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

Percentage Accurate: 99.9% → 99.9%

Time: 15.0s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 89.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - z\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.3 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 z)))
   (if (<= x -1.2e+40)
     t_2
     (if (<= x 1.2e+72)
       (- (log t) (+ y z))
       (if (<= x 8.3e+99) t_2 (- t_1 y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -1.2e+40) {
		tmp = t_2;
	} else if (x <= 1.2e+72) {
		tmp = log(t) - (y + z);
	} else if (x <= 8.3e+99) {
		tmp = t_2;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - z
    if (x <= (-1.2d+40)) then
        tmp = t_2
    else if (x <= 1.2d+72) then
        tmp = log(t) - (y + z)
    else if (x <= 8.3d+99) then
        tmp = t_2
    else
        tmp = t_1 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -1.2e+40) {
		tmp = t_2;
	} else if (x <= 1.2e+72) {
		tmp = Math.log(t) - (y + z);
	} else if (x <= 8.3e+99) {
		tmp = t_2;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - z
	tmp = 0
	if x <= -1.2e+40:
		tmp = t_2
	elif x <= 1.2e+72:
		tmp = math.log(t) - (y + z)
	elif x <= 8.3e+99:
		tmp = t_2
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - z)
	tmp = 0.0
	if (x <= -1.2e+40)
		tmp = t_2;
	elseif (x <= 1.2e+72)
		tmp = Float64(log(t) - Float64(y + z));
	elseif (x <= 8.3e+99)
		tmp = t_2;
	else
		tmp = Float64(t_1 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - z;
	tmp = 0.0;
	if (x <= -1.2e+40)
		tmp = t_2;
	elseif (x <= 1.2e+72)
		tmp = log(t) - (y + z);
	elseif (x <= 8.3e+99)
		tmp = t_2;
	else
		tmp = t_1 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - z), $MachinePrecision]}, If[LessEqual[x, -1.2e+40], t$95$2, If[LessEqual[x, 1.2e+72], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.3e+99], t$95$2, N[(t$95$1 - y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2e40 or 1.20000000000000005e72 < x < 8.3e99

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -1.2e40 < x < 1.20000000000000005e72

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.0%

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

   if 8.3e99 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 91.7%

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

Alternative 3: 68.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) - y\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+45}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- z) y)))
   (if (<= z -1.2e+15)
     t_1
     (if (<= z 4.6e+45) (- (log t) y) (if (<= z 3.3e+76) (* x (log y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z - y;
	double tmp;
	if (z <= -1.2e+15) {
		tmp = t_1;
	} else if (z <= 4.6e+45) {
		tmp = log(t) - y;
	} else if (z <= 3.3e+76) {
		tmp = x * log(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z - y
    if (z <= (-1.2d+15)) then
        tmp = t_1
    else if (z <= 4.6d+45) then
        tmp = log(t) - y
    else if (z <= 3.3d+76) then
        tmp = x * log(y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -z - y;
	double tmp;
	if (z <= -1.2e+15) {
		tmp = t_1;
	} else if (z <= 4.6e+45) {
		tmp = Math.log(t) - y;
	} else if (z <= 3.3e+76) {
		tmp = x * Math.log(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z - y
	tmp = 0
	if z <= -1.2e+15:
		tmp = t_1
	elif z <= 4.6e+45:
		tmp = math.log(t) - y
	elif z <= 3.3e+76:
		tmp = x * math.log(y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) - y)
	tmp = 0.0
	if (z <= -1.2e+15)
		tmp = t_1;
	elseif (z <= 4.6e+45)
		tmp = Float64(log(t) - y);
	elseif (z <= 3.3e+76)
		tmp = Float64(x * log(y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z - y;
	tmp = 0.0;
	if (z <= -1.2e+15)
		tmp = t_1;
	elseif (z <= 4.6e+45)
		tmp = log(t) - y;
	elseif (z <= 3.3e+76)
		tmp = x * log(y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) - y), $MachinePrecision]}, If[LessEqual[z, -1.2e+15], t$95$1, If[LessEqual[z, 4.6e+45], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[z, 3.3e+76], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e15 or 3.3000000000000001e76 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.9%

