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

Percentage Accurate: 99.9% → 99.9%

Time: 12.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

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: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -200000000000:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;t\_2 \leq 0.02:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -4e+151)
     t_2
     (if (<= t_2 -200000000000.0)
       (- (- z) y)
       (if (<= t_2 0.02) (- (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 <= -4e+151) {
		tmp = t_2;
	} else if (t_2 <= -200000000000.0) {
		tmp = -z - y;
	} else if (t_2 <= 0.02) {
		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 <= (-4d+151)) then
        tmp = t_2
    else if (t_2 <= (-200000000000.0d0)) then
        tmp = -z - y
    else if (t_2 <= 0.02d0) 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 <= -4e+151) {
		tmp = t_2;
	} else if (t_2 <= -200000000000.0) {
		tmp = -z - y;
	} else if (t_2 <= 0.02) {
		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 <= -4e+151:
		tmp = t_2
	elif t_2 <= -200000000000.0:
		tmp = -z - y
	elif t_2 <= 0.02:
		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 <= -4e+151)
		tmp = t_2;
	elseif (t_2 <= -200000000000.0)
		tmp = Float64(Float64(-z) - y);
	elseif (t_2 <= 0.02)
		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 <= -4e+151)
		tmp = t_2;
	elseif (t_2 <= -200000000000.0)
		tmp = -z - y;
	elseif (t_2 <= 0.02)
		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, -4e+151], t$95$2, If[LessEqual[t$95$2, -200000000000.0], N[((-z) - y), $MachinePrecision], If[LessEqual[t$95$2, 0.02], 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) < -4.00000000000000007e151

   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 87.9%

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

   if -4.00000000000000007e151 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e11

   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 z around inf 97.8%

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

      1. associate--l+ 97.8%

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

      2. associate-/l* 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in z around inf 84.0%

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

   if -2e11 < (-.f64 (*.f64 x (log.f64 y)) y) < 0.0200000000000000004

   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 99.0%

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

   6. Taylor expanded in y around 0 96.0%

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

   if 0.0200000000000000004 < (-.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 96.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -4 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -200000000000:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 0.02:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -200000000000:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -4e+151)
     t_2
     (if (<= t_2 -200000000000.0)
       (- (- z) y)
       (if (<= t_2 5e+45) (- (log t) z) t_1)))))

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 <= -4e+151) {
		tmp = t_2;
	} else if (t_2 <= -200000000000.0) {
		tmp = -z - y;
	} else if (t_2 <= 5e+45) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-4d+151)) then
        tmp = t_2
    else if (t_2 <= (-200000000000.0d0)) then
        tmp = -z - y
    else if (t_2 <= 5d+45) 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);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -4e+151) {
		tmp = t_2;
	} else if (t_2 <= -200000000000.0) {
		tmp = -z - y;
	} else if (t_2 <= 5e+45) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	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 <= -4e+151:
		tmp = t_2
	elif t_2 <= -200000000000.0:
		tmp = -z - y
	elif t_2 <= 5e+45:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	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 <= -4e+151)
		tmp = t_2;
	elseif (t_2 <= -200000000000.0)
		tmp = Float64(Float64(-z) - y);
	elseif (t_2 <= 5e+45)
		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);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -4e+151)
		tmp = t_2;
	elseif (t_2 <= -200000000000.0)
		tmp = -z - y;
	elseif (t_2 <= 5e+45)
		tmp = log(t) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+151], t$95$2, If[LessEqual[t$95$2, -200000000000.0], N[((-z) - y), $MachinePrecision], If[LessEqual[t$95$2, 5e+45], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -4.00000000000000007e151

   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 87.9%

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

   if -4.00000000000000007e151 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e11

   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 z around inf 97.8%

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

      1. associate--l+ 97.8%

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

      2. associate-/l* 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in z around inf 84.0%

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

   if -2e11 < (-.f64 (*.f64 x (log.f64 y)) y) < 5e45

   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 92.8%

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

   6. Taylor expanded in y around 0 90.2%

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

   if 5e45 < (-.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. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 84.6%

