           (if (<= t_2 1e-70) (- (log t) z) (- t_1 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double t_3 = -y - z;
	double tmp;
	if (t_2 <= -1e+197) {
		tmp = t_2;
	} else if (t_2 <= -1e+147) {
		tmp = t_3;
	} else if (t_2 <= -2e+80) {
		tmp = t_2;
	} else if (t_2 <= -20000.0) {
		tmp = t_3;
	} else if (t_2 <= 1e-70) {
		tmp = log(t) - z;
	} else {
		tmp = t_1 - 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    t_3 = -y - z
    if (t_2 <= (-1d+197)) then
        tmp = t_2
    else if (t_2 <= (-1d+147)) then
        tmp = t_3
    else if (t_2 <= (-2d+80)) then
        tmp = t_2
    else if (t_2 <= (-20000.0d0)) then
        tmp = t_3
    else if (t_2 <= 1d-70) then
        tmp = log(t) - z
    else
        tmp = t_1 - 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);
	double t_2 = t_1 - y;
	double t_3 = -y - z;
	double tmp;
	if (t_2 <= -1e+197) {
		tmp = t_2;
	} else if (t_2 <= -1e+147) {
		tmp = t_3;
	} else if (t_2 <= -2e+80) {
		tmp = t_2;
	} else if (t_2 <= -20000.0) {
		tmp = t_3;
	} else if (t_2 <= 1e-70) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	t_3 = -y - z
	tmp = 0
	if t_2 <= -1e+197:
		tmp = t_2
	elif t_2 <= -1e+147:
		tmp = t_3
	elif t_2 <= -2e+80:
		tmp = t_2
	elif t_2 <= -20000.0:
		tmp = t_3
	elif t_2 <= 1e-70:
		tmp = math.log(t) - z
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	t_3 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (t_2 <= -1e+197)
		tmp = t_2;
	elseif (t_2 <= -1e+147)
		tmp = t_3;
	elseif (t_2 <= -2e+80)
		tmp = t_2;
	elseif (t_2 <= -20000.0)
		tmp = t_3;
	elseif (t_2 <= 1e-70)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	t_3 = -y - z;
	tmp = 0.0;
	if (t_2 <= -1e+197)
		tmp = t_2;
	elseif (t_2 <= -1e+147)
		tmp = t_3;
	elseif (t_2 <= -2e+80)
		tmp = t_2;
	elseif (t_2 <= -20000.0)
		tmp = t_3;
	elseif (t_2 <= 1e-70)
		tmp = log(t) - z;
	else
		tmp = t_1 - z;
	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]}, Block[{t$95$3 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+197], t$95$2, If[LessEqual[t$95$2, -1e+147], t$95$3, If[LessEqual[t$95$2, -2e+80], t$95$2, If[LessEqual[t$95$2, -20000.0], t$95$3, If[LessEqual[t$95$2, 1e-70], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -9.9999999999999995e196 or -9.9999999999999998e146 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e80

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around 0 89.3%

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

   if -9.9999999999999995e196 < (-.f64 (*.f64 x (log.f64 y)) y) < -9.9999999999999998e146 or -2e80 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e4

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 95.5%

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

   6. Taylor expanded in x around 0 88.8%

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

      1. neg-mul-1 88.8%

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

      2. distribute-neg-in 88.8%

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

      3. unsub-neg 88.8%

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

   8. Simplified 88.8%

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

   if -2e4 < (-.f64 (*.f64 x (log.f64 y)) y) < 9.99999999999999996e-71

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.2%

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

      1. neg-mul-1 98.2%

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

   7. Simplified 98.2%

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

   if 9.99999999999999996e-71 < (-.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. Step-by-step derivation

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 97.5%

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

   6. Taylor expanded in y around 0 95.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -1 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -1 \cdot 10^{+147}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -20000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq 10^{-70}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+38} \lor \neg \left(t\_2 \leq 10^{-70}\right):\\ \;\;\;\;t\_1 - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (or (<= t_2 -1e+38) (not (<= t_2 1e-70)))
     (- t_1 (+ y z))
     (- (- (log t) z) y))))

