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

Percentage Accurate: 99.9% → 99.9%

Time: 13.2s

Alternatives: 12

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - y), $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. sub-neg 99.9%

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

   3. sub-neg 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-udef 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 3 \cdot 10^{-5}:\\ \;\;\;\;\left(\log t + t_1\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 3e-5) (- (+ (log t) t_1) z) (- (- t_1 y) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 3e-5) {
		tmp = (log(t) + t_1) - z;
	} else {
		tmp = (t_1 - 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) :: tmp
    t_1 = x * log(y)
    if (y <= 3d-5) then
        tmp = (log(t) + t_1) - z
    else
        tmp = (t_1 - y) - 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 tmp;
	if (y <= 3e-5) {
		tmp = (Math.log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 3e-5:
		tmp = (math.log(t) + t_1) - z
	else:
		tmp = (t_1 - y) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 3e-5)
		tmp = Float64(Float64(log(t) + t_1) - z);
	else
		tmp = Float64(Float64(t_1 - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 3e-5)
		tmp = (log(t) + t_1) - z;
	else
		tmp = (t_1 - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 3e-5], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3.00000000000000008e-5

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 99.4%

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

   if 3.00000000000000008e-5 < 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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-5}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \end{array} \]

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 69.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ t_3 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+101}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -3.5e+68)
     t_2
     (if (<= x -1.18e-32)
       t_3
       (if (<= x -1.3e-152)
         t_1
         (if (<= x 6.2e-205)
           t_3
           (if (<= x 5.8e-117) t_1 (if (<= x 6.5e+101) 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 <= -3.5e+68) {
		tmp = t_2;
	} else if (x <= -1.18e-32) {
		tmp = t_3;
	} else if (x <= -1.3e-152) {
		tmp = t_1;
	} else if (x <= 6.2e-205) {
		tmp = t_3;
	} else if (x <= 5.8e-117) {
		tmp = t_1;
	} else if (x <= 6.5e+101) {
		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 <= (-3.5d+68)) then
        tmp = t_2
    else if (x <= (-1.18d-32)) then
        tmp = t_3
    else if (x <= (-1.3d-152)) then
        tmp = t_1
    else if (x <= 6.2d-205) then
        tmp = t_3
    else if (x <= 5.8d-117) then
        tmp = t_1
    else if (x <= 6.5d+101) 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 <= -3.5e+68) {
		tmp = t_2;
	} else if (x <= -1.18e-32) {
		tmp = t_3;
	} else if (x <= -1.3e-152) {
		tmp = t_1;
	} else if (x <= 6.2e-205) {
		tmp = t_3;
	} else if (x <= 5.8e-117) {
		tmp = t_1;
	} else if (x <= 6.5e+101) {
		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 <= -3.5e+68:
		tmp = t_2
	elif x <= -1.18e-32:
		tmp = t_3
	elif x <= -1.3e-152:
		tmp = t_1
	elif x <= 6.2e-205:
		tmp = t_3
	elif x <= 5.8e-117:
		tmp = t_1
	elif x <= 6.5e+101:
		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 <= -3.5e+68)
		tmp = t_2;
	elseif (x <= -1.18e-32)
		tmp = t_3;
	elseif (x <= -1.3e-152)
		tmp = t_1;
	elseif (x <= 6.2e-205)
		tmp = t_3;
	elseif (x <= 5.8e-117)
		tmp = t_1;
	elseif (x <= 6.5e+101)
		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 <= -3.5e+68)
		tmp = t_2;
	elseif (x <= -1.18e-32)
		tmp = t_3;
	elseif (x <= -1.3e-152)
		tmp = t_1;
	elseif (x <= 6.2e-205)
		tmp = t_3;
	elseif (x <= 5.8e-117)
		tmp = t_1;
	elseif (x <= 6.5e+101)
		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, -3.5e+68], t$95$2, If[LessEqual[x, -1.18e-32], t$95$3, If[LessEqual[x, -1.3e-152], t$95$1, If[LessEqual[x, 6.2e-205], t$95$3, If[LessEqual[x, 5.8e-117], t$95$1, If[LessEqual[x, 6.5e+101], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999977e68 or 6.50000000000000016e101 < 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%

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

   3. Simplified 99.7%

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

      1. add-cbrt-cube 12.2%

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

      2. pow3 12.2%

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

      3. associate--l- 12.2%

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

   5. Applied egg-rr 12.2%

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

   6. Taylor expanded in y around 0 12.0%

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

   7. Taylor expanded in x around inf 74.4%

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

   if -3.49999999999999977e68 < x < -1.17999999999999997e-32 or -1.30000000000000006e-152 < x < 6.19999999999999965e-205 or 5.8000000000000001e-117 < x < 6.50000000000000016e101

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 85.5%

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

   5. Taylor expanded in x around 0 78.7%

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

      1. neg-mul-1 78.7%

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

   7. Simplified 78.7%

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

   if -1.17999999999999997e-32 < x < -1.30000000000000006e-152 or 6.19999999999999965e-205 < x < 5.8000000000000001e-117

