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

Percentage Accurate: 99.9% → 99.9%

Time: 14.8s

Alternatives: 14

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 99.9%

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

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

   3. sub-neg 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   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-udef 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. Final simplification 99.9%

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

Alternative 2: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq -1000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+34}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)) (t_2 (- (- y) z)))
   (if (<= t_1 -5e+222)
     t_1
     (if (<= t_1 -2e+68)
       t_2
       (if (<= t_1 -5.4e+42)
         t_1
         (if (<= t_1 -1000.0) t_2 (if (<= t_1 1e+34) (- (log t) z) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double t_2 = -y - z;
	double tmp;
	if (t_1 <= -5e+222) {
		tmp = t_1;
	} else if (t_1 <= -2e+68) {
		tmp = t_2;
	} else if (t_1 <= -5.4e+42) {
		tmp = t_1;
	} else if (t_1 <= -1000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+34) {
		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)) - y
    t_2 = -y - z
    if (t_1 <= (-5d+222)) then
        tmp = t_1
    else if (t_1 <= (-2d+68)) then
        tmp = t_2
    else if (t_1 <= (-5.4d+42)) then
        tmp = t_1
    else if (t_1 <= (-1000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1d+34) 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 t_2 = -y - z;
	double tmp;
	if (t_1 <= -5e+222) {
		tmp = t_1;
	} else if (t_1 <= -2e+68) {
		tmp = t_2;
	} else if (t_1 <= -5.4e+42) {
		tmp = t_1;
	} else if (t_1 <= -1000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+34) {
		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
	t_2 = -y - z
	tmp = 0
	if t_1 <= -5e+222:
		tmp = t_1
	elif t_1 <= -2e+68:
		tmp = t_2
	elif t_1 <= -5.4e+42:
		tmp = t_1
	elif t_1 <= -1000.0:
		tmp = t_2
	elif t_1 <= 1e+34:
		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)
	t_2 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (t_1 <= -5e+222)
		tmp = t_1;
	elseif (t_1 <= -2e+68)
		tmp = t_2;
	elseif (t_1 <= -5.4e+42)
		tmp = t_1;
	elseif (t_1 <= -1000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+34)
		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;
	t_2 = -y - z;
	tmp = 0.0;
	if (t_1 <= -5e+222)
		tmp = t_1;
	elseif (t_1 <= -2e+68)
		tmp = t_2;
	elseif (t_1 <= -5.4e+42)
		tmp = t_1;
	elseif (t_1 <= -1000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+34)
		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]}, Block[{t$95$2 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+222], t$95$1, If[LessEqual[t$95$1, -2e+68], t$95$2, If[LessEqual[t$95$1, -5.4e+42], t$95$1, If[LessEqual[t$95$1, -1000.0], t$95$2, If[LessEqual[t$95$1, 1e+34], 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) < -5.00000000000000023e222 or -1.99999999999999991e68 < (-.f64 (*.f64 x (log.f64 y)) y) < -5.4000000000000001e42 or 9.99999999999999946e33 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. add-cube-cbrt 98.8%

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

      2. pow3 98.8%

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

   7. Applied egg-rr 98.8%

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

   8. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right) - y} \]
   9. Step-by-step derivation

      1. pow-base-1 88.9%

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

      2. *-lft-identity 88.9%

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

   10. Simplified 88.9%

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

   if -5.00000000000000023e222 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.99999999999999991e68 or -5.4000000000000001e42 < (-.f64 (*.f64 x (log.f64 y)) y) < -1e3

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 96.2%

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

      1. add-cube-cbrt 96.0%

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

      2. pow3 96.0%

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

   7. Applied egg-rr 96.0%

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

   8. Taylor expanded in x around 0 79.6%

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

      1. neg-mul-1 79.6%

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

      2. neg-sub0 79.6%

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

      3. associate--r+ 79.6%

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

      4. neg-sub0 79.6%

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

   10. Simplified 79.6%

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

   if -1e3 < (-.f64 (*.f64 x (log.f64 y)) y) < 9.99999999999999946e33

   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%

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

   3. Simplified 99.9%

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

      1. add-log-exp 55.9%

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

      2. associate--r- 55.9%

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

      3. exp-sum 55.9%

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

      4. associate--l- 55.9%

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

      5. add-exp-log 55.9%

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

   6. Applied egg-rr 55.9%

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

   7. Taylor expanded in x around 0 54.8%

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

      1. distribute-neg-in 54.8%

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

      2. unsub-neg 54.8%

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

   9. Simplified 54.8%

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

   10. Taylor expanded in y around 0 53.0%

       \[\leadsto \color{blue}{\log \left(t \cdot e^{-z}\right)} \]
   11. Step-by-step derivation