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

   6. Taylor expanded in x around inf 84.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -4 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -200000000000:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;x \leq 3700000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t\_1\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.6e+53)
     (- t_1 y)
     (if (<= x 3700000000000.0) (- (- (log t) z) y) (- (+ (log t) t_1) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.6e+53) {
		tmp = t_1 - y;
	} else if (x <= 3700000000000.0) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = (log(t) + 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) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.6d+53)) then
        tmp = t_1 - y
    else if (x <= 3700000000000.0d0) then
        tmp = (log(t) - z) - y
    else
        tmp = (log(t) + 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 tmp;
	if (x <= -1.6e+53) {
		tmp = t_1 - y;
	} else if (x <= 3700000000000.0) {
		tmp = (Math.log(t) - z) - y;
	} else {
		tmp = (Math.log(t) + t_1) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.6e+53:
		tmp = t_1 - y
	elif x <= 3700000000000.0:
		tmp = (math.log(t) - z) - y
	else:
		tmp = (math.log(t) + t_1) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.6e+53)
		tmp = Float64(t_1 - y);
	elseif (x <= 3700000000000.0)
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = Float64(Float64(log(t) + t_1) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.6e+53)
		tmp = t_1 - y;
	elseif (x <= 3700000000000.0)
		tmp = (log(t) - z) - y;
	else
		tmp = (log(t) + 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]}, If[LessEqual[x, -1.6e+53], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, 3700000000000.0], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e53

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 93.7%

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

   if -1.6e53 < x < 3.7e12

   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 96.5%

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

   if 3.7e12 < x

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 85.6%

      \[\leadsto \color{blue}{\left(\log t + x \cdot \log y\right) - z} \]
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: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;x \leq 3800000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.95e+51)
     (- t_1 y)
     (if (<= x 3800000000000.0) (- (- (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 tmp;
	if (x <= -2.95e+51) {
		tmp = t_1 - y;
	} else if (x <= 3800000000000.0) {
		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) :: tmp
    t_1 = x * log(y)
    if (x <= (-2.95d+51)) then
        tmp = t_1 - y
    else if (x <= 3800000000000.0d0) 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 tmp;
	if (x <= -2.95e+51) {
		tmp = t_1 - y;
	} else if (x <= 3800000000000.0) {
		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)
	tmp = 0
	if x <= -2.95e+51:
		tmp = t_1 - y
	elif x <= 3800000000000.0:
		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))
	tmp = 0.0
	if (x <= -2.95e+51)
		tmp = Float64(t_1 - y);
	elseif (x <= 3800000000000.0)
		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);
	tmp = 0.0;
	if (x <= -2.95e+51)
		tmp = t_1 - y;
	elseif (x <= 3800000000000.0)
		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]}, If[LessEqual[x, -2.95e+51], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, 3800000000000.0], 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 x < -2.94999999999999991e51

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 93.7%

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

   if -2.94999999999999991e51 < x < 3.8e12

   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 96.5%

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

   if 3.8e12 < 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 z around inf 85.2%

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

Alternative 8: 71.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+170} \lor \neg \left(x \leq 3 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.2e+170) (not (<= x 3e+128))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+170) || !(x <= 3e+128)) {
		tmp = x * log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.2d+170)) .or. (.not. (x <= 3d+128))) then
        tmp = x * log(y)
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+170) || !(x <= 3e+128)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.2e+170) or not (x <= 3e+128):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.2e+170) || !(x <= 3e+128))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.2e+170) || ~((x <= 3e+128)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.2e+170], N[Not[LessEqual[x, 3e+128]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1999999999999996e170 or 2.9999999999999998e128 < x

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 77.5%

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

   6. Taylor expanded in x around inf 77.5%

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

   if -5.1999999999999996e170 < x < 2.9999999999999998e128

   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 z around inf 96.8%

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

      1. associate--l+ 96.8%

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

      2. associate-/l* 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in z around inf 71.1%

      \[\leadsto z \cdot \color{blue}{-1} - y \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+170} \lor \neg \left(x \leq 3 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{-219}:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.95e-219) (log t) (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.95e-219) {
		tmp = log(t);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.95d-219) then
        tmp = log(t)
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.95e-219) {
		tmp = Math.log(t);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.95e-219:
		tmp = math.log(t)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.95e-219)
		tmp = log(t);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.95e-219)
		tmp = log(t);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.95e-219], N[Log[t], $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.94999999999999994e-219

