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

Percentage Accurate: 99.9% → 99.9%

Time: 17.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. associate--l+ 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 87.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -500:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-29}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -2e+176)
     t_2
     (if (<= t_2 -500.0)
       (- (- y) z)
       (if (<= t_2 -2e-29)
         (- (log t) y)
         (if (<= t_2 5e-8) (- (log t) z) (- t_1 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -2e+176) {
		tmp = t_2;
	} else if (t_2 <= -500.0) {
		tmp = -y - z;
	} else if (t_2 <= -2e-29) {
		tmp = log(t) - y;
	} else if (t_2 <= 5e-8) {
		tmp = log(t) - z;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-2d+176)) then
        tmp = t_2
    else if (t_2 <= (-500.0d0)) then
        tmp = -y - z
    else if (t_2 <= (-2d-29)) then
        tmp = log(t) - y
    else if (t_2 <= 5d-8) then
        tmp = log(t) - z
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -2e+176) {
		tmp = t_2;
	} else if (t_2 <= -500.0) {
		tmp = -y - z;
	} else if (t_2 <= -2e-29) {
		tmp = Math.log(t) - y;
	} else if (t_2 <= 5e-8) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -2e+176:
		tmp = t_2
	elif t_2 <= -500.0:
		tmp = -y - z
	elif t_2 <= -2e-29:
		tmp = math.log(t) - y
	elif t_2 <= 5e-8:
		tmp = math.log(t) - z
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -2e+176)
		tmp = t_2;
	elseif (t_2 <= -500.0)
		tmp = Float64(Float64(-y) - z);
	elseif (t_2 <= -2e-29)
		tmp = Float64(log(t) - y);
	elseif (t_2 <= 5e-8)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -2e+176)
		tmp = t_2;
	elseif (t_2 <= -500.0)
		tmp = -y - z;
	elseif (t_2 <= -2e-29)
		tmp = log(t) - y;
	elseif (t_2 <= 5e-8)
		tmp = log(t) - z;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+176], t$95$2, If[LessEqual[t$95$2, -500.0], N[((-y) - z), $MachinePrecision], If[LessEqual[t$95$2, -2e-29], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$2, 5e-8], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -2e176

   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 85.9%

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

   if -2e176 < (-.f64 (*.f64 x (log.f64 y)) y) < -500

   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 87.8%

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

      1. +-commutative 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

      4. log-rec 87.8%

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

      5. mul-1-neg 87.8%

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

      6. associate-/l* 87.8%

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

      7. mul-1-neg 87.8%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in z around -inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in y around inf 76.0%

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

   12. Taylor expanded in y around 0 83.7%

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

       1. mul-1-neg 83.7%

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

       2. sub-neg 83.7%

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

       3. mul-1-neg 83.7%

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

   14. Simplified 83.7%

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

   if -500 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.99999999999999989e-29

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. mul-1-neg 85.5%

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

   7. Simplified 85.5%

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

   8. Taylor expanded in y around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. sub-neg 85.5%

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

   10. Simplified 85.5%

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

   if -1.99999999999999989e-29 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999998e-8

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.1%

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

      1. neg-mul-1 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in z around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. sub-neg 99.1%

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

   10. Simplified 99.1%

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

   if 4.9999999999999998e-8 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 97.5%

      \[\leadsto x \cdot \log y - \color{blue}{z} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -500:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-29}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -2e+176)
     t_1
     (if (<= t_1 -500.0)
       (- (- y) z)
       (if (<= t_1 -2e-29)
         (- (log t) y)
         (if (<= t_1 5e-8) (- (log t) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -2e+176) {
		tmp = t_1;
	} else if (t_1 <= -500.0) {
		tmp = -y - z;
	} else if (t_1 <= -2e-29) {
		tmp = log(t) - y;
	} else if (t_1 <= 5e-8) {
		tmp = log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if (t_1 <= (-2d+176)) then
        tmp = t_1
    else if (t_1 <= (-500.0d0)) then
        tmp = -y - z
    else if (t_1 <= (-2d-29)) then
        tmp = log(t) - y
    else if (t_1 <= 5d-8) then
        tmp = log(t) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if (t_1 <= -2e+176) {
		tmp = t_1;
	} else if (t_1 <= -500.0) {
		tmp = -y - z;
	} else if (t_1 <= -2e-29) {
		tmp = Math.log(t) - y;
	} else if (t_1 <= 5e-8) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if t_1 <= -2e+176:
		tmp = t_1
	elif t_1 <= -500.0:
		tmp = -y - z
	elif t_1 <= -2e-29:
		tmp = math.log(t) - y
	elif t_1 <= 5e-8:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -2e+176)
		tmp = t_1;
	elseif (t_1 <= -500.0)
		tmp = Float64(Float64(-y) - z);
	elseif (t_1 <= -2e-29)
		tmp = Float64(log(t) - y);
	elseif (t_1 <= 5e-8)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if (t_1 <= -2e+176)
		tmp = t_1;
	elseif (t_1 <= -500.0)
		tmp = -y - z;
	elseif (t_1 <= -2e-29)
		tmp = log(t) - y;
	elseif (t_1 <= 5e-8)
		tmp = log(t) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+176], t$95$1, If[LessEqual[t$95$1, -500.0], N[((-y) - z), $MachinePrecision], If[LessEqual[t$95$1, -2e-29], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$1, 5e-8], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -2e176 or 4.9999999999999998e-8 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 82.5%

