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

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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. sub-neg 99.8%

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

   3. +-commutative 99.8%

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

   4. associate--l+ 99.8%

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

   5. sub-neg 99.8%

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

   6. +-commutative 99.8%

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

   7. unsub-neg 99.8%

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

   8. fma-undefine 99.8%

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

   9. neg-sub0 99.8%

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

   10. associate-+l- 99.8%

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

   11. neg-sub0 99.8%

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

   12. +-commutative 99.8%

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

   13. unsub-neg 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -20000000000000:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{elif}\;t\_2 \leq 10:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -2e+105)
     t_2
     (if (<= t_2 -20000000000000.0)
       (- (* x (/ z (- x))) y)
       (if (<= t_2 10.0) (- (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+105) {
		tmp = t_2;
	} else if (t_2 <= -20000000000000.0) {
		tmp = (x * (z / -x)) - y;
	} else if (t_2 <= 10.0) {
		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+105)) then
        tmp = t_2
    else if (t_2 <= (-20000000000000.0d0)) then
        tmp = (x * (z / -x)) - y
    else if (t_2 <= 10.0d0) 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+105) {
		tmp = t_2;
	} else if (t_2 <= -20000000000000.0) {
		tmp = (x * (z / -x)) - y;
	} else if (t_2 <= 10.0) {
		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+105:
		tmp = t_2
	elif t_2 <= -20000000000000.0:
		tmp = (x * (z / -x)) - y
	elif t_2 <= 10.0:
		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+105)
		tmp = t_2;
	elseif (t_2 <= -20000000000000.0)
		tmp = Float64(Float64(x * Float64(z / Float64(-x))) - y);
	elseif (t_2 <= 10.0)
		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+105)
		tmp = t_2;
	elseif (t_2 <= -20000000000000.0)
		tmp = (x * (z / -x)) - y;
	elseif (t_2 <= 10.0)
		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+105], t$95$2, If[LessEqual[t$95$2, -20000000000000.0], N[(N[(x * N[(z / (-x)), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$2, 10.0], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999999e105

   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 88.5%

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

   if -1.9999999999999999e105 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e13

   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 inf 94.2%

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

      1. associate--l+ 94.2%

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

      2. div-sub 94.2%

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

   7. Simplified 94.2%

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

   8. Taylor expanded in z around inf 77.2%

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

      1. neg-mul-1 77.2%

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

      2. distribute-neg-frac 77.2%

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

   10. Simplified 77.2%

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

   if -2e13 < (-.f64 (*.f64 x (log.f64 y)) y) < 10

   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. Taylor expanded in x around 0 97.9%

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

   6. Taylor expanded in y around 0 95.8%

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

   if 10 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 95.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -20000000000000:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 10:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -20000000000000:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -2e+105)
     t_1
     (if (<= t_1 -20000000000000.0)
       (- (* x (/ z (- x))) y)
       (if (<= t_1 10.0) (- (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+105) {
		tmp = t_1;
	} else if (t_1 <= -20000000000000.0) {
		tmp = (x * (z / -x)) - y;
	} else if (t_1 <= 10.0) {
		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+105)) then
        tmp = t_1
    else if (t_1 <= (-20000000000000.0d0)) then
        tmp = (x * (z / -x)) - y
    else if (t_1 <= 10.0d0) 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+105) {
		tmp = t_1;
	} else if (t_1 <= -20000000000000.0) {
		tmp = (x * (z / -x)) - y;
	} else if (t_1 <= 10.0) {
		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+105:
		tmp = t_1
	elif t_1 <= -20000000000000.0:
		tmp = (x * (z / -x)) - y
	elif t_1 <= 10.0:
		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+105)
		tmp = t_1;
	elseif (t_1 <= -20000000000000.0)
		tmp = Float64(Float64(x * Float64(z / Float64(-x))) - y);
	elseif (t_1 <= 10.0)
		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+105)
		tmp = t_1;
	elseif (t_1 <= -20000000000000.0)
		tmp = (x * (z / -x)) - y;
	elseif (t_1 <= 10.0)
		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+105], t$95$1, If[LessEqual[t$95$1, -20000000000000.0], N[(N[(x * N[(z / (-x)), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$1, 10.0], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999999e105 or 10 < (-.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 84.0%

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

   if -1.9999999999999999e105 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e13