   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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around 0 87.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-32}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-152}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-205}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-117}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+101}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 5: 68.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-153}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-119}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- y) z)))
   (if (<= x -2.2e+68)
     t_1
     (if (<= x -1.35e-32)
       t_2
       (if (<= x -6e-153)
         (- (log t) y)
         (if (<= x 9.5e-248)
           t_2
           (if (<= x 2.2e-119)
             (- (log t) z)
             (if (<= x 1.1e+103) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -2.2e+68) {
		tmp = t_1;
	} else if (x <= -1.35e-32) {
		tmp = t_2;
	} else if (x <= -6e-153) {
		tmp = log(t) - y;
	} else if (x <= 9.5e-248) {
		tmp = t_2;
	} else if (x <= 2.2e-119) {
		tmp = log(t) - z;
	} else if (x <= 1.1e+103) {
		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 = x * log(y)
    t_2 = -y - z
    if (x <= (-2.2d+68)) then
        tmp = t_1
    else if (x <= (-1.35d-32)) then
        tmp = t_2
    else if (x <= (-6d-153)) then
        tmp = log(t) - y
    else if (x <= 9.5d-248) then
        tmp = t_2
    else if (x <= 2.2d-119) then
        tmp = log(t) - z
    else if (x <= 1.1d+103) 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 = x * Math.log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -2.2e+68) {
		tmp = t_1;
	} else if (x <= -1.35e-32) {
		tmp = t_2;
	} else if (x <= -6e-153) {
		tmp = Math.log(t) - y;
	} else if (x <= 9.5e-248) {
		tmp = t_2;
	} else if (x <= 2.2e-119) {
		tmp = Math.log(t) - z;
	} else if (x <= 1.1e+103) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = -y - z
	tmp = 0
	if x <= -2.2e+68:
		tmp = t_1
	elif x <= -1.35e-32:
		tmp = t_2
	elif x <= -6e-153:
		tmp = math.log(t) - y
	elif x <= 9.5e-248:
		tmp = t_2
	elif x <= 2.2e-119:
		tmp = math.log(t) - z
	elif x <= 1.1e+103:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (x <= -2.2e+68)
		tmp = t_1;
	elseif (x <= -1.35e-32)
		tmp = t_2;
	elseif (x <= -6e-153)
		tmp = Float64(log(t) - y);
	elseif (x <= 9.5e-248)
		tmp = t_2;
	elseif (x <= 2.2e-119)
		tmp = Float64(log(t) - z);
	elseif (x <= 1.1e+103)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = -y - z;
	tmp = 0.0;
	if (x <= -2.2e+68)
		tmp = t_1;
	elseif (x <= -1.35e-32)
		tmp = t_2;
	elseif (x <= -6e-153)
		tmp = log(t) - y;
	elseif (x <= 9.5e-248)
		tmp = t_2;
	elseif (x <= 2.2e-119)
		tmp = log(t) - z;
	elseif (x <= 1.1e+103)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -2.2e+68], t$95$1, If[LessEqual[x, -1.35e-32], t$95$2, If[LessEqual[x, -6e-153], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 9.5e-248], t$95$2, If[LessEqual[x, 2.2e-119], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 1.1e+103], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.19999999999999987e68 or 1.09999999999999996e103 < 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%

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

   3. Simplified 99.7%

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

      1. add-cbrt-cube 12.2%

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

      2. pow3 12.2%

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

      3. associate--l- 12.2%

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

   5. Applied egg-rr 12.2%

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

   6. Taylor expanded in y around 0 12.0%

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

   7. Taylor expanded in x around inf 74.4%

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

   if -2.19999999999999987e68 < x < -1.3499999999999999e-32 or -6e-153 < x < 9.49999999999999971e-248 or 2.2000000000000001e-119 < x < 1.09999999999999996e103

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 88.7%

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

   5. Taylor expanded in x around 0 81.1%

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

      1. neg-mul-1 81.1%

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

   7. Simplified 81.1%

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

   if -1.3499999999999999e-32 < x < -6e-153

   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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around 0 90.3%

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

   if 9.49999999999999971e-248 < x < 2.2000000000000001e-119

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. fma-def 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in x around 0 76.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-153}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-119}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+103}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 6: 99.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.76 \lor \neg \left(x \leq 2.1 \cdot 10^{-16}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.76) (not (<= x 2.1e-16)))
   (- (- (* x (log y)) y) z)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.76) || !(x <= 2.1e-16)) {
		tmp = ((x * log(y)) - 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) :: tmp
    if ((x <= (-0.76d0)) .or. (.not. (x <= 2.1d-16))) then
        tmp = ((x * log(y)) - 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 tmp;
	if ((x <= -0.76) || !(x <= 2.1e-16)) {
		tmp = ((x * Math.log(y)) - y) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.76) or not (x <= 2.1e-16):
		tmp = ((x * math.log(y)) - y) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.76) || !(x <= 2.1e-16))
		tmp = Float64(Float64(Float64(x * log(y)) - y) - z);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.76) || ~((x <= 2.1e-16)))
		tmp = ((x * log(y)) - y) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.76], N[Not[LessEqual[x, 2.1e-16]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.76000000000000001 or 2.1000000000000001e-16 < 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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 98.4%

