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

Percentage Accurate: 99.9% → 99.9%

Time: 10.9s

Alternatives: 11

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 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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. Final simplification 99.9%

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

Alternative 2: 97.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t\_1 - \left(y + z\right)\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-71}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5e+46)
     (- t_1 (+ y z))
     (if (<= t_2 4e-71) (- (log t) (+ y 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 tmp;
	if (t_2 <= -5e+46) {
		tmp = t_1 - (y + z);
	} else if (t_2 <= 4e-71) {
		tmp = log(t) - (y + 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) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-5d+46)) then
        tmp = t_1 - (y + z)
    else if (t_2 <= 4d-71) then
        tmp = log(t) - (y + 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 tmp;
	if (t_2 <= -5e+46) {
		tmp = t_1 - (y + z);
	} else if (t_2 <= 4e-71) {
		tmp = Math.log(t) - (y + 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
	tmp = 0
	if t_2 <= -5e+46:
		tmp = t_1 - (y + z)
	elif t_2 <= 4e-71:
		tmp = math.log(t) - (y + 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)
	tmp = 0.0
	if (t_2 <= -5e+46)
		tmp = Float64(t_1 - Float64(y + z));
	elseif (t_2 <= 4e-71)
		tmp = Float64(log(t) - Float64(y + 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;
	tmp = 0.0;
	if (t_2 <= -5e+46)
		tmp = t_1 - (y + z);
	elseif (t_2 <= 4e-71)
		tmp = log(t) - (y + 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]}, If[LessEqual[t$95$2, -5e+46], N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e-71], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5.0000000000000002e46

   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 99.9%

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

   if -5.0000000000000002e46 < (-.f64 (*.f64 x (log.f64 y)) y) < 3.9999999999999997e-71

   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. Taylor expanded in x around 0 99.0%

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

   if 3.9999999999999997e-71 < (-.f64 (*.f64 x (log.f64 y)) y)

   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 99.7%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \log y - \left(y + z\right)\\ \mathbf{elif}\;x \cdot \log y - y \leq 4 \cdot 10^{-71}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 4: 69.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ t_3 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-281}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-123}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)) (t_2 (* x (log y))) (t_3 (- (- y) z)))
   (if (<= x -1.05e+68)
     t_2
     (if (<= x -1.8e-281)
       t_3
       (if (<= x 1.5e-206)
         t_1
         (if (<= x 7e-123)
           t_3
           (if (<= x 8.5e-58) t_1 (if (<= x 1.7e+121) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double t_2 = x * log(y);
	double t_3 = -y - z;
	double tmp;
	if (x <= -1.05e+68) {
		tmp = t_2;
	} else if (x <= -1.8e-281) {
		tmp = t_3;
	} else if (x <= 1.5e-206) {
		tmp = t_1;
	} else if (x <= 7e-123) {
		tmp = t_3;
	} else if (x <= 8.5e-58) {
		tmp = t_1;
	} else if (x <= 1.7e+121) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = log(t) - y
    t_2 = x * log(y)
    t_3 = -y - z
    if (x <= (-1.05d+68)) then
        tmp = t_2
    else if (x <= (-1.8d-281)) then
        tmp = t_3
    else if (x <= 1.5d-206) then
        tmp = t_1
    else if (x <= 7d-123) then
        tmp = t_3
    else if (x <= 8.5d-58) then
        tmp = t_1
    else if (x <= 1.7d+121) then
        tmp = t_3
    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 = Math.log(t) - y;
	double t_2 = x * Math.log(y);
	double t_3 = -y - z;
	double tmp;
	if (x <= -1.05e+68) {
		tmp = t_2;
	} else if (x <= -1.8e-281) {
		tmp = t_3;
	} else if (x <= 1.5e-206) {
		tmp = t_1;
	} else if (x <= 7e-123) {
		tmp = t_3;
	} else if (x <= 8.5e-58) {
		tmp = t_1;
	} else if (x <= 1.7e+121) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	t_2 = x * math.log(y)
	t_3 = -y - z
	tmp = 0
	if x <= -1.05e+68:
		tmp = t_2
	elif x <= -1.8e-281:
		tmp = t_3
	elif x <= 1.5e-206:
		tmp = t_1
	elif x <= 7e-123:
		tmp = t_3
	elif x <= 8.5e-58:
		tmp = t_1
	elif x <= 1.7e+121:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	t_2 = Float64(x * log(y))
	t_3 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (x <= -1.05e+68)
		tmp = t_2;
	elseif (x <= -1.8e-281)
		tmp = t_3;
	elseif (x <= 1.5e-206)
		tmp = t_1;
	elseif (x <= 7e-123)
		tmp = t_3;
	elseif (x <= 8.5e-58)
		tmp = t_1;
	elseif (x <= 1.7e+121)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	t_2 = x * log(y);
	t_3 = -y - z;
	tmp = 0.0;
	if (x <= -1.05e+68)
		tmp = t_2;
	elseif (x <= -1.8e-281)
		tmp = t_3;
	elseif (x <= 1.5e-206)
		tmp = t_1;
	elseif (x <= 7e-123)
		tmp = t_3;
	elseif (x <= 8.5e-58)
		tmp = t_1;
	elseif (x <= 1.7e+121)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -1.05e+68], t$95$2, If[LessEqual[x, -1.8e-281], t$95$3, If[LessEqual[x, 1.5e-206], t$95$1, If[LessEqual[x, 7e-123], t$95$3, If[LessEqual[x, 8.5e-58], t$95$1, If[LessEqual[x, 1.7e+121], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e68 or 1.70000000000000005e121 < 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. Step-by-step derivation