       1. log-prod 53.0%

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

       2. rem-log-exp 94.7%

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

       3. sub-neg 94.7%

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

   12. Simplified 94.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -1000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq 10^{+34}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t_1 - y\\ t_3 := \left(-y\right) - z\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{+68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq -1000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0.02:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)) (t_3 (- (- y) z)))
   (if (<= t_2 -5e+222)
     t_2
     (if (<= t_2 -2e+68)
       t_3
       (if (<= t_2 -5.4e+42)
         t_2
         (if (<= t_2 -1000.0)
           t_3
           (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 t_3 = -y - z;
	double tmp;
	if (t_2 <= -5e+222) {
		tmp = t_2;
	} else if (t_2 <= -2e+68) {
		tmp = t_3;
	} else if (t_2 <= -5.4e+42) {
		tmp = t_2;
	} else if (t_2 <= -1000.0) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    t_3 = -y - z
    if (t_2 <= (-5d+222)) then
        tmp = t_2
    else if (t_2 <= (-2d+68)) then
        tmp = t_3
    else if (t_2 <= (-5.4d+42)) then
        tmp = t_2
    else if (t_2 <= (-1000.0d0)) then
        tmp = t_3
    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 t_3 = -y - z;
	double tmp;
	if (t_2 <= -5e+222) {
		tmp = t_2;
	} else if (t_2 <= -2e+68) {
		tmp = t_3;
	} else if (t_2 <= -5.4e+42) {
		tmp = t_2;
	} else if (t_2 <= -1000.0) {
		tmp = t_3;
	} 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
	t_3 = -y - z
	tmp = 0
	if t_2 <= -5e+222:
		tmp = t_2
	elif t_2 <= -2e+68:
		tmp = t_3
	elif t_2 <= -5.4e+42:
		tmp = t_2
	elif t_2 <= -1000.0:
		tmp = t_3
	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)
	t_3 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (t_2 <= -5e+222)
		tmp = t_2;
	elseif (t_2 <= -2e+68)
		tmp = t_3;
	elseif (t_2 <= -5.4e+42)
		tmp = t_2;
	elseif (t_2 <= -1000.0)
		tmp = t_3;
	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;
	t_3 = -y - z;
	tmp = 0.0;
	if (t_2 <= -5e+222)
		tmp = t_2;
	elseif (t_2 <= -2e+68)
		tmp = t_3;
	elseif (t_2 <= -5.4e+42)
		tmp = t_2;
	elseif (t_2 <= -1000.0)
		tmp = t_3;
	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]}, Block[{t$95$3 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+222], t$95$2, If[LessEqual[t$95$2, -2e+68], t$95$3, If[LessEqual[t$95$2, -5.4e+42], t$95$2, If[LessEqual[t$95$2, -1000.0], t$95$3, 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) < -5.00000000000000023e222 or -1.99999999999999991e68 < (-.f64 (*.f64 x (log.f64 y)) y) < -5.4000000000000001e42

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. add-cube-cbrt 99.0%

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

      2. pow3 99.1%

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

   7. Applied egg-rr 99.1%

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

   8. Taylor expanded in z around 0 95.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right) - y} \]
   9. Step-by-step derivation

      1. pow-base-1 95.0%

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

      2. *-lft-identity 95.0%

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

   10. Simplified 95.0%

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

   if -5.00000000000000023e222 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.99999999999999991e68 or -5.4000000000000001e42 < (-.f64 (*.f64 x (log.f64 y)) y) < -1e3