   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 inf 94.2%

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

      1. associate--l+ 94.2%

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

      2. div-sub 94.2%

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

   7. Simplified 94.2%

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

   8. Taylor expanded in z around inf 77.2%

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

      1. neg-mul-1 77.2%

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

      2. distribute-neg-frac 77.2%

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

   10. Simplified 77.2%

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

   if -2e13 < (-.f64 (*.f64 x (log.f64 y)) y) < 10

   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. Taylor expanded in x around 0 97.9%

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

   6. Taylor expanded in y around 0 95.8%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -20000000000000:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 10:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -2e+105) t_2 (if (<= t_2 10.0) (- (- (log t) z) y) (- 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+105) {
		tmp = t_2;
	} else if (t_2 <= 10.0) {
		tmp = (log(t) - z) - y;
	} 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+105)) then
        tmp = t_2
    else if (t_2 <= 10.0d0) then
        tmp = (log(t) - z) - y
    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+105) {
		tmp = t_2;
	} else if (t_2 <= 10.0) {
		tmp = (Math.log(t) - z) - y;
	} 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+105:
		tmp = t_2
	elif t_2 <= 10.0:
		tmp = (math.log(t) - z) - y
	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+105)
		tmp = t_2;
	elseif (t_2 <= 10.0)
		tmp = Float64(Float64(log(t) - z) - y);
	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+105)
		tmp = t_2;
	elseif (t_2 <= 10.0)
		tmp = (log(t) - z) - y;
	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+105], t$95$2, If[LessEqual[t$95$2, 10.0], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999999e105

   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 88.5%

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

   if -1.9999999999999999e105 < (-.f64 (*.f64 x (log.f64 y)) y) < 10

   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+ 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 92.6%

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

   if 10 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 95.8%

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

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

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(x * log(y)) - Float64(y + Float64(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[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + N[(z - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   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. 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 7: 65.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := x \cdot \frac{z}{-x} - y\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-248}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-45}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (* x (/ z (- x))) y)))
   (if (<= x -2.15e+136)
     t_1
     (if (<= x -7e-115)
       t_2
       (if (<= x 1.46e-248)
         (- (log t) y)
         (if (<= x 2e-45) (- (log t) z) (if (<= x 1.62e+109) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (x * (z / -x)) - y;
	double tmp;
	if (x <= -2.15e+136) {
		tmp = t_1;
	} else if (x <= -7e-115) {
		tmp = t_2;
	} else if (x <= 1.46e-248) {
		tmp = log(t) - y;
	} else if (x <= 2e-45) {
		tmp = log(t) - z;
	} else if (x <= 1.62e+109) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (x * (z / -x)) - y
    if (x <= (-2.15d+136)) then
        tmp = t_1
    else if (x <= (-7d-115)) then
        tmp = t_2
    else if (x <= 1.46d-248) then
        tmp = log(t) - y
    else if (x <= 2d-45) then
        tmp = log(t) - z
    else if (x <= 1.62d+109) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = (x * (z / -x)) - y;
	double tmp;
	if (x <= -2.15e+136) {
		tmp = t_1;
	} else if (x <= -7e-115) {
		tmp = t_2;
	} else if (x <= 1.46e-248) {
		tmp = Math.log(t) - y;
	} else if (x <= 2e-45) {
		tmp = Math.log(t) - z;
	} else if (x <= 1.62e+109) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = (x * (z / -x)) - y
	tmp = 0
	if x <= -2.15e+136:
		tmp = t_1
	elif x <= -7e-115:
		tmp = t_2
	elif x <= 1.46e-248:
		tmp = math.log(t) - y
	elif x <= 2e-45:
		tmp = math.log(t) - z
	elif x <= 1.62e+109:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(x * Float64(z / Float64(-x))) - y)
	tmp = 0.0
	if (x <= -2.15e+136)
		tmp = t_1;
	elseif (x <= -7e-115)
		tmp = t_2;
	elseif (x <= 1.46e-248)
		tmp = Float64(log(t) - y);
	elseif (x <= 2e-45)
		tmp = Float64(log(t) - z);
	elseif (x <= 1.62e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = (x * (z / -x)) - y;
	tmp = 0.0;
	if (x <= -2.15e+136)
		tmp = t_1;
	elseif (x <= -7e-115)
		tmp = t_2;
	elseif (x <= 1.46e-248)
		tmp = log(t) - y;
	elseif (x <= 2e-45)
		tmp = log(t) - z;
	elseif (x <= 1.62e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(z / (-x)), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -2.15e+136], t$95$1, If[LessEqual[x, -7e-115], t$95$2, If[LessEqual[x, 1.46e-248], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 2e-45], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 1.62e+109], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1499999999999999e136 or 1.62e109 < x