      1. add-cube-cbrt 98.0%

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

      2. pow3 97.9%

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

   7. Applied egg-rr 97.9%

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

   8. Taylor expanded in x around inf 75.8%

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

   if -1.05e68 < x < -1.80000000000000003e-281 or 1.5000000000000001e-206 < x < 6.9999999999999997e-123 or 8.5000000000000004e-58 < x < 1.70000000000000005e121

   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 87.7%

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

   6. Taylor expanded in x around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. distribute-lft-in 80.3%

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

      3. neg-mul-1 80.3%

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

      4. unsub-neg 80.3%

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

      5. mul-1-neg 80.3%

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

   8. Simplified 80.3%

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

   if -1.80000000000000003e-281 < x < 1.5000000000000001e-206 or 6.9999999999999997e-123 < x < 8.5000000000000004e-58

   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 y around inf 86.3%

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

      1. mul-1-neg 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in y around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. sub-neg 86.3%

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

   10. Simplified 86.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-281}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-206}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-123}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-58}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - z\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+49}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 z)))
   (if (<= x -2.15e+24)
     t_2
     (if (<= x 2.3e+49)
       (- (log t) (+ y z))
       (if (<= x 3.3e+182) t_2 (- t_1 y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -2.15e+24) {
		tmp = t_2;
	} else if (x <= 2.3e+49) {
		tmp = log(t) - (y + z);
	} else if (x <= 3.3e+182) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - z
    if (x <= (-2.15d+24)) then
        tmp = t_2
    else if (x <= 2.3d+49) then
        tmp = log(t) - (y + z)
    else if (x <= 3.3d+182) then
        tmp = t_2
    else
        tmp = 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 t_2 = t_1 - z;
	double tmp;
	if (x <= -2.15e+24) {
		tmp = t_2;
	} else if (x <= 2.3e+49) {
		tmp = Math.log(t) - (y + z);
	} else if (x <= 3.3e+182) {
		tmp = t_2;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - z
	tmp = 0
	if x <= -2.15e+24:
		tmp = t_2
	elif x <= 2.3e+49:
		tmp = math.log(t) - (y + z)
	elif x <= 3.3e+182:
		tmp = t_2
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - z)
	tmp = 0.0
	if (x <= -2.15e+24)
		tmp = t_2;
	elseif (x <= 2.3e+49)
		tmp = Float64(log(t) - Float64(y + z));
	elseif (x <= 3.3e+182)
		tmp = t_2;
	else
		tmp = Float64(t_1 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - z;
	tmp = 0.0;
	if (x <= -2.15e+24)
		tmp = t_2;
	elseif (x <= 2.3e+49)
		tmp = log(t) - (y + z);
	elseif (x <= 3.3e+182)
		tmp = t_2;
	else
		tmp = 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]}, Block[{t$95$2 = N[(t$95$1 - z), $MachinePrecision]}, If[LessEqual[x, -2.15e+24], t$95$2, If[LessEqual[x, 2.3e+49], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+182], t$95$2, N[(t$95$1 - y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.14999999999999994e24 or 2.30000000000000002e49 < x < 3.3000000000000001e182

   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 90.9%

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

   if -2.14999999999999994e24 < x < 2.30000000000000002e49

   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 x around 0 99.0%

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

   if 3.3000000000000001e182 < 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 93.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+49}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+182}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+68} \lor \neg \left(x \leq 8 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.05e+68) (not (<= x 8e+120)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e+68) || !(x <= 8e+120)) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (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 <= (-1.05d+68)) .or. (.not. (x <= 8d+120))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (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 <= -1.05e+68) || !(x <= 8e+120)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.05e+68) or not (x <= 8e+120):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.05e+68) || !(x <= 8e+120))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.05e+68) || ~((x <= 8e+120)))
		tmp = x * log(y);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.05e+68], N[Not[LessEqual[x, 8e+120]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e68 or 7.9999999999999998e120 < 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. Step-by-step derivation