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

   if -2e176 < (-.f64 (*.f64 x (log.f64 y)) y) < -500

   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 87.8%

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

      1. +-commutative 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

      4. log-rec 87.8%

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

      5. mul-1-neg 87.8%

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

      6. associate-/l* 87.8%

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

      7. mul-1-neg 87.8%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in z around -inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in y around inf 76.0%

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

   12. Taylor expanded in y around 0 83.7%

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

       1. mul-1-neg 83.7%

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

       2. sub-neg 83.7%

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

       3. mul-1-neg 83.7%

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

   14. Simplified 83.7%

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

   if -500 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.99999999999999989e-29

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. mul-1-neg 85.5%

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

   7. Simplified 85.5%

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

   8. Taylor expanded in y around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. sub-neg 85.5%

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

   10. Simplified 85.5%

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

   if -1.99999999999999989e-29 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999998e-8

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.1%

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

      1. neg-mul-1 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in z around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. sub-neg 99.1%

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

   10. Simplified 99.1%

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

Alternative 4: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. sub-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--l+ 99.9%

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

   5. sub-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-undefine 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

Alternative 5: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+91}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e+57)
   (- (* x (log y)) z)
   (if (<= x 1.22e+91) (- (- (log t) z) y) (fma (log y) x (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+57) {
		tmp = (x * log(y)) - z;
	} else if (x <= 1.22e+91) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = fma(log(y), x, -z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.3e+57)
		tmp = Float64(Float64(x * log(y)) - z);
	elseif (x <= 1.22e+91)
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = fma(log(y), x, Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.3e+57], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 1.22e+91], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999999e57

   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%

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

   if -2.2999999999999999e57 < x < 1.2199999999999999e91

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.0%

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

   if 1.2199999999999999e91 < 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 87.7%

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

      1. *-commutative 87.7%

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

      2. fma-neg 87.8%

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

   7. Applied egg-rr 87.8%

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

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 7: 70.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -4 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.22 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+159} \lor \neg \left(x \leq 3 \cdot 10^{+160}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- y) z)))
   (if (<= x -4e+130)
     t_1
     (if (<= x -1.4e+113)
       t_2
       (if (<= x -2.22e+108)
         t_1
         (if (<= x 4.1e+95)
           t_2
           (if (or (<= x 1.25e+159) (not (<= x 3e+160))) t_1 (- z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -4e+130) {
		tmp = t_1;
	} else if (x <= -1.4e+113) {
		tmp = t_2;
	} else if (x <= -2.22e+108) {
		tmp = t_1;
	} else if (x <= 4.1e+95) {
		tmp = t_2;
	} else if ((x <= 1.25e+159) || !(x <= 3e+160)) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = -y - z
    if (x <= (-4d+130)) then
        tmp = t_1
    else if (x <= (-1.4d+113)) then
        tmp = t_2
    else if (x <= (-2.22d+108)) then
        tmp = t_1
    else if (x <= 4.1d+95) then
        tmp = t_2
    else if ((x <= 1.25d+159) .or. (.not. (x <= 3d+160))) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -4e+130) {
		tmp = t_1;
	} else if (x <= -1.4e+113) {
		tmp = t_2;
	} else if (x <= -2.22e+108) {
		tmp = t_1;
	} else if (x <= 4.1e+95) {
		tmp = t_2;
	} else if ((x <= 1.25e+159) || !(x <= 3e+160)) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = -y - z
	tmp = 0
	if x <= -4e+130:
		tmp = t_1
	elif x <= -1.4e+113:
		tmp = t_2
	elif x <= -2.22e+108:
		tmp = t_1
	elif x <= 4.1e+95:
		tmp = t_2
	elif (x <= 1.25e+159) or not (x <= 3e+160):
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (x <= -4e+130)
		tmp = t_1;
	elseif (x <= -1.4e+113)
		tmp = t_2;
	elseif (x <= -2.22e+108)
		tmp = t_1;
	elseif (x <= 4.1e+95)
		tmp = t_2;
	elseif ((x <= 1.25e+159) || !(x <= 3e+160))
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = -y - z;
	tmp = 0.0;
	if (x <= -4e+130)
		tmp = t_1;
	elseif (x <= -1.4e+113)
		tmp = t_2;
	elseif (x <= -2.22e+108)
		tmp = t_1;
	elseif (x <= 4.1e+95)
		tmp = t_2;
	elseif ((x <= 1.25e+159) || ~((x <= 3e+160)))
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -4e+130], t$95$1, If[LessEqual[x, -1.4e+113], t$95$2, If[LessEqual[x, -2.22e+108], t$95$1, If[LessEqual[x, 4.1e+95], t$95$2, If[Or[LessEqual[x, 1.25e+159], N[Not[LessEqual[x, 3e+160]], $MachinePrecision]], t$95$1, (-z)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0000000000000002e130 or -1.39999999999999999e113 < x < -2.22e108 or 4.09999999999999986e95 < x < 1.25000000000000001e159 or 2.9999999999999999e160 < x