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

   if -0.76000000000000001 < x < 2.1000000000000001e-16

   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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.76 \lor \neg \left(x \leq 2.1 \cdot 10^{-16}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 7: 89.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+53} \lor \neg \left(x \leq 6.9 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e+53) (not (<= x 6.9e+40)))
   (- (* x (log y)) z)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e+53) || !(x <= 6.9e+40)) {
		tmp = (x * log(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) :: tmp
    if ((x <= (-8.5d+53)) .or. (.not. (x <= 6.9d+40))) then
        tmp = (x * log(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 tmp;
	if ((x <= -8.5e+53) || !(x <= 6.9e+40)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.5e+53) or not (x <= 6.9e+40):
		tmp = (x * math.log(y)) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.5e+53) || !(x <= 6.9e+40))
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.5e+53) || ~((x <= 6.9e+40)))
		tmp = (x * log(y)) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.5e+53], N[Not[LessEqual[x, 6.9e+40]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000002e53 or 6.9000000000000003e40 < 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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in x around inf 87.1%

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

   if -8.5000000000000002e53 < x < 6.9000000000000003e40

   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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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. Taylor expanded in x around 0 96.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+53} \lor \neg \left(x \leq 6.9 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 8: 71.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+68} \lor \neg \left(x \leq 1.35 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.52e+68) (not (<= x 1.35e+101))) (* x (log y)) (- (- y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.52e+68) || !(x <= 1.35e+101)) {
		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 <= (-1.52d+68)) .or. (.not. (x <= 1.35d+101))) 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 <= -1.52e+68) || !(x <= 1.35e+101)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.52e+68) or not (x <= 1.35e+101):
		tmp = x * math.log(y)
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.52e+68) || !(x <= 1.35e+101))
		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 <= -1.52e+68) || ~((x <= 1.35e+101)))
		tmp = x * log(y);
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.52e+68], N[Not[LessEqual[x, 1.35e+101]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52000000000000008e68 or 1.35000000000000003e101 < 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%

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

   3. Simplified 99.7%

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

      1. add-cbrt-cube 12.2%

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

      2. pow3 12.2%

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

      3. associate--l- 12.2%

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

   5. Applied egg-rr 12.2%

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

   6. Taylor expanded in y around 0 12.0%

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

   7. Taylor expanded in x around inf 74.4%

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

   if -1.52000000000000008e68 < x < 1.35000000000000003e101

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 79.8%

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

   5. Taylor expanded in x around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+68} \lor \neg \left(x \leq 1.35 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]

Alternative 9: 77.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.15e+73) (- (* x (log y)) z) (- (- y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.15e+73) {
		tmp = (x * log(y)) - z;
	} 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 (y <= 2.15d+73) then
        tmp = (x * log(y)) - z
    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 (y <= 2.15e+73) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.15e+73:
		tmp = (x * math.log(y)) - z
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.15e+73)
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.15e+73)
		tmp = (x * log(y)) - z;
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.15e+73], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.15000000000000007e73

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 79.7%

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

   5. Taylor expanded in x around inf 76.5%

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

   if 2.15000000000000007e73 < 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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in x around 0 90.3%

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

      1. neg-mul-1 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]

Alternative 10: 48.5% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 4.5e+76) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.5e+76) {
		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 <= 4.5d+76) 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 <= 4.5e+76) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.5e+76:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.5e+76)
		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 <= 4.5e+76)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.5e+76], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 4.4999999999999997e76

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 35.9%

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

      1. neg-mul-1 35.9%

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

   6. Simplified 35.9%

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

   if 4.4999999999999997e76 < 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. sub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. +-commutative 99.9%

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

      7. unsub-neg 99.9%

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

      8. fma-udef 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. neg-sub0 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 90.2%

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

   5. Taylor expanded in y around inf 81.1%

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

      1. mul-1-neg 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 11: 58.6% 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%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 87.0%

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

5. Taylor expanded in x around 0 57.3%

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

   1. neg-mul-1 57.3%

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

7. Simplified 57.3%

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

8. Final simplification 57.3%

   \[\leadsto \left(-y\right) - z \]

Alternative 12: 30.1% 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 99.9%

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

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

   3. sub-neg 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-udef 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 69.5%

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

5. Taylor expanded in y around inf 32.6%

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

   1. mul-1-neg 32.6%

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

7. Simplified 32.6%

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

8. Final simplification 32.6%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023321 
(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)))