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 89.9%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -2.1499999999999999e136 < x < -7.0000000000000004e-115 or 1.99999999999999997e-45 < x < 1.62e109

   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. Taylor expanded in x around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 71.7%

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

      1. neg-mul-1 71.7%

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

      2. distribute-neg-frac 71.7%

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

   10. Simplified 71.7%

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

   if -7.0000000000000004e-115 < x < 1.4599999999999999e-248

   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 0 100.0%

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

   6. Taylor expanded in z around 0 75.5%

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

   if 1.4599999999999999e-248 < x < 1.99999999999999997e-45

   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 0 100.0%

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

   6. Taylor expanded in y around 0 80.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-248}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-45}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := x \cdot \frac{z}{-x} - y\\ \mathbf{if}\;x \leq -4 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-185}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (* x (/ z (- x))) y)))
   (if (<= x -4e+135)
     t_1
     (if (<= x -3.6e-115)
       t_2
       (if (<= x 2.45e-185)
         (- (log t) y)
         (if (<= x 1.85e-45) (- z) (if (<= x 2.1e+108) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (x * (z / -x)) - y;
	double tmp;
	if (x <= -4e+135) {
		tmp = t_1;
	} else if (x <= -3.6e-115) {
		tmp = t_2;
	} else if (x <= 2.45e-185) {
		tmp = log(t) - y;
	} else if (x <= 1.85e-45) {
		tmp = -z;
	} else if (x <= 2.1e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (x * (z / -x)) - y
    if (x <= (-4d+135)) then
        tmp = t_1
    else if (x <= (-3.6d-115)) then
        tmp = t_2
    else if (x <= 2.45d-185) then
        tmp = log(t) - y
    else if (x <= 1.85d-45) then
        tmp = -z
    else if (x <= 2.1d+108) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = (x * (z / -x)) - y;
	double tmp;
	if (x <= -4e+135) {
		tmp = t_1;
	} else if (x <= -3.6e-115) {
		tmp = t_2;
	} else if (x <= 2.45e-185) {
		tmp = Math.log(t) - y;
	} else if (x <= 1.85e-45) {
		tmp = -z;
	} else if (x <= 2.1e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = (x * (z / -x)) - y
	tmp = 0
	if x <= -4e+135:
		tmp = t_1
	elif x <= -3.6e-115:
		tmp = t_2
	elif x <= 2.45e-185:
		tmp = math.log(t) - y
	elif x <= 1.85e-45:
		tmp = -z
	elif x <= 2.1e+108:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(x * Float64(z / Float64(-x))) - y)
	tmp = 0.0
	if (x <= -4e+135)
		tmp = t_1;
	elseif (x <= -3.6e-115)
		tmp = t_2;
	elseif (x <= 2.45e-185)
		tmp = Float64(log(t) - y);
	elseif (x <= 1.85e-45)
		tmp = Float64(-z);
	elseif (x <= 2.1e+108)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = (x * (z / -x)) - y;
	tmp = 0.0;
	if (x <= -4e+135)
		tmp = t_1;
	elseif (x <= -3.6e-115)
		tmp = t_2;
	elseif (x <= 2.45e-185)
		tmp = log(t) - y;
	elseif (x <= 1.85e-45)
		tmp = -z;
	elseif (x <= 2.1e+108)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(z / (-x)), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -4e+135], t$95$1, If[LessEqual[x, -3.6e-115], t$95$2, If[LessEqual[x, 2.45e-185], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 1.85e-45], (-z), If[LessEqual[x, 2.1e+108], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.99999999999999985e135 or 2.1000000000000001e108 < x

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 89.9%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -3.99999999999999985e135 < x < -3.60000000000000009e-115 or 1.85e-45 < x < 2.1000000000000001e108

   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. Taylor expanded in x around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 71.7%