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 <= -1e+38) || !(t_2 <= 1e-70)) {
		tmp = t_1 - (y + z);
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if ((t_2 <= (-1d+38)) .or. (.not. (t_2 <= 1d-70))) then
        tmp = t_1 - (y + z)
    else
        tmp = (log(t) - z) - y
    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 <= -1e+38) || !(t_2 <= 1e-70)) {
		tmp = t_1 - (y + z);
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	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 <= -1e+38) or not (t_2 <= 1e-70):
		tmp = t_1 - (y + z)
	else:
		tmp = (math.log(t) - z) - y
	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 <= -1e+38) || !(t_2 <= 1e-70))
		tmp = Float64(t_1 - Float64(y + z));
	else
		tmp = Float64(Float64(log(t) - z) - y);
	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 <= -1e+38) || ~((t_2 <= 1e-70)))
		tmp = t_1 - (y + z);
	else
		tmp = (log(t) - z) - y;
	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[Or[LessEqual[t$95$2, -1e+38], N[Not[LessEqual[t$95$2, 1e-70]], $MachinePrecision]], N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -9.99999999999999977e37 or 9.99999999999999996e-71 < (-.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. Step-by-step derivation

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.2%

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

   if -9.99999999999999977e37 < (-.f64 (*.f64 x (log.f64 y)) y) < 9.99999999999999996e-71

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -1 \cdot 10^{+38} \lor \neg \left(x \cdot \log y - y \leq 10^{-70}\right):\\ \;\;\;\;x \cdot \log y - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+38} \lor \neg \left(z \leq 2.2 \cdot 10^{-21}\right):\\ \;\;\;\;t\_1 - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t\_1\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (or (<= z -1.5e+38) (not (<= z 2.2e-21)))
     (- t_1 (+ y z))
     (- (+ (log t) t_1) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if ((z <= -1.5e+38) || !(z <= 2.2e-21)) {
		tmp = t_1 - (y + z);
	} else {
		tmp = (log(t) + t_1) - 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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if ((z <= (-1.5d+38)) .or. (.not. (z <= 2.2d-21))) then
        tmp = t_1 - (y + z)
    else
        tmp = (log(t) + t_1) - y
    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 ((z <= -1.5e+38) || !(z <= 2.2e-21)) {
		tmp = t_1 - (y + z);
	} else {
		tmp = (Math.log(t) + t_1) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if (z <= -1.5e+38) or not (z <= 2.2e-21):
		tmp = t_1 - (y + z)
	else:
		tmp = (math.log(t) + t_1) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if ((z <= -1.5e+38) || !(z <= 2.2e-21))
		tmp = Float64(t_1 - Float64(y + z));
	else
		tmp = Float64(Float64(log(t) + t_1) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if ((z <= -1.5e+38) || ~((z <= 2.2e-21)))
		tmp = t_1 - (y + z);
	else
		tmp = (log(t) + t_1) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.5e+38], N[Not[LessEqual[z, 2.2e-21]], $MachinePrecision]], N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5000000000000001e38 or 2.2000000000000001e-21 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 98.7%