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 96.2%

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

      1. add-cube-cbrt 96.0%

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

      2. pow3 96.0%

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

   7. Applied egg-rr 96.0%

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

   8. Taylor expanded in x around 0 79.6%

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

      1. neg-mul-1 79.6%

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

      2. neg-sub0 79.6%

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

      3. associate--r+ 79.6%

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

      4. neg-sub0 79.6%

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

   10. Simplified 79.6%

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

   if -1e3 < (-.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%

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

   3. Simplified 100.0%

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

      1. add-log-exp 58.6%

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

      2. associate--r- 58.6%

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

      3. exp-sum 58.6%

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

      4. associate--l- 58.6%

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

      5. add-exp-log 58.6%

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

   6. Applied egg-rr 58.6%

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

   7. Taylor expanded in x around 0 57.5%

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

      1. distribute-neg-in 57.5%

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

      2. unsub-neg 57.5%

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

   9. Simplified 57.5%

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

   10. Taylor expanded in y around 0 55.5%

       \[\leadsto \color{blue}{\log \left(t \cdot e^{-z}\right)} \]
   11. Step-by-step derivation

       1. log-prod 55.5%

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

       2. rem-log-exp 95.2%

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

       3. sub-neg 95.2%

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

   12. Simplified 95.2%

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

   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%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. add-cube-cbrt 98.6%

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

      2. pow3 98.5%

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

   7. Applied egg-rr 98.5%

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

   8. Taylor expanded in y around 0 97.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right) - z} \]
   9. Step-by-step derivation

      1. pow-base-1 97.8%

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

      2. *-lft-identity 97.8%

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

   10. Simplified 97.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -1000:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq 0.02:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t_1 - y\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;t_2 \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0.02:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5e+222)
     t_2
     (if (<= t_2 -2e+68)
       (- (- y) z)
       (if (<= t_2 -5.4e+42)
         t_2
         (if (<= t_2 0.02) (- (- (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 <= -5e+222) {
		tmp = t_2;
	} else if (t_2 <= -2e+68) {
		tmp = -y - z;
	} else if (t_2 <= -5.4e+42) {
		tmp = t_2;
	} else if (t_2 <= 0.02) {
		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 <= (-5d+222)) then
        tmp = t_2
    else if (t_2 <= (-2d+68)) then
        tmp = -y - z
    else if (t_2 <= (-5.4d+42)) then
        tmp = t_2
    else if (t_2 <= 0.02d0) 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 <= -5e+222) {
		tmp = t_2;
	} else if (t_2 <= -2e+68) {
		tmp = -y - z;
	} else if (t_2 <= -5.4e+42) {
		tmp = t_2;
	} else if (t_2 <= 0.02) {
		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 <= -5e+222:
		tmp = t_2
	elif t_2 <= -2e+68:
		tmp = -y - z
	elif t_2 <= -5.4e+42:
		tmp = t_2
	elif t_2 <= 0.02:
		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 <= -5e+222)
		tmp = t_2;
	elseif (t_2 <= -2e+68)
		tmp = Float64(Float64(-y) - z);
	elseif (t_2 <= -5.4e+42)
		tmp = t_2;
	elseif (t_2 <= 0.02)
		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 <= -5e+222)
		tmp = t_2;
	elseif (t_2 <= -2e+68)
		tmp = -y - z;
	elseif (t_2 <= -5.4e+42)
		tmp = t_2;
	elseif (t_2 <= 0.02)
		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, -5e+222], t$95$2, If[LessEqual[t$95$2, -2e+68], N[((-y) - z), $MachinePrecision], If[LessEqual[t$95$2, -5.4e+42], t$95$2, If[LessEqual[t$95$2, 0.02], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5.00000000000000023e222 or -1.99999999999999991e68 < (-.f64 (*.f64 x (log.f64 y)) y) < -5.4000000000000001e42

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. add-cube-cbrt 99.0%

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

      2. pow3 99.1%

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

   7. Applied egg-rr 99.1%

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

   8. Taylor expanded in z around 0 95.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right) - y} \]
   9. Step-by-step derivation

      1. pow-base-1 95.0%

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

      2. *-lft-identity 95.0%

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

   10. Simplified 95.0%

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

   if -5.00000000000000023e222 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.99999999999999991e68

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in x around 0 81.9%

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

      1. neg-mul-1 81.9%

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

      2. neg-sub0 81.9%

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

      3. associate--r+ 81.9%

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

      4. neg-sub0 81.9%

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

   10. Simplified 81.9%

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

   if -5.4000000000000001e42 < (-.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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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 93.2%

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

   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%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. add-cube-cbrt 98.6%

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

      2. pow3 98.5%

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

   7. Applied egg-rr 98.5%

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

   8. Taylor expanded in y around 0 97.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right) - z} \]
   9. Step-by-step derivation