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

      1. neg-mul-1 71.7%

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

      2. distribute-neg-frac 71.7%

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

   10. Simplified 71.7%

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

   if -3.60000000000000009e-115 < x < 2.4500000000000001e-185

   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. Taylor expanded in x around 0 99.9%

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

   6. Taylor expanded in z around 0 73.2%

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

   if 2.4500000000000001e-185 < x < 1.85e-45

   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 z around inf 62.6%

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

      1. neg-mul-1 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-185}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10500 \lor \neg \left(x \leq 15500\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{\log y}{z} + \frac{-1}{x}\right)\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -10500.0) (not (<= x 15500.0)))
   (- (* x (* z (+ (/ (log y) z) (/ -1.0 x)))) y)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -10500.0) || !(x <= 15500.0)) {
		tmp = (x * (z * ((log(y) / z) + (-1.0 / x)))) - y;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-10500.0d0)) .or. (.not. (x <= 15500.0d0))) then
        tmp = (x * (z * ((log(y) / z) + ((-1.0d0) / x)))) - y
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -10500.0) || !(x <= 15500.0)) {
		tmp = (x * (z * ((Math.log(y) / z) + (-1.0 / x)))) - y;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -10500.0) or not (x <= 15500.0):
		tmp = (x * (z * ((math.log(y) / z) + (-1.0 / x)))) - y
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -10500.0) || !(x <= 15500.0))
		tmp = Float64(Float64(x * Float64(z * Float64(Float64(log(y) / z) + Float64(-1.0 / x)))) - y);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -10500.0) || ~((x <= 15500.0)))
		tmp = (x * (z * ((log(y) / z) + (-1.0 / x)))) - y;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -10500.0], N[Not[LessEqual[x, 15500.0]], $MachinePrecision]], N[(N[(x * N[(z * N[(N[(N[Log[y], $MachinePrecision] / z), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -10500 or 15500 < 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. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. +-commutative 99.7%

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

      7. unsub-neg 99.7%

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

      8. fma-undefine 99.7%

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

      9. neg-sub0 99.7%

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

      10. associate-+l- 99.7%

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

      11. neg-sub0 99.7%

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

      12. +-commutative 99.7%

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

      13. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. div-sub 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. mul-1-neg 99.6%

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

      6. unsub-neg 99.6%

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

   10. Simplified 99.6%

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

   11. Taylor expanded in x around inf 98.9%

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

   if -10500 < x < 15500

   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+ 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 98.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10500 \lor \neg \left(x \leq 15500\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{\log y}{z} + \frac{-1}{x}\right)\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+135} \lor \neg \left(x \leq 1.7 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.1e+135) (not (<= x 1.7e+109)))
   (* x (log y))
   (- (* x (/ z (- x))) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e+135) || !(x <= 1.7e+109)) {
		tmp = x * log(y);
	} else {
		tmp = (x * (z / -x)) - 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 <= (-4.1d+135)) .or. (.not. (x <= 1.7d+109))) then
        tmp = x * log(y)
    else
        tmp = (x * (z / -x)) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e+135) || !(x <= 1.7e+109)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (x * (z / -x)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.1e+135) or not (x <= 1.7e+109):
		tmp = x * math.log(y)
	else:
		tmp = (x * (z / -x)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.1e+135) || !(x <= 1.7e+109))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(x * Float64(z / Float64(-x))) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.1e+135) || ~((x <= 1.7e+109)))
		tmp = x * log(y);
	else
		tmp = (x * (z / -x)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.1e+135], N[Not[LessEqual[x, 1.7e+109]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(z / (-x)), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1e135 or 1.70000000000000003e109 < x

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 89.9%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -4.1e135 < x < 1.70000000000000003e109

   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. Taylor expanded in x around inf 85.9%

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

      1. associate--l+ 85.9%

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

      2. div-sub 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in z around inf 58.9%

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

      1. neg-mul-1 58.9%

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

      2. distribute-neg-frac 58.9%

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

   10. Simplified 58.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+135} \lor \neg \left(x \leq 1.7 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.5% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 295000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 295000000.0) (- z) (- (* x (/ z (- x))) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 295000000.0) {
		tmp = -z;
	} else {
		tmp = (x * (z / -x)) - 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 <= 295000000.0d0) then
        tmp = -z
    else
        tmp = (x * (z / -x)) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 295000000.0) {
		tmp = -z;
	} else {
		tmp = (x * (z / -x)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 295000000.0:
		tmp = -z
	else:
		tmp = (x * (z / -x)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 295000000.0)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * Float64(z / Float64(-x))) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 295000000.0)
		tmp = -z;
	else
		tmp = (x * (z / -x)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 295000000.0], (-z), N[(N[(x * N[(z / (-x)), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.95e8