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. +-commutative 99.5%

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

      3. associate--r+ 99.5%

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

      4. div-sub 99.5%

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

      5. div-sub 99.5%

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

      6. associate--l- 99.5%

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

      7. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around inf 81.6%

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

   if -4.0000000000000002e130 < x < -1.39999999999999999e113 or -2.22e108 < x < 4.09999999999999986e95

   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 91.0%

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

      1. +-commutative 91.0%

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

      2. mul-1-neg 91.0%

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

      3. unsub-neg 91.0%

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

      4. log-rec 91.0%

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

      5. mul-1-neg 91.0%

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

      6. associate-/l* 91.0%

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

      7. mul-1-neg 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in z around -inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. *-commutative 91.0%

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

      3. distribute-rgt-neg-in 91.0%

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

   10. Simplified 74.8%

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

   11. Taylor expanded in y around inf 61.9%

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

   12. Taylor expanded in y around 0 69.7%

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

       1. mul-1-neg 69.7%

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

       2. sub-neg 69.7%

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

       3. mul-1-neg 69.7%

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

   14. Simplified 69.7%

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

   if 1.25000000000000001e159 < x < 2.9999999999999999e160

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+113}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq -2.22 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+95}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+159} \lor \neg \left(x \leq 3 \cdot 10^{+160}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) - z\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-65}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- y) z)))
   (if (<= z -1.6e+40)
     t_1
     (if (<= z -8.5e+19)
       (* x (log y))
       (if (<= z 5.9e-65) (- (log t) y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -y - z;
	double tmp;
	if (z <= -1.6e+40) {
		tmp = t_1;
	} else if (z <= -8.5e+19) {
		tmp = x * log(y);
	} else if (z <= 5.9e-65) {
		tmp = log(t) - 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 = -y - z
    if (z <= (-1.6d+40)) then
        tmp = t_1
    else if (z <= (-8.5d+19)) then
        tmp = x * log(y)
    else if (z <= 5.9d-65) then
        tmp = log(t) - 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 = -y - z;
	double tmp;
	if (z <= -1.6e+40) {
		tmp = t_1;
	} else if (z <= -8.5e+19) {
		tmp = x * Math.log(y);
	} else if (z <= 5.9e-65) {
		tmp = Math.log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -y - z
	tmp = 0
	if z <= -1.6e+40:
		tmp = t_1
	elif z <= -8.5e+19:
		tmp = x * math.log(y)
	elif z <= 5.9e-65:
		tmp = math.log(t) - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (z <= -1.6e+40)
		tmp = t_1;
	elseif (z <= -8.5e+19)
		tmp = Float64(x * log(y));
	elseif (z <= 5.9e-65)
		tmp = Float64(log(t) - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -y - z;
	tmp = 0.0;
	if (z <= -1.6e+40)
		tmp = t_1;
	elseif (z <= -8.5e+19)
		tmp = x * log(y);
	elseif (z <= 5.9e-65)
		tmp = log(t) - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[z, -1.6e+40], t$95$1, If[LessEqual[z, -8.5e+19], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e-65], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e40 or 5.89999999999999978e-65 < z

   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 74.1%

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

      1. +-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

      4. log-rec 74.1%

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

      5. mul-1-neg 74.1%

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

      6. associate-/l* 74.1%

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

      7. mul-1-neg 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in z around -inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. distribute-rgt-neg-in 85.6%

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

   10. Simplified 85.5%

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

   11. Taylor expanded in y around inf 75.5%

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

   12. Taylor expanded in y around 0 76.3%

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

       1. mul-1-neg 76.3%

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

       2. sub-neg 76.3%

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

       3. mul-1-neg 76.3%

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

   14. Simplified 76.3%

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

   if -1.5999999999999999e40 < z < -8.5e19

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate--r+ 99.3%

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

      4. div-sub 99.3%

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

      5. div-sub 99.3%

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

      6. associate--l- 99.3%

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

      7. +-commutative 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in x around inf 77.5%