      1. pow-base-1 97.8%

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

      2. *-lft-identity 97.8%

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

   10. Simplified 97.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \cdot \log y - y \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 0.02:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t_1 \leq -30000 \lor \neg \left(t_1 \leq 0.02\right):\\ \;\;\;\;t_1 - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (or (<= t_1 -30000.0) (not (<= t_1 0.02)))
     (- t_1 z)
     (- (- (log t) z) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if ((t_1 <= -30000.0) || !(t_1 <= 0.02)) {
		tmp = t_1 - z;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if ((t_1 <= (-30000.0d0)) .or. (.not. (t_1 <= 0.02d0))) then
        tmp = t_1 - z
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if ((t_1 <= -30000.0) || !(t_1 <= 0.02)) {
		tmp = t_1 - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if (t_1 <= -30000.0) or not (t_1 <= 0.02):
		tmp = t_1 - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if ((t_1 <= -30000.0) || !(t_1 <= 0.02))
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	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 <= -30000.0) || ~((t_1 <= 0.02)))
		tmp = t_1 - z;
	else
		tmp = (log(t) - z) - y;
	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[Or[LessEqual[t$95$1, -30000.0], N[Not[LessEqual[t$95$1, 0.02]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -3e4 or 0.0200000000000000004 < (-.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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.7%

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

   if -3e4 < (-.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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -30000 \lor \neg \left(x \cdot \log y - y \leq 0.02\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t_1 \leq -30000:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \left(-y\right) - z\right)\\ \mathbf{elif}\;t_1 \leq 0.02:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -30000.0)
     (fma (log y) x (- (- y) z))
     (if (<= t_1 0.02) (- (- (log t) z) y) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -30000.0) {
		tmp = fma(log(y), x, (-y - z));
	} else if (t_1 <= 0.02) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -30000.0)
		tmp = fma(log(y), x, Float64(Float64(-y) - z));
	elseif (t_1 <= 0.02)
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = Float64(t_1 - z);
	end
	return 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, -30000.0], N[(N[Log[y], $MachinePrecision] * x + N[((-y) - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.02], 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) < -3e4

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 98.5%

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

      1. add-cube-cbrt 98.0%

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

      2. pow3 98.1%

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

   7. Applied egg-rr 98.1%

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

      1. rem-cube-cbrt 98.5%

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

      2. associate--l- 98.5%

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

      3. *-commutative 98.5%

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

      4. fma-neg 98.5%

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

   9. Applied egg-rr 98.5%

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

   if -3e4 < (-.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%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      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-udef 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%

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

   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%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -30000:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \left(-y\right) - z\right)\\ \mathbf{elif}\;x \cdot \log y - y \leq 0.02:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 460:\\ \;\;\;\;\left(\log t + t_1\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 460.0) (- (+ (log t) t_1) z) (- (- t_1 y) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 460.0) {
		tmp = (log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 460.0d0) then
        tmp = (log(t) + t_1) - z
    else
        tmp = (t_1 - y) - 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 (y <= 460.0) {
		tmp = (Math.log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 460.0:
		tmp = (math.log(t) + t_1) - z
	else:
		tmp = (t_1 - y) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 460.0)
		tmp = Float64(Float64(log(t) + t_1) - z);
	else
		tmp = Float64(Float64(t_1 - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 460.0)
		tmp = (log(t) + t_1) - z;
	else
		tmp = (t_1 - y) - 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[y, 460.0], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 460