   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. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-undefine 99.8%

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

      9. neg-sub0 99.8%

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

      10. associate-+l- 99.8%

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

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 37.6%

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

      1. neg-mul-1 37.6%

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

   7. Simplified 37.6%

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

   if 2.95e8 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      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. Taylor expanded in x around inf 89.2%

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

      1. associate--l+ 89.2%

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

      2. div-sub 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in z around inf 66.8%

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

      1. neg-mul-1 66.8%

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

      2. distribute-neg-frac 66.8%

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

   10. Simplified 66.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 295000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-x} - y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.4% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2650000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2650000000.0) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2650000000.0) {
		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 <= 2650000000.0d0) 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 <= 2650000000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2650000000.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2650000000.0)
		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 <= 2650000000.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2650000000.0], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.65e9

   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. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-undefine 99.8%

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

      9. neg-sub0 99.8%

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

      10. associate-+l- 99.8%

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

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 37.6%

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

      1. neg-mul-1 37.6%

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

   7. Simplified 37.6%

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

   if 2.65e9 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      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. Taylor expanded in y around inf 61.3%

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

      1. neg-mul-1 61.3%

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

   7. Simplified 61.3%

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

Alternative 13: 30.0% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   2. sub-neg 99.8%

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

   3. +-commutative 99.8%

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

   4. associate--l+ 99.8%

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

   5. sub-neg 99.8%

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

   6. +-commutative 99.8%

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

   7. unsub-neg 99.8%

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

   8. fma-undefine 99.8%

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

   9. neg-sub0 99.8%

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

   10. associate-+l- 99.8%

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

   11. neg-sub0 99.8%

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

   12. +-commutative 99.8%

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

   13. unsub-neg 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 31.3%

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

   1. neg-mul-1 31.3%

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

7. Simplified 31.3%

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

Alternative 14: 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 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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. sub-neg 99.8%

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

   3. +-commutative 99.8%

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

   4. associate--l+ 99.8%

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

   5. sub-neg 99.8%

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

   6. +-commutative 99.8%

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

   7. unsub-neg 99.8%

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

   8. fma-undefine 99.8%

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

   9. neg-sub0 99.8%

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

   10. associate-+l- 99.8%

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

   11. neg-sub0 99.8%

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

   12. +-commutative 99.8%

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

   13. unsub-neg 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 27.5%

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

   1. neg-mul-1 27.5%

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

7. Simplified 27.5%

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

   1. neg-sub0 27.5%

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

   2. sub-neg 27.5%

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

   3. add-sqr-sqrt 10.1%

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

   4. sqrt-unprod 4.6%

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

   5. sqr-neg 4.6%

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

   6. sqrt-unprod 0.9%

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

   7. add-sqr-sqrt 2.3%

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

9. Applied egg-rr 2.3%

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

    1. +-lft-identity 2.3%

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

11. Simplified 2.3%

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

Alternative 15: 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 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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. sub-neg 99.8%

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

   3. +-commutative 99.8%

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

   4. associate--l+ 99.8%

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

   5. sub-neg 99.8%

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

   6. +-commutative 99.8%

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

   7. unsub-neg 99.8%

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

   8. fma-undefine 99.8%

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

   9. neg-sub0 99.8%

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

   10. associate-+l- 99.8%

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

   11. neg-sub0 99.8%

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

   12. +-commutative 99.8%

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

   13. unsub-neg 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 31.3%

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

   1. neg-mul-1 31.3%

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

7. Simplified 31.3%

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

   1. neg-sub0 31.3%

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

   2. sub-neg 31.3%

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

   3. add-sqr-sqrt 0.0%

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

   4. sqrt-unprod 2.1%

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

   5. sqr-neg 2.1%

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

   6. sqrt-unprod 2.1%

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

   7. add-sqr-sqrt 2.1%

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

9. Applied egg-rr 2.1%

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

    1. +-lft-identity 2.1%

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

11. Simplified 2.1%

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

Reproduce

herbie shell --seed 2024163 
(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)))