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

   if -1.5000000000000001e38 < z < 2.2000000000000001e-21

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-undefine 99.8%

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

      9. neg-sub0 99.8%

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

      10. associate-+l- 99.8%

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

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. +-commutative 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+38} \lor \neg \left(z \leq 2.2 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \log y - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 7: 67.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ \mathbf{if}\;y \leq 3.8 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 110000000:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)) (t_2 (* x (log y))))
   (if (<= y 3.8e-190)
     t_1
     (if (<= y 1.32e-157)
       t_2
       (if (<= y 5.9e-27)
         t_1
         (if (<= y 4.6e-10)
           t_2
           (if (<= y 110000000.0) (- (log t) y) (- (- y) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double t_2 = x * log(y);
	double tmp;
	if (y <= 3.8e-190) {
		tmp = t_1;
	} else if (y <= 1.32e-157) {
		tmp = t_2;
	} else if (y <= 5.9e-27) {
		tmp = t_1;
	} else if (y <= 4.6e-10) {
		tmp = t_2;
	} else if (y <= 110000000.0) {
		tmp = log(t) - y;
	} else {
		tmp = -y - 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) :: t_2
    real(8) :: tmp
    t_1 = log(t) - z
    t_2 = x * log(y)
    if (y <= 3.8d-190) then
        tmp = t_1
    else if (y <= 1.32d-157) then
        tmp = t_2
    else if (y <= 5.9d-27) then
        tmp = t_1
    else if (y <= 4.6d-10) then
        tmp = t_2
    else if (y <= 110000000.0d0) then
        tmp = log(t) - y
    else
        tmp = -y - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - z;
	double t_2 = x * Math.log(y);
	double tmp;
	if (y <= 3.8e-190) {
		tmp = t_1;
	} else if (y <= 1.32e-157) {
		tmp = t_2;
	} else if (y <= 5.9e-27) {
		tmp = t_1;
	} else if (y <= 4.6e-10) {
		tmp = t_2;
	} else if (y <= 110000000.0) {
		tmp = Math.log(t) - y;
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	t_2 = x * math.log(y)
	tmp = 0
	if y <= 3.8e-190:
		tmp = t_1
	elif y <= 1.32e-157:
		tmp = t_2
	elif y <= 5.9e-27:
		tmp = t_1
	elif y <= 4.6e-10:
		tmp = t_2
	elif y <= 110000000.0:
		tmp = math.log(t) - y
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	t_2 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 3.8e-190)
		tmp = t_1;
	elseif (y <= 1.32e-157)
		tmp = t_2;
	elseif (y <= 5.9e-27)
		tmp = t_1;
	elseif (y <= 4.6e-10)
		tmp = t_2;
	elseif (y <= 110000000.0)
		tmp = Float64(log(t) - y);
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	t_2 = x * log(y);
	tmp = 0.0;
	if (y <= 3.8e-190)
		tmp = t_1;
	elseif (y <= 1.32e-157)
		tmp = t_2;
	elseif (y <= 5.9e-27)
		tmp = t_1;
	elseif (y <= 4.6e-10)
		tmp = t_2;
	elseif (y <= 110000000.0)
		tmp = log(t) - y;
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 3.8e-190], t$95$1, If[LessEqual[y, 1.32e-157], t$95$2, If[LessEqual[y, 5.9e-27], t$95$1, If[LessEqual[y, 4.6e-10], t$95$2, If[LessEqual[y, 110000000.0], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], N[((-y) - z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 3.7999999999999998e-190 or 1.3200000000000001e-157 < y < 5.8999999999999998e-27

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate--l+ 99.8%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. neg-mul-1 67.2%

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

   7. Simplified 67.2%

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

   if 3.7999999999999998e-190 < y < 1.3200000000000001e-157 or 5.8999999999999998e-27 < y < 4.60000000000000014e-10

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 90.1%

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

   6. Taylor expanded in x around inf 76.9%

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

   if 4.60000000000000014e-10 < y < 1.1e8

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 72.5%

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

   if 1.1e8 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in x around 0 83.8%