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

   6. Taylor expanded in y around -inf 56.8%

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

      1. associate-*r* 56.8%

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

      2. neg-mul-1 56.8%

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

      3. +-commutative 56.8%

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

      4. distribute-lft-in 56.8%

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

      5. *-rgt-identity 56.8%

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

      6. unsub-neg 56.8%

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

      7. distribute-lft-neg-in 56.8%

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

      8. mul-1-neg 56.8%

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

      9. distribute-rgt-neg-out 56.8%

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

      10. remove-double-neg 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in z around inf 81.8%

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

       1. neg-mul-1 81.8%

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

   11. Simplified 81.8%

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

   if -1.2e15 < z < 4.60000000000000025e45

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. associate--l+ 98.5%

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

      2. div-sub 98.5%

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

   7. Simplified 98.5%

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

   8. Taylor expanded in z around 0 96.4%

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

   9. Taylor expanded in x around 0 66.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - \frac{\log t}{y}\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 66.5%

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

       2. distribute-rgt-neg-in 66.5%

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

       3. neg-sub0 66.5%

          \[\leadsto y \cdot \color{blue}{\left(0 - \left(1 - \frac{\log t}{y}\right)\right)} \]

       4. associate--r- 66.5%

          \[\leadsto y \cdot \color{blue}{\left(\left(0 - 1\right) + \frac{\log t}{y}\right)} \]

       5. metadata-eval 66.5%

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

   11. Simplified 66.5%

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

   12. Taylor expanded in y around 0 67.2%

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

       1. mul-1-neg 67.2%

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

       2. unsub-neg 67.2%

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

   14. Simplified 67.2%

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

   if 4.60000000000000025e45 < z < 3.3000000000000001e76

   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. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. add-cube-cbrt 98.7%

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

      3. associate-*l* 98.7%

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

      4. fma-neg 98.7%

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

      5. pow2 98.7%

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

      6. associate-+r- 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around inf 83.3%

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

      1. *-commutative 83.3%

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

   9. Simplified 83.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+45}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+116} \lor \neg \left(x \leq 4.65 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e+116) (not (<= x 4.65e-60)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e+116) || !(x <= 4.65e-60)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-9d+116)) .or. (.not. (x <= 4.65d-60))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e+116) || !(x <= 4.65e-60)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e+116) or not (x <= 4.65e-60):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e+116) || !(x <= 4.65e-60))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9e+116) || ~((x <= 4.65e-60)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e+116], N[Not[LessEqual[x, 4.65e-60]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000032e116 or 4.6500000000000001e-60 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 83.6%

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

   if -9.00000000000000032e116 < x < 4.6500000000000001e-60

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+116} \lor \neg \left(x \leq 4.65 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+88} \lor \neg \left(x \leq 1.1 \cdot 10^{+74}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.42e+88) (not (<= x 1.1e+74)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.42e+88) || !(x <= 1.1e+74)) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.42d+88)) .or. (.not. (x <= 1.1d+74))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.42e+88) || !(x <= 1.1e+74)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.42e+88) or not (x <= 1.1e+74):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.42e+88) || !(x <= 1.1e+74))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.42e+88) || ~((x <= 1.1e+74)))
		tmp = x * log(y);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.42e+88], N[Not[LessEqual[x, 1.1e+74]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.41999999999999996e88 or 1.1000000000000001e74 < x

   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. *-commutative 99.8%

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

      2. add-cube-cbrt 98.7%

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

      3. associate-*l* 98.7%

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

      4. fma-neg 98.7%

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

      5. pow2 98.7%

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

      6. associate-+r- 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around inf 64.7%

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

      1. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if -1.41999999999999996e88 < x < 1.1000000000000001e74

