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

Percentage Accurate: 99.9% → 99.9%

Time: 11.3s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * log(y)) + ((log(t) - z) - y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 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 3: 61.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - z\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-297}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) z)))
   (if (<= x -9.8e+76)
     t_1
     (if (<= x -2.3e-41)
       t_2
       (if (<= x -5e-297) (- (log t) y) (if (<= x 5.6e+91) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - z;
	double tmp;
	if (x <= -9.8e+76) {
		tmp = t_1;
	} else if (x <= -2.3e-41) {
		tmp = t_2;
	} else if (x <= -5e-297) {
		tmp = log(t) - y;
	} else if (x <= 5.6e+91) {
		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 = log(t) - z
    if (x <= (-9.8d+76)) then
        tmp = t_1
    else if (x <= (-2.3d-41)) then
        tmp = t_2
    else if (x <= (-5d-297)) then
        tmp = log(t) - y
    else if (x <= 5.6d+91) 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 = Math.log(t) - z;
	double tmp;
	if (x <= -9.8e+76) {
		tmp = t_1;
	} else if (x <= -2.3e-41) {
		tmp = t_2;
	} else if (x <= -5e-297) {
		tmp = Math.log(t) - y;
	} else if (x <= 5.6e+91) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - z
	tmp = 0
	if x <= -9.8e+76:
		tmp = t_1
	elif x <= -2.3e-41:
		tmp = t_2
	elif x <= -5e-297:
		tmp = math.log(t) - y
	elif x <= 5.6e+91:
		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(log(t) - z)
	tmp = 0.0
	if (x <= -9.8e+76)
		tmp = t_1;
	elseif (x <= -2.3e-41)
		tmp = t_2;
	elseif (x <= -5e-297)
		tmp = Float64(log(t) - y);
	elseif (x <= 5.6e+91)
		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 = log(t) - z;
	tmp = 0.0;
	if (x <= -9.8e+76)
		tmp = t_1;
	elseif (x <= -2.3e-41)
		tmp = t_2;
	elseif (x <= -5e-297)
		tmp = log(t) - y;
	elseif (x <= 5.6e+91)
		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[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -9.8e+76], t$95$1, If[LessEqual[x, -2.3e-41], t$95$2, If[LessEqual[x, -5e-297], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 5.6e+91], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.80000000000000053e76 or 5.5999999999999997e91 < 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 87.0%

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

   6. Taylor expanded in z around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-rgt-neg-in 58.7%

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

      3. mul-1-neg 58.7%

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

      4. associate-*r/ 58.7%

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

      5. unsub-neg 58.7%

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

      6. associate-*r/ 58.7%

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

      7. *-rgt-identity 58.7%

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

      8. times-frac 58.7%

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

      9. /-rgt-identity 58.7%

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

      10. associate-/r/ 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in z around 0 80.2%

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

   if -9.80000000000000053e76 < x < -2.3000000000000001e-41 or -5e-297 < x < 5.5999999999999997e91

   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 z around inf 64.0%

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

      1. neg-mul-1 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. sub-neg 64.0%

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

   10. Simplified 64.0%

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

   if -2.3000000000000001e-41 < x < -5e-297

   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 70.7%

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

      1. mul-1-neg 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in y around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. sub-neg 70.7%