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

      1. neg-mul-1 83.8%

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

      2. distribute-neg-in 83.8%

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

      3. unsub-neg 83.8%

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

   8. Simplified 83.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{-190}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-27}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 110000000:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+111} \lor \neg \left(x \leq 2 \cdot 10^{+100}\right) \land \left(x \leq 5.8 \cdot 10^{+140} \lor \neg \left(x \leq 4.9 \cdot 10^{+207}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e+111)
         (and (not (<= x 2e+100)) (or (<= x 5.8e+140) (not (<= x 4.9e+207)))))
   (* x (log y))
   (- (- y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+111) || (!(x <= 2e+100) && ((x <= 5.8e+140) || !(x <= 4.9e+207)))) {
		tmp = x * log(y);
	} else {
		tmp = -y - 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 <= (-1.6d+111)) .or. (.not. (x <= 2d+100)) .and. (x <= 5.8d+140) .or. (.not. (x <= 4.9d+207))) then
        tmp = x * log(y)
    else
        tmp = -y - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+111) || (!(x <= 2e+100) && ((x <= 5.8e+140) || !(x <= 4.9e+207)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e+111) or (not (x <= 2e+100) and ((x <= 5.8e+140) or not (x <= 4.9e+207))):
		tmp = x * math.log(y)
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e+111) || (!(x <= 2e+100) && ((x <= 5.8e+140) || !(x <= 4.9e+207))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.6e+111) || (~((x <= 2e+100)) && ((x <= 5.8e+140) || ~((x <= 4.9e+207)))))
		tmp = x * log(y);
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e+111], And[N[Not[LessEqual[x, 2e+100]], $MachinePrecision], Or[LessEqual[x, 5.8e+140], N[Not[LessEqual[x, 4.9e+207]], $MachinePrecision]]]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e111 or 2.00000000000000003e100 < x < 5.7999999999999998e140 or 4.9e207 < x

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in x around inf 74.9%

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

   if -1.6e111 < x < 2.00000000000000003e100 or 5.7999999999999998e140 < x < 4.9e207

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 86.2%

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

   6. Taylor expanded in x around 0 74.7%

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

      1. neg-mul-1 74.7%

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

      2. distribute-neg-in 74.7%

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

      3. unsub-neg 74.7%

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

   8. Simplified 74.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+111} \lor \neg \left(x \leq 2 \cdot 10^{+100}\right) \land \left(x \leq 5.8 \cdot 10^{+140} \lor \neg \left(x \leq 4.9 \cdot 10^{+207}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) - z\\ t_2 := \log t - y\\ \mathbf{if}\;z \leq -450:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- y) z)) (t_2 (- (log t) y)))
   (if (<= z -450.0)
     t_1
     (if (<= z 5.5e-243)
       t_2
       (if (<= z 1.55e-187) (* x (log y)) (if (<= z 2.2e-21) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -y - z;
	double t_2 = log(t) - y;
	double tmp;
	if (z <= -450.0) {
		tmp = t_1;
	} else if (z <= 5.5e-243) {
		tmp = t_2;
	} else if (z <= 1.55e-187) {
		tmp = x * log(y);
	} else if (z <= 2.2e-21) {
		tmp = t_2;
	} 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 = -y - z
    t_2 = log(t) - y
    if (z <= (-450.0d0)) then
        tmp = t_1
    else if (z <= 5.5d-243) then
        tmp = t_2
    else if (z <= 1.55d-187) then
        tmp = x * log(y)
    else if (z <= 2.2d-21) then
        tmp = t_2
    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 t_2 = Math.log(t) - y;
	double tmp;
	if (z <= -450.0) {
		tmp = t_1;
	} else if (z <= 5.5e-243) {
		tmp = t_2;
	} else if (z <= 1.55e-187) {
		tmp = x * Math.log(y);
	} else if (z <= 2.2e-21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -y - z
	t_2 = math.log(t) - y
	tmp = 0
	if z <= -450.0:
		tmp = t_1
	elif z <= 5.5e-243:
		tmp = t_2
	elif z <= 1.55e-187:
		tmp = x * math.log(y)
	elif z <= 2.2e-21:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-y) - z)
	t_2 = Float64(log(t) - y)
	tmp = 0.0
	if (z <= -450.0)
		tmp = t_1;
	elseif (z <= 5.5e-243)
		tmp = t_2;
	elseif (z <= 1.55e-187)
		tmp = Float64(x * log(y));
	elseif (z <= 2.2e-21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -y - z;
	t_2 = log(t) - y;
	tmp = 0.0;
	if (z <= -450.0)
		tmp = t_1;
	elseif (z <= 5.5e-243)
		tmp = t_2;
	elseif (z <= 1.55e-187)
		tmp = x * log(y);
	elseif (z <= 2.2e-21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-y) - z), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[z, -450.0], t$95$1, If[LessEqual[z, 5.5e-243], t$95$2, If[LessEqual[z, 1.55e-187], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-21], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -450 or 2.2000000000000001e-21 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 98.8%