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

   if -8.5e19 < z < 5.89999999999999978e-65

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate--l+ 99.8%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 69.4%

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

      1. mul-1-neg 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in y around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. sub-neg 69.4%

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

   10. Simplified 69.4%

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

Alternative 9: 89.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+57} \lor \neg \left(x \leq 2.6 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6e+57) (not (<= x 2.6e+92)))
   (- (* x (log y)) z)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e+57) || !(x <= 2.6e+92)) {
		tmp = (x * log(y)) - z;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6d+57)) .or. (.not. (x <= 2.6d+92))) then
        tmp = (x * log(y)) - z
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e+57) || !(x <= 2.6e+92)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6e+57) or not (x <= 2.6e+92):
		tmp = (x * math.log(y)) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6e+57) || !(x <= 2.6e+92))
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6e+57) || ~((x <= 2.6e+92)))
		tmp = (x * log(y)) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6e+57], N[Not[LessEqual[x, 2.6e+92]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999999e57 or 2.5999999999999999e92 < 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 87.3%

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

   if -5.9999999999999999e57 < x < 2.5999999999999999e92

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+57} \lor \neg \left(x \leq 2.6 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.0% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.9e+72) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.9e+72) {
		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 <= 2.9d+72) 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 <= 2.9e+72) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.9e+72:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.9e+72)
		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 <= 2.9e+72)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.9e+72], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.90000000000000017e72

   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 68.0%

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

   6. Taylor expanded in x around 0 32.0%

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

      1. neg-mul-1 32.0%

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

   8. Simplified 32.0%

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

   if 2.90000000000000017e72 < y

   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 67.0%

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

      1. mul-1-neg 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in y around inf 67.0%

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

      1. mul-1-neg 67.0%

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

   10. Simplified 67.0%

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

Alternative 11: 57.7% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. 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 81.0%

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

   1. +-commutative 81.0%

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

   2. mul-1-neg 81.0%

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

   3. unsub-neg 81.0%

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

   4. log-rec 81.0%

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

   5. mul-1-neg 81.0%

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

   6. associate-/l* 81.0%

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

   7. mul-1-neg 81.0%

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

7. Simplified 81.0%

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

8. Taylor expanded in z around -inf 77.6%

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

   1. mul-1-neg 77.6%

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

   2. *-commutative 77.6%

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

   3. distribute-rgt-neg-in 77.6%

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

10. Simplified 66.1%

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

11. Taylor expanded in y around inf 48.2%

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

12. Taylor expanded in y around 0 54.9%

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

    1. mul-1-neg 54.9%

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

    2. sub-neg 54.9%

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

    3. mul-1-neg 54.9%

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

14. Simplified 54.9%

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

Alternative 12: 29.6% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-y)

Derivation

1. Initial program 99.9%

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

   1. 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 47.0%

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

   1. mul-1-neg 47.0%

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

7. Simplified 47.0%

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

8. Taylor expanded in y around inf 29.8%

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

   1. mul-1-neg 29.8%

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

10. Simplified 29.8%

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

Alternative 13: 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. 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 inf 78.3%

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

   1. associate--l+ 78.3%

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

   2. +-commutative 78.3%

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

   3. associate--r+ 78.3%

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

   4. div-sub 78.3%

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

   5. div-sub 78.7%

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

   6. associate--l- 78.7%

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

   7. +-commutative 78.7%

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

7. Simplified 78.7%

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

   1. add-cube-cbrt 77.3%

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

   2. pow3 77.3%

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

9. Applied egg-rr 77.3%

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

10. Taylor expanded in x around 0 51.1%

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

    1. associate-*r/ 63.3%

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

12. Applied egg-rr 63.3%

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

    1. *-commutative 63.3%

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

14. Simplified 63.3%

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

15. Taylor expanded in y around inf 27.3%

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

    1. associate-*r* 27.3%

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

    2. neg-mul-1 27.3%

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

17. Simplified 27.3%

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

    1. *-commutative 27.3%

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

    2. associate-/l* 29.8%

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

    3. add-sqr-sqrt 12.8%

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

    4. sqrt-unprod 10.2%

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

    5. sqr-neg 10.2%

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

    6. sqrt-unprod 1.2%

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

    7. add-sqr-sqrt 2.3%

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

    8. *-inverses 2.3%

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

19. Applied egg-rr 2.3%

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

    1. *-rgt-identity 2.3%

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

21. Simplified 2.3%

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

Reproduce

herbie shell --seed 2024107 
(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)))