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+88} \lor \neg \left(x \leq 1.1 \cdot 10^{+74}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+87} \lor \neg \left(x \leq 4.8 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.8e+87) (not (<= x 4.8e+73))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e+87) || !(x <= 4.8e+73)) {
		tmp = x * log(y);
	} else {
		tmp = -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 <= (-2.8d+87)) .or. (.not. (x <= 4.8d+73))) then
        tmp = x * log(y)
    else
        tmp = -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 <= -2.8e+87) || !(x <= 4.8e+73)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.8e+87) or not (x <= 4.8e+73):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.8e+87) || !(x <= 4.8e+73))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.8e+87) || ~((x <= 4.8e+73)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.8e+87], N[Not[LessEqual[x, 4.8e+73]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000015e87 or 4.80000000000000004e73 < x

   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. *-commutative 99.8%

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

      2. add-cube-cbrt 98.7%

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

      3. associate-*l* 98.7%

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

      4. fma-neg 98.7%

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

      5. pow2 98.7%

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

      6. associate-+r- 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around inf 64.7%

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

      1. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if -2.80000000000000015e87 < x < 4.80000000000000004e73

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.2%

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

   6. Taylor expanded in y around -inf 83.0%

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

      1. associate-*r* 83.0%

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

      2. neg-mul-1 83.0%

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

      3. +-commutative 83.0%

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

      4. distribute-lft-in 83.0%

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

      5. *-rgt-identity 83.0%

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

      6. unsub-neg 83.0%

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

      7. distribute-lft-neg-in 83.0%

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

      8. mul-1-neg 83.0%

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

      9. distribute-rgt-neg-out 83.0%

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

      10. remove-double-neg 83.0%

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

   8. Simplified 83.0%

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

   9. Taylor expanded in z around inf 71.6%

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

       1. neg-mul-1 71.6%

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

   11. Simplified 71.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+87} \lor \neg \left(x \leq 4.8 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.25e-7) (- (log t) z) (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.25e-7) {
		tmp = log(t) - z;
	} else {
		tmp = -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 (y <= 1.25d-7) then
        tmp = log(t) - z
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.25e-7) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.25e-7:
		tmp = math.log(t) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.25e-7)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.25e-7)
		tmp = log(t) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.25e-7], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.24999999999999994e-7

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 68.2%

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

   6. Taylor expanded in y around 0 68.1%

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

   if 1.24999999999999994e-7 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.6%

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

   6. Taylor expanded in y around -inf 80.5%

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

      1. associate-*r* 80.5%

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

      2. neg-mul-1 80.5%

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

      3. +-commutative 80.5%

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

      4. distribute-lft-in 80.5%

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

      5. *-rgt-identity 80.5%

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

      6. unsub-neg 80.5%

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

      7. distribute-lft-neg-in 80.5%

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

      8. mul-1-neg 80.5%

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

      9. distribute-rgt-neg-out 80.5%

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

      10. remove-double-neg 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in z around inf 78.8%

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

       1. neg-mul-1 78.8%

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

   11. Simplified 78.8%

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

Alternative 8: 47.5% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 230000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 230000000.0) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 230000000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 230000000.0d0) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 230000000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 230000000.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 230000000.0)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 230000000.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 230000000.0], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.3e8

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 40.7%

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

      1. mul-1-neg 40.7%

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

   7. Simplified 40.7%

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

   if 2.3e8 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

   7. Simplified 67.8%

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

Alternative 9: 57.8% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0 73.9%

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

6. Taylor expanded in y around -inf 62.6%

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

   1. associate-*r* 62.6%

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

   2. neg-mul-1 62.6%

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

   3. +-commutative 62.6%

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

   4. distribute-lft-in 62.6%

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

   5. *-rgt-identity 62.6%

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

   6. unsub-neg 62.6%

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

   7. distribute-lft-neg-in 62.6%

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

   8. mul-1-neg 62.6%

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

   9. distribute-rgt-neg-out 62.6%

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

   10. remove-double-neg 62.6%

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

8. Simplified 62.6%

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

9. Taylor expanded in z around inf 58.1%

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

    1. neg-mul-1 58.1%

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

11. Simplified 58.1%

    \[\leadsto \color{blue}{\left(-z\right)} - y \]
12. Add Preprocessing

Alternative 10: 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 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 31.3%