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 98.2%

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

   if 460 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 460:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 9: 68.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ t_3 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -6.3 \cdot 10^{+187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+196}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)) (t_2 (* x (log y))) (t_3 (- (- y) z)))
   (if (<= x -6.3e+187)
     t_2
     (if (<= x 9.2e-229)
       t_3
       (if (<= x 2.05e-173)
         t_1
         (if (<= x 8e-118)
           t_3
           (if (<= x 8e-22) t_1 (if (<= x 3.05e+196) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double t_2 = x * log(y);
	double t_3 = -y - z;
	double tmp;
	if (x <= -6.3e+187) {
		tmp = t_2;
	} else if (x <= 9.2e-229) {
		tmp = t_3;
	} else if (x <= 2.05e-173) {
		tmp = t_1;
	} else if (x <= 8e-118) {
		tmp = t_3;
	} else if (x <= 8e-22) {
		tmp = t_1;
	} else if (x <= 3.05e+196) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = log(t) - y
    t_2 = x * log(y)
    t_3 = -y - z
    if (x <= (-6.3d+187)) then
        tmp = t_2
    else if (x <= 9.2d-229) then
        tmp = t_3
    else if (x <= 2.05d-173) then
        tmp = t_1
    else if (x <= 8d-118) then
        tmp = t_3
    else if (x <= 8d-22) then
        tmp = t_1
    else if (x <= 3.05d+196) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - y;
	double t_2 = x * Math.log(y);
	double t_3 = -y - z;
	double tmp;
	if (x <= -6.3e+187) {
		tmp = t_2;
	} else if (x <= 9.2e-229) {
		tmp = t_3;
	} else if (x <= 2.05e-173) {
		tmp = t_1;
	} else if (x <= 8e-118) {
		tmp = t_3;
	} else if (x <= 8e-22) {
		tmp = t_1;
	} else if (x <= 3.05e+196) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	t_2 = x * math.log(y)
	t_3 = -y - z
	tmp = 0
	if x <= -6.3e+187:
		tmp = t_2
	elif x <= 9.2e-229:
		tmp = t_3
	elif x <= 2.05e-173:
		tmp = t_1
	elif x <= 8e-118:
		tmp = t_3
	elif x <= 8e-22:
		tmp = t_1
	elif x <= 3.05e+196:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	t_2 = Float64(x * log(y))
	t_3 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (x <= -6.3e+187)
		tmp = t_2;
	elseif (x <= 9.2e-229)
		tmp = t_3;
	elseif (x <= 2.05e-173)
		tmp = t_1;
	elseif (x <= 8e-118)
		tmp = t_3;
	elseif (x <= 8e-22)
		tmp = t_1;
	elseif (x <= 3.05e+196)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	t_2 = x * log(y);
	t_3 = -y - z;
	tmp = 0.0;
	if (x <= -6.3e+187)
		tmp = t_2;
	elseif (x <= 9.2e-229)
		tmp = t_3;
	elseif (x <= 2.05e-173)
		tmp = t_1;
	elseif (x <= 8e-118)
		tmp = t_3;
	elseif (x <= 8e-22)
		tmp = t_1;
	elseif (x <= 3.05e+196)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -6.3e+187], t$95$2, If[LessEqual[x, 9.2e-229], t$95$3, If[LessEqual[x, 2.05e-173], t$95$1, If[LessEqual[x, 8e-118], t$95$3, If[LessEqual[x, 8e-22], t$95$1, If[LessEqual[x, 3.05e+196], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.30000000000000005e187 or 3.05000000000000018e196 < x

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.1%

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

   if -6.30000000000000005e187 < x < 9.19999999999999983e-229 or 2.0499999999999999e-173 < x < 7.99999999999999988e-118 or 8.0000000000000004e-22 < x < 3.05000000000000018e196

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 89.6%

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

      1. add-cube-cbrt 89.2%

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

      2. pow3 89.3%

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

   7. Applied egg-rr 89.3%

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

   8. Taylor expanded in x around 0 71.0%

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

      1. neg-mul-1 71.0%

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

      2. neg-sub0 71.0%

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

      3. associate--r+ 71.0%

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

      4. neg-sub0 71.0%

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

   10. Simplified 71.0%

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

   if 9.19999999999999983e-229 < x < 2.0499999999999999e-173 or 7.99999999999999988e-118 < x < 8.0000000000000004e-22

   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%

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

   3. Simplified 100.0%

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

      1. add-log-exp 51.0%

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

      2. associate--r- 51.0%

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

      3. exp-sum 51.0%

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

      4. associate--l- 51.0%

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

      5. add-exp-log 51.0%

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

   6. Applied egg-rr 51.0%

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

   7. Taylor expanded in x around 0 51.0%

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

      1. distribute-neg-in 51.0%

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

      2. unsub-neg 51.0%

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

   9. Simplified 51.0%

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

   10. Taylor expanded in z around 0 47.7%

       \[\leadsto \color{blue}{\log \left(t \cdot e^{-y}\right)} \]
   11. Step-by-step derivation