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. associate--l+ 99.7%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 44.3%

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

      1. mul-1-neg 44.3%

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

   7. Simplified 44.3%

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

   8. Taylor expanded in y around 0 44.3%

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

   if 1.94999999999999994e-219 < 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 z around inf 89.3%

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

      1. associate--l+ 89.3%

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

      2. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in z around inf 63.2%

      \[\leadsto z \cdot \color{blue}{-1} - y \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{-219}:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.5% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.2 \cdot 10^{+101}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 9.2e+101) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.2e+101) {
		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 <= 9.2d+101) 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 <= 9.2e+101) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.2e+101:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.2e+101)
		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 <= 9.2e+101)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.2e+101], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 9.2000000000000005e101

   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 x around 0 65.2%

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

   6. Taylor expanded in z around inf 36.6%

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

      1. neg-mul-1 36.6%

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

   8. Simplified 36.6%

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

   if 9.2000000000000005e101 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate--l+ 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 69.6%

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

      1. mul-1-neg 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in y around inf 69.6%

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

      1. mul-1-neg 69.6%

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

   10. Simplified 69.6%

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

Alternative 11: 57.9% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
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 89.2%

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

   1. associate--l+ 89.2%

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

   2. associate-/l* 89.2%

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

7. Simplified 89.2%

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

8. Taylor expanded in z around inf 57.1%

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

9. Final simplification 57.1%

   \[\leadsto \left(-z\right) - y \]
10. Add Preprocessing

Alternative 12: 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. sub-neg 99.8%

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

   2. associate--l+ 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 44.1%

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

   1. mul-1-neg 44.1%

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

7. Simplified 44.1%

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

8. Taylor expanded in y around inf 31.0%

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

   1. mul-1-neg 31.0%

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

10. Simplified 31.0%

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

Alternative 13: 2.3% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. sub-neg 99.8%

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

   2. associate--l+ 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 44.1%

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

   1. mul-1-neg 44.1%

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

7. Simplified 44.1%

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

8. Taylor expanded in y around inf 31.0%

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

   1. mul-1-neg 31.0%

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

10. Simplified 31.0%

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

    1. add-sqr-sqrt 0.0%

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

    2. sqrt-unprod 2.1%

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

    3. sqr-neg 2.1%

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

    4. sqrt-unprod 2.2%

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

    5. add-sqr-sqrt 2.2%

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

    6. add-exp-log 2.2%

       \[\leadsto \color{blue}{e^{\log y}} \]

    7. add-cube-cbrt 2.2%

       \[\leadsto e^{\log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)}} \]

    8. unpow2 2.2%

       \[\leadsto e^{\log \left(\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \sqrt[3]{y}\right)} \]

    9. sum-log 2.2%

       \[\leadsto e^{\color{blue}{\log \left({\left(\sqrt[3]{y}\right)}^{2}\right) + \log \left(\sqrt[3]{y}\right)}} \]

    10. +-commutative 2.2%

        \[\leadsto e^{\color{blue}{\log \left(\sqrt[3]{y}\right) + \log \left({\left(\sqrt[3]{y}\right)}^{2}\right)}} \]

    11. exp-sum 2.2%

        \[\leadsto \color{blue}{e^{\log \left(\sqrt[3]{y}\right)} \cdot e^{\log \left({\left(\sqrt[3]{y}\right)}^{2}\right)}} \]

    12. add-exp-log 2.2%

        \[\leadsto \color{blue}{\sqrt[3]{y}} \cdot e^{\log \left({\left(\sqrt[3]{y}\right)}^{2}\right)} \]

    13. add-exp-log 2.2%

        \[\leadsto \sqrt[3]{y} \cdot \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \]

12. Applied egg-rr 2.2%

    \[\leadsto \color{blue}{\sqrt[3]{y} \cdot {\left(\sqrt[3]{y}\right)}^{2}} \]
13. Step-by-step derivation

    1. unpow2 2.2%

       \[\leadsto \sqrt[3]{y} \cdot \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \]

    2. rem-3cbrt-rft 2.2%

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

14. Simplified 2.2%

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

Reproduce

herbie shell --seed 2024152 
(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)))