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

   1. mul-1-neg 31.3%

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

7. Simplified 31.3%

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

Alternative 11: 2.3% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 82.1%

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

   1. associate--l+ 82.1%

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

   2. associate-/l* 82.1%

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

7. Simplified 82.1%

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

8. Taylor expanded in y around inf 72.0%

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

10. Simplified 62.1%

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

11. Taylor expanded in z around inf 17.8%

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

    1. associate-*r/ 17.8%

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

    2. neg-mul-1 17.8%

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

13. Simplified 17.8%

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

    1. associate-*r/ 25.8%

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

15. Applied egg-rr 25.8%

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

    1. associate-/l* 17.8%

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

    2. add-sqr-sqrt 9.6%

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

    3. sqrt-unprod 7.4%

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

    4. sqr-neg 7.4%

       \[\leadsto y \cdot \frac{\sqrt{\color{blue}{z \cdot z}}}{y} \]

    5. sqrt-unprod 1.0%

       \[\leadsto y \cdot \frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{y} \]

    6. add-sqr-sqrt 2.2%

       \[\leadsto y \cdot \frac{\color{blue}{z}}{y} \]

17. Applied egg-rr 2.2%

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

    1. associate-*r/ 2.4%

       \[\leadsto \color{blue}{\frac{y \cdot z}{y}} \]

    2. *-commutative 2.4%

       \[\leadsto \frac{\color{blue}{z \cdot y}}{y} \]

    3. associate-*r/ 2.3%

       \[\leadsto \color{blue}{z \cdot \frac{y}{y}} \]

    4. *-inverses 2.3%

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

    5. *-rgt-identity 2.3%

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

19. Simplified 2.3%

    \[\leadsto \color{blue}{z} \]
20. Add Preprocessing

Alternative 12: 2.3% 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 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 82.1%

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

   1. associate--l+ 82.1%

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

   2. associate-/l* 82.1%

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

7. Simplified 82.1%

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

   1. clear-num 82.1%

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

   2. inv-pow 82.1%

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

9. Applied egg-rr 82.1%

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

    1. distribute-lft-in 82.1%

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

    2. associate--r+ 82.1%

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

    3. fma-neg 82.1%

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

    4. unpow-1 82.1%

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

    5. metadata-eval 82.1%

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

11. Applied egg-rr 82.1%

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

    1. distribute-lft-in 82.1%

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

    2. +-commutative 82.1%

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

    3. associate-+l- 82.1%

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

    4. fma-undefine 82.1%

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

    5. associate-*r/ 82.1%

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

    6. *-rgt-identity 82.1%

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

13. Simplified 82.1%

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

14. Taylor expanded in y around inf 22.1%

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

    1. neg-mul-1 22.1%

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

    2. distribute-neg-frac2 22.1%

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

16. Simplified 22.1%

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

    1. clear-num 22.0%

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

    2. un-div-inv 22.8%

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

    3. add-sqr-sqrt 10.2%

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

    4. sqrt-unprod 7.6%

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

    5. sqr-neg 7.6%

       \[\leadsto \frac{z}{\frac{\sqrt{\color{blue}{z \cdot z}}}{y}} \]

    6. sqrt-unprod 0.9%

       \[\leadsto \frac{z}{\frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{y}} \]

    7. add-sqr-sqrt 2.1%

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

18. Applied egg-rr 2.1%

    \[\leadsto \color{blue}{\frac{z}{\frac{z}{y}}} \]
19. Step-by-step derivation

    1. associate-/r/ 2.1%

       \[\leadsto \color{blue}{\frac{z}{z} \cdot y} \]

    2. *-inverses 2.1%

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

    3. *-lft-identity 2.1%

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

20. Simplified 2.1%

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

Reproduce

herbie shell --seed 2024105 
(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)))