       1. exp-neg 47.7%

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

       2. associate-*r/ 47.7%

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

       3. log-div 50.5%

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

       4. *-rgt-identity 50.5%

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

       5. rem-log-exp 82.5%

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

   12. Simplified 82.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-229}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-173}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-118}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-22}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+196}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-187}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-22}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- y) z)))
   (if (<= x -2.8e+189)
     t_1
     (if (<= x 4e-284)
       t_2
       (if (<= x 2.5e-187)
         (- (log t) z)
         (if (<= x 2.4e-118)
           t_2
           (if (<= x 6.8e-22)
             (- (log t) y)
             (if (<= x 3.05e+196) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -2.8e+189) {
		tmp = t_1;
	} else if (x <= 4e-284) {
		tmp = t_2;
	} else if (x <= 2.5e-187) {
		tmp = log(t) - z;
	} else if (x <= 2.4e-118) {
		tmp = t_2;
	} else if (x <= 6.8e-22) {
		tmp = log(t) - y;
	} else if (x <= 3.05e+196) {
		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 = -y - z
    if (x <= (-2.8d+189)) then
        tmp = t_1
    else if (x <= 4d-284) then
        tmp = t_2
    else if (x <= 2.5d-187) then
        tmp = log(t) - z
    else if (x <= 2.4d-118) then
        tmp = t_2
    else if (x <= 6.8d-22) then
        tmp = log(t) - y
    else if (x <= 3.05d+196) 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 = -y - z;
	double tmp;
	if (x <= -2.8e+189) {
		tmp = t_1;
	} else if (x <= 4e-284) {
		tmp = t_2;
	} else if (x <= 2.5e-187) {
		tmp = Math.log(t) - z;
	} else if (x <= 2.4e-118) {
		tmp = t_2;
	} else if (x <= 6.8e-22) {
		tmp = Math.log(t) - y;
	} else if (x <= 3.05e+196) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = -y - z
	tmp = 0
	if x <= -2.8e+189:
		tmp = t_1
	elif x <= 4e-284:
		tmp = t_2
	elif x <= 2.5e-187:
		tmp = math.log(t) - z
	elif x <= 2.4e-118:
		tmp = t_2
	elif x <= 6.8e-22:
		tmp = math.log(t) - y
	elif x <= 3.05e+196:
		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(-y) - z)
	tmp = 0.0
	if (x <= -2.8e+189)
		tmp = t_1;
	elseif (x <= 4e-284)
		tmp = t_2;
	elseif (x <= 2.5e-187)
		tmp = Float64(log(t) - z);
	elseif (x <= 2.4e-118)
		tmp = t_2;
	elseif (x <= 6.8e-22)
		tmp = Float64(log(t) - y);
	elseif (x <= 3.05e+196)
		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 = -y - z;
	tmp = 0.0;
	if (x <= -2.8e+189)
		tmp = t_1;
	elseif (x <= 4e-284)
		tmp = t_2;
	elseif (x <= 2.5e-187)
		tmp = log(t) - z;
	elseif (x <= 2.4e-118)
		tmp = t_2;
	elseif (x <= 6.8e-22)
		tmp = log(t) - y;
	elseif (x <= 3.05e+196)
		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[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -2.8e+189], t$95$1, If[LessEqual[x, 4e-284], t$95$2, If[LessEqual[x, 2.5e-187], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 2.4e-118], t$95$2, If[LessEqual[x, 6.8e-22], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 3.05e+196], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.80000000000000006e189 or 3.05000000000000018e196 < x

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.1%

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

   if -2.80000000000000006e189 < x < 4.00000000000000015e-284 or 2.4999999999999998e-187 < x < 2.4000000000000001e-118 or 6.7999999999999997e-22 < x < 3.05000000000000018e196

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 89.5%

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

      1. add-cube-cbrt 89.1%

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

      2. pow3 89.2%

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

   7. Applied egg-rr 89.2%

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

   8. Taylor expanded in x around 0 70.8%

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

      1. neg-mul-1 70.8%

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

      2. neg-sub0 70.8%

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

      3. associate--r+ 70.8%

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

      4. neg-sub0 70.8%

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

   10. Simplified 70.8%

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

   if 4.00000000000000015e-284 < x < 2.4999999999999998e-187

   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%

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

   3. Simplified 100.0%

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

      1. add-log-exp 55.8%

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

      2. associate--r- 55.8%

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

      3. exp-sum 55.8%

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

      4. associate--l- 55.8%

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

      5. add-exp-log 55.8%

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

   6. Applied egg-rr 55.8%

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

   7. Taylor expanded in x around 0 55.8%

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

      1. distribute-neg-in 55.8%

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

      2. unsub-neg 55.8%

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

   9. Simplified 55.8%

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

   10. Taylor expanded in y around 0 51.8%

       \[\leadsto \color{blue}{\log \left(t \cdot e^{-z}\right)} \]
   11. Step-by-step derivation