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

   10. Simplified 70.7%

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

Alternative 4: 59.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-34}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.85:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+88}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -6.2e+75)
     t_1
     (if (<= x -3.4e-34)
       (- z)
       (if (<= x 1.85) (- (log t) y) (if (<= x 6.8e+88) (- z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -6.2e+75) {
		tmp = t_1;
	} else if (x <= -3.4e-34) {
		tmp = -z;
	} else if (x <= 1.85) {
		tmp = log(t) - y;
	} else if (x <= 6.8e+88) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-6.2d+75)) then
        tmp = t_1
    else if (x <= (-3.4d-34)) then
        tmp = -z
    else if (x <= 1.85d0) then
        tmp = log(t) - y
    else if (x <= 6.8d+88) then
        tmp = -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -6.2e+75) {
		tmp = t_1;
	} else if (x <= -3.4e-34) {
		tmp = -z;
	} else if (x <= 1.85) {
		tmp = Math.log(t) - y;
	} else if (x <= 6.8e+88) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -6.2e+75:
		tmp = t_1
	elif x <= -3.4e-34:
		tmp = -z
	elif x <= 1.85:
		tmp = math.log(t) - y
	elif x <= 6.8e+88:
		tmp = -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -6.2e+75)
		tmp = t_1;
	elseif (x <= -3.4e-34)
		tmp = Float64(-z);
	elseif (x <= 1.85)
		tmp = Float64(log(t) - y);
	elseif (x <= 6.8e+88)
		tmp = Float64(-z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -6.2e+75)
		tmp = t_1;
	elseif (x <= -3.4e-34)
		tmp = -z;
	elseif (x <= 1.85)
		tmp = log(t) - y;
	elseif (x <= 6.8e+88)
		tmp = -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+75], t$95$1, If[LessEqual[x, -3.4e-34], (-z), If[LessEqual[x, 1.85], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 6.8e+88], (-z), t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2000000000000002e75 or 6.80000000000000008e88 < 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 87.0%

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

   6. Taylor expanded in z around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-rgt-neg-in 58.7%

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

      3. mul-1-neg 58.7%

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

      4. associate-*r/ 58.7%

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

      5. unsub-neg 58.7%

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

      6. associate-*r/ 58.7%

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

      7. *-rgt-identity 58.7%

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

      8. times-frac 58.7%

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

      9. /-rgt-identity 58.7%

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

      10. associate-/r/ 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in z around 0 80.2%

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

   if -6.2000000000000002e75 < x < -3.4000000000000001e-34 or 1.8500000000000001 < x < 6.80000000000000008e88

   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. Step-by-step derivation

      1. add-cbrt-cube 99.8%

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

      2. pow3 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 57.7%

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

      1. neg-mul-1 57.7%

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

   9. Simplified 57.7%

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

   if -3.4000000000000001e-34 < x < 1.8500000000000001

   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 y around inf 62.1%

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

      1. mul-1-neg 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in y around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. sub-neg 62.1%

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

   10. Simplified 62.1%

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

Alternative 5: 49.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-297}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+88}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.2e+76)
     t_1
     (if (<= x -1.8e-41)
       (- z)
       (if (<= x -1.8e-297) (- y) (if (<= x 7.5e+88) (- z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -3.2e+76) {
		tmp = t_1;
	} else if (x <= -1.8e-41) {
		tmp = -z;
	} else if (x <= -1.8e-297) {
		tmp = -y;
	} else if (x <= 7.5e+88) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-3.2d+76)) then
        tmp = t_1
    else if (x <= (-1.8d-41)) then
        tmp = -z
    else if (x <= (-1.8d-297)) then
        tmp = -y
    else if (x <= 7.5d+88) then
        tmp = -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -3.2e+76) {
		tmp = t_1;
	} else if (x <= -1.8e-41) {
		tmp = -z;
	} else if (x <= -1.8e-297) {
		tmp = -y;
	} else if (x <= 7.5e+88) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -3.2e+76:
		tmp = t_1
	elif x <= -1.8e-41:
		tmp = -z
	elif x <= -1.8e-297:
		tmp = -y
	elif x <= 7.5e+88:
		tmp = -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.2e+76)
		tmp = t_1;
	elseif (x <= -1.8e-41)
		tmp = Float64(-z);
	elseif (x <= -1.8e-297)
		tmp = Float64(-y);
	elseif (x <= 7.5e+88)
		tmp = Float64(-z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -3.2e+76)
		tmp = t_1;
	elseif (x <= -1.8e-41)
		tmp = -z;
	elseif (x <= -1.8e-297)
		tmp = -y;
	elseif (x <= 7.5e+88)
		tmp = -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+76], t$95$1, If[LessEqual[x, -1.8e-41], (-z), If[LessEqual[x, -1.8e-297], (-y), If[LessEqual[x, 7.5e+88], (-z), t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999976e76 or 7.50000000000000031e88 < 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 87.0%

