Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.1% → 96.5%

Time: 8.7s

Alternatives: 7

Speedup: 1.3