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

   6. Taylor expanded in x around 0 79.6%

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

      1. neg-mul-1 79.6%

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

      2. distribute-neg-in 79.6%

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

      3. unsub-neg 79.6%

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

   8. Simplified 79.6%

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

   if -450 < z < 5.50000000000000004e-243 or 1.5500000000000001e-187 < z < 2.2000000000000001e-21

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-undefine 99.8%

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

      9. neg-sub0 99.8%

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

      10. associate-+l- 99.8%

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

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. +-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 67.2%

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

   if 5.50000000000000004e-243 < z < 1.5500000000000001e-187

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 92.3%

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

   6. Taylor expanded in x around inf 79.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -450:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-243}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-21}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+147}:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+24} \lor \neg \left(x \leq 1.25 \cdot 10^{+35}\right):\\ \;\;\;\;t\_1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.7e+147)
     (- t_1 z)
     (if (or (<= x -2.7e+24) (not (<= x 1.25e+35)))
       (- t_1 y)
       (- (- (log t) z) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.7e+147) {
		tmp = t_1 - z;
	} else if ((x <= -2.7e+24) || !(x <= 1.25e+35)) {
		tmp = t_1 - y;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.7d+147)) then
        tmp = t_1 - z
    else if ((x <= (-2.7d+24)) .or. (.not. (x <= 1.25d+35))) then
        tmp = t_1 - y
    else
        tmp = (log(t) - z) - y
    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 <= -1.7e+147) {
		tmp = t_1 - z;
	} else if ((x <= -2.7e+24) || !(x <= 1.25e+35)) {
		tmp = t_1 - y;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.7e+147:
		tmp = t_1 - z
	elif (x <= -2.7e+24) or not (x <= 1.25e+35):
		tmp = t_1 - y
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.7e+147)
		tmp = Float64(t_1 - z);
	elseif ((x <= -2.7e+24) || !(x <= 1.25e+35))
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.7e+147)
		tmp = t_1 - z;
	elseif ((x <= -2.7e+24) || ~((x <= 1.25e+35)))
		tmp = t_1 - y;
	else
		tmp = (log(t) - z) - y;
	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, -1.7e+147], N[(t$95$1 - z), $MachinePrecision], If[Or[LessEqual[x, -2.7e+24], N[Not[LessEqual[x, 1.25e+35]], $MachinePrecision]], N[(t$95$1 - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e147

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around 0 89.4%

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

   if -1.7e147 < x < -2.7e24 or 1.25000000000000005e35 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around 0 90.0%

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

   if -2.7e24 < x < 1.25000000000000005e35

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+24} \lor \neg \left(x \leq 1.25 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.0% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 20000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 20000.0) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 20000.0) {
		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 <= 20000.0d0) 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 <= 20000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 20000.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 20000.0)
		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 <= 20000.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 20000.0], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2e4

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 79.3%

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

   6. Taylor expanded in z around inf 40.1%

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

      1. neg-mul-1 40.1%

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

   8. Simplified 40.1%

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

   if 2e4 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 98.2%

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

   6. Taylor expanded in y around inf 67.2%

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

      1. neg-mul-1 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 20000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.5% accurate, 52.3× 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 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 89.3%

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

6. Taylor expanded in x around 0 62.8%

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

   1. neg-mul-1 62.8%

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

   2. distribute-neg-in 62.8%

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

   3. unsub-neg 62.8%

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

8. Simplified 62.8%

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

9. Final simplification 62.8%

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

Alternative 13: 29.6% accurate, 104.5× 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. Step-by-step derivation

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 89.3%

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

6. Taylor expanded in y around inf 37.0%

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

   1. neg-mul-1 37.0%

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

8. Simplified 37.0%

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

9. Final simplification 37.0%

   \[\leadsto -y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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)))