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

   6. Taylor expanded in z around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-rgt-neg-in 58.7%

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

      3. mul-1-neg 58.7%

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

      4. associate-*r/ 58.7%

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

      5. unsub-neg 58.7%

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

      6. associate-*r/ 58.7%

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

      7. *-rgt-identity 58.7%

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

      8. times-frac 58.7%

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

      9. /-rgt-identity 58.7%

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

      10. associate-/r/ 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in z around 0 80.2%

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

   if -3.19999999999999976e76 < x < -1.8e-41 or -1.79999999999999997e-297 < x < 7.50000000000000031e88

   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. Step-by-step derivation

      1. add-cbrt-cube 99.9%

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

      2. pow3 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 46.9%

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

      1. neg-mul-1 46.9%

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

   9. Simplified 46.9%

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

   if -1.8e-41 < x < -1.79999999999999997e-297

   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. Step-by-step derivation

      1. add-cbrt-cube 100.0%

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

      2. pow3 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 52.7%

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

      1. mul-1-neg 52.7%

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

   9. Simplified 52.7%

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

Alternative 6: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+76} \lor \neg \left(x \leq 9 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.8e+76) (not (<= x 9e+64)))
   (- (* x (log y)) y)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.8e+76) || !(x <= 9e+64)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-9.8d+76)) .or. (.not. (x <= 9d+64))) then
        tmp = (x * log(y)) - y
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.8e+76) || !(x <= 9e+64)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.8e+76) or not (x <= 9e+64):
		tmp = (x * math.log(y)) - y
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.8e+76) || !(x <= 9e+64))
		tmp = Float64(Float64(x * log(y)) - y);
	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 <= -9.8e+76) || ~((x <= 9e+64)))
		tmp = (x * log(y)) - y;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.8e+76], N[Not[LessEqual[x, 9e+64]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.80000000000000053e76 or 8.99999999999999946e64 < 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 y around inf 91.7%

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

   if -9.80000000000000053e76 < x < 8.99999999999999946e64

   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- 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. Step-by-step derivation

      1. add-cbrt-cube 99.9%

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

      2. pow3 99.9%

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

   6. Applied egg-rr 99.9%

      \[\leadsto x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - \left(y + \left(z - \log t\right)\right) \]
   7. Step-by-step derivation

      1. unpow3 99.9%

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

      2. pow2 99.9%

         \[\leadsto x \cdot \sqrt[3]{\color{blue}{{\log y}^{2}} \cdot \log y} - \left(y + \left(z - \log t\right)\right) \]

   8. Applied egg-rr 99.9%

      \[\leadsto x \cdot \sqrt[3]{\color{blue}{{\log y}^{2} \cdot \log y}} - \left(y + \left(z - \log t\right)\right) \]

   9. Taylor expanded in x around 0 94.8%

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

       1. +-commutative 94.8%

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

       2. associate--r+ 94.9%

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

   11. Simplified 94.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+76} \lor \neg \left(x \leq 9 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+76} \lor \neg \left(x \leq 7.8 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.3e+76) (not (<= x 7.8e+64)))
   (- (* x (log y)) y)
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.3e+76) || !(x <= 7.8e+64)) {
		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 <= (-1.3d+76)) .or. (.not. (x <= 7.8d+64))) 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 <= -1.3e+76) || !(x <= 7.8e+64)) {
		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 <= -1.3e+76) or not (x <= 7.8e+64):
		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 <= -1.3e+76) || !(x <= 7.8e+64))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.3e+76) || ~((x <= 7.8e+64)))
		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, -1.3e+76], N[Not[LessEqual[x, 7.8e+64]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e76 or 7.7999999999999996e64 < 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 y around inf 91.7%

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

   if -1.3e76 < x < 7.7999999999999996e64

   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- 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. Step-by-step derivation