       1. log-prod 51.8%

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

       2. rem-log-exp 81.9%

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

       3. sub-neg 81.9%

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

   12. Simplified 81.9%

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

   if 2.4000000000000001e-118 < x < 6.7999999999999997e-22

   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%

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

   3. Simplified 100.0%

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

      1. add-log-exp 46.4%

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

      2. associate--r- 46.4%

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

      3. exp-sum 46.4%

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

      4. associate--l- 46.4%

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

      5. add-exp-log 46.4%

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

   6. Applied egg-rr 46.4%

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

   7. Taylor expanded in x around 0 46.4%

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

      1. distribute-neg-in 46.4%

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

      2. unsub-neg 46.4%

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

   9. Simplified 46.4%

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

   10. Taylor expanded in z around 0 44.7%

       \[\leadsto \color{blue}{\log \left(t \cdot e^{-y}\right)} \]
   11. Step-by-step derivation

       1. exp-neg 44.7%

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

       2. associate-*r/ 44.7%

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

       3. log-div 48.9%

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

       4. *-rgt-identity 48.9%

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

       5. rem-log-exp 83.9%

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

   12. Simplified 83.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-284}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-187}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-118}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-22}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+196}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+188} \lor \neg \left(x \leq 1.75 \cdot 10^{+197}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e+188) (not (<= x 1.75e+197))) (* x (log y)) (- (- y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+188) || !(x <= 1.75e+197)) {
		tmp = x * log(y);
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.8d+188)) .or. (.not. (x <= 1.75d+197))) then
        tmp = x * log(y)
    else
        tmp = -y - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+188) || !(x <= 1.75e+197)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e+188) or not (x <= 1.75e+197):
		tmp = x * math.log(y)
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e+188) || !(x <= 1.75e+197))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e+188) || ~((x <= 1.75e+197)))
		tmp = x * log(y);
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e+188], N[Not[LessEqual[x, 1.75e+197]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e188 or 1.75e197 < x

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.1%

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

   if -3.7999999999999998e188 < x < 1.75e197

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. add-cube-cbrt 82.9%

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

      2. pow3 82.9%

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

   7. Applied egg-rr 82.9%

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

   8. Taylor expanded in x around 0 67.6%

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

      1. neg-mul-1 67.6%

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

      2. neg-sub0 67.6%

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

      3. associate--r+ 67.6%

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

      4. neg-sub0 67.6%

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

   10. Simplified 67.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+188} \lor \neg \left(x \leq 1.75 \cdot 10^{+197}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.5% accurate, 34.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+101} \lor \neg \left(z \leq 3.9 \cdot 10^{+133}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e+101) (not (<= z 3.9e+133))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e+101) || !(z <= 3.9e+133)) {
		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 ((z <= (-1.25d+101)) .or. (.not. (z <= 3.9d+133))) 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 ((z <= -1.25e+101) || !(z <= 3.9e+133)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e+101) or not (z <= 3.9e+133):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e+101) || !(z <= 3.9e+133))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.25e+101) || ~((z <= 3.9e+133)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e+101], N[Not[LessEqual[z, 3.9e+133]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999997e101 or 3.90000000000000014e133 < z

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. neg-mul-1 78.0%

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

   7. Simplified 78.0%

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

   if -1.24999999999999997e101 < z < 3.90000000000000014e133

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 37.3%

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

      1. neg-mul-1 37.3%

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

   7. Simplified 37.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+101} \lor \neg \left(z \leq 3.9 \cdot 10^{+133}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.8% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 86.0%

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

   1. add-cube-cbrt 85.5%

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

   2. pow3 85.6%

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

7. Applied egg-rr 85.6%

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

8. Taylor expanded in x around 0 57.1%

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

   1. neg-mul-1 57.1%

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

   2. neg-sub0 57.1%

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

   3. associate--r+ 57.1%

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

   4. neg-sub0 57.1%

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

10. Simplified 57.1%

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

11. Final simplification 57.1%

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

Alternative 14: 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 99.9%

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

   1. associate-+l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 28.9%

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

   1. neg-mul-1 28.9%

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

7. Simplified 28.9%

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

8. Final simplification 28.9%

   \[\leadsto -y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024013 
(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)))