      1. add-cube-cbrt 98.0%

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

      2. pow3 97.9%

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

   7. Applied egg-rr 97.9%

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

   8. Taylor expanded in x around inf 75.8%

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

   if -1.05e68 < x < 7.9999999999999998e120

   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 x around 0 93.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+68} \lor \neg \left(x \leq 8 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+67} \lor \neg \left(x \leq 1.05 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e+67) (not (<= x 1.05e+42)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e+67) || !(x <= 1.05e+42)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (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 <= (-9d+67)) .or. (.not. (x <= 1.05d+42))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (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 <= -9e+67) || !(x <= 1.05e+42)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e+67) or not (x <= 1.05e+42):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e+67) || !(x <= 1.05e+42))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9e+67) || ~((x <= 1.05e+42)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e+67], N[Not[LessEqual[x, 1.05e+42]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999997e67 or 1.04999999999999998e42 < 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 83.0%

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

   if -8.9999999999999997e67 < x < 1.04999999999999998e42

   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 x around 0 98.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+67} \lor \neg \left(x \leq 1.05 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+68} \lor \neg \left(x \leq 1.25 \cdot 10^{+121}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.05e+68) (not (<= x 1.25e+121))) (* x (log y)) (- (- y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e+68) || !(x <= 1.25e+121)) {
		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 <= (-1.05d+68)) .or. (.not. (x <= 1.25d+121))) 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 <= -1.05e+68) || !(x <= 1.25e+121)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.05e+68) or not (x <= 1.25e+121):
		tmp = x * math.log(y)
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.05e+68) || !(x <= 1.25e+121))
		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 <= -1.05e+68) || ~((x <= 1.25e+121)))
		tmp = x * log(y);
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.05e+68], N[Not[LessEqual[x, 1.25e+121]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e68 or 1.25000000000000002e121 < 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. Step-by-step derivation

      1. add-cube-cbrt 98.0%

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

      2. pow3 97.9%

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

   7. Applied egg-rr 97.9%

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

   8. Taylor expanded in x around inf 75.8%

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

   if -1.05e68 < x < 1.25000000000000002e121

   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 80.1%

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

   6. Taylor expanded in x around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. distribute-lft-in 74.2%

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

      3. neg-mul-1 74.2%

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

      4. unsub-neg 74.2%

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

      5. mul-1-neg 74.2%

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

   8. Simplified 74.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+68} \lor \neg \left(x \leq 1.25 \cdot 10^{+121}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.8% accurate, 17.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+71} \lor \neg \left(z \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+71) (not (<= z 1.35e-9))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+71) || !(z <= 1.35e-9)) {
		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 ((z <= (-4.8d+71)) .or. (.not. (z <= 1.35d-9))) 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 ((z <= -4.8e+71) || !(z <= 1.35e-9)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e+71) or not (z <= 1.35e-9):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e+71) || !(z <= 1.35e-9))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e+71) || ~((z <= 1.35e-9)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e+71], N[Not[LessEqual[z, 1.35e-9]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999961e71 or 1.3500000000000001e-9 < z

   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. Step-by-step derivation

      1. add-cube-cbrt 99.5%

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

      2. pow3 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in z around inf 63.1%

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

      1. mul-1-neg 63.1%

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

   9. Simplified 63.1%

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

   if -4.79999999999999961e71 < z < 1.3500000000000001e-9

   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. Step-by-step derivation

      1. add-cube-cbrt 99.2%

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

      2. pow3 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 39.1%

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

      1. neg-mul-1 39.1%

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

   9. Simplified 39.1%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+71} \lor \neg \left(z \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.1% 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 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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 86.9%

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

6. Taylor expanded in x around 0 56.6%

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

   1. +-commutative 56.6%

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

   2. distribute-lft-in 56.6%

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

   3. neg-mul-1 56.6%

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

   4. unsub-neg 56.6%

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

   5. mul-1-neg 56.6%

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

8. Simplified 56.6%

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

9. Final simplification 56.6%

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

Alternative 11: 29.1% 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 99.8%

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

   1. add-cube-cbrt 99.4%

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

   2. pow3 99.3%

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

6. Applied egg-rr 99.3%

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

7. Taylor expanded in y around inf 29.0%

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

   1. neg-mul-1 29.0%

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

9. Simplified 29.0%

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

10. Final simplification 29.0%

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

Reproduce

herbie shell --seed 2024059 
(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)))