      1. add-cbrt-cube 99.9%

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

      2. pow3 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 94.8%

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

      1. associate--r+ 94.9%

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

   9. Simplified 94.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+76} \lor \neg \left(x \leq 7.8 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+75} \lor \neg \left(x \leq 5.8 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.6e+75) (not (<= x 5.8e+65)))
   (- (* x (log y)) y)
   (- (log t) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e+75) || !(x <= 5.8e+65)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (z + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.6d+75)) .or. (.not. (x <= 5.8d+65))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e+75) || !(x <= 5.8e+65)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.6e+75) or not (x <= 5.8e+65):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (z + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.6e+75) || !(x <= 5.8e+65))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.6e+75) || ~((x <= 5.8e+65)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.6e+75], N[Not[LessEqual[x, 5.8e+65]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e75 or 5.8000000000000001e65 < 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 y around inf 91.7%

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

   if -3.6e75 < x < 5.8000000000000001e65

   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 94.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+75} \lor \neg \left(x \leq 5.8 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+78} \lor \neg \left(x \leq 1.9 \cdot 10^{+89}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.1e+78) (not (<= x 1.9e+89)))
   (* x (log y))
   (- (log t) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e+78) || !(x <= 1.9e+89)) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (z + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.1d+78)) .or. (.not. (x <= 1.9d+89))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e+78) || !(x <= 1.9e+89)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.1e+78) or not (x <= 1.9e+89):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (z + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.1e+78) || !(x <= 1.9e+89))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.1e+78) || ~((x <= 1.9e+89)))
		tmp = x * log(y);
	else
		tmp = log(t) - (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.1e+78], N[Not[LessEqual[x, 1.9e+89]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000007e78 or 1.90000000000000012e89 < 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 87.0%

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

   6. Taylor expanded in z around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-rgt-neg-in 58.7%

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

      3. mul-1-neg 58.7%

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

      4. associate-*r/ 58.7%

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

      5. unsub-neg 58.7%

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

      6. associate-*r/ 58.7%

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

      7. *-rgt-identity 58.7%

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

      8. times-frac 58.7%

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

      9. /-rgt-identity 58.7%

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

      10. associate-/r/ 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in z around 0 80.2%

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

   if -1.10000000000000007e78 < x < 1.90000000000000012e89

   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 94.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+78} \lor \neg \left(x \leq 1.9 \cdot 10^{+89}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.1% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+81}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 3.4e+81) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.4e+81) {
		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 <= 3.4d+81) 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 <= 3.4e+81) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.4e+81:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.4e+81)
		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 <= 3.4e+81)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.4e+81], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3.40000000000000003e81

   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-cbrt-cube 99.6%

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

      2. pow3 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 36.0%

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

      1. neg-mul-1 36.0%

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

   9. Simplified 36.0%

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

   if 3.40000000000000003e81 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

      1. add-cbrt-cube 99.9%

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

      2. pow3 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. mul-1-neg 68.5%

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

   9. Simplified 68.5%

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

Alternative 11: 29.7% 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- 99.9%

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

   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. Step-by-step derivation

   1. add-cbrt-cube 99.7%

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

   2. pow3 99.7%

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

6. Applied egg-rr 99.7%

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

7. Taylor expanded in y around inf 28.2%

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

   1. mul-1-neg 28.2%

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

9. Simplified 28.2%

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

Alternative 12: 2.2% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. add-cbrt-cube 99.7%

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

   2. pow3 99.7%

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

6. Applied egg-rr 99.7%

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

7. Taylor expanded in y around inf 28.2%

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

   1. mul-1-neg 28.2%

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

9. Simplified 28.2%

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

    1. neg-sub0 28.2%

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

    2. sub-neg 28.2%

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

    3. add-sqr-sqrt 0.0%

       \[\leadsto 0 + \color{blue}{\sqrt{-y} \cdot \sqrt{-y}} \]

    4. sqrt-unprod 2.2%

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

    5. sqr-neg 2.2%

       \[\leadsto 0 + \sqrt{\color{blue}{y \cdot y}} \]

    6. sqrt-unprod 2.2%

       \[\leadsto 0 + \color{blue}{\sqrt{y} \cdot \sqrt{y}} \]

    7. add-sqr-sqrt 2.2%

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

11. Applied egg-rr 2.2%

    \[\leadsto \color{blue}{0 + y} \]
12. Step-by-step derivation

    1. +-lft-identity 2.2%

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

13. Simplified 2.2%

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

Reproduce

herbie shell --seed 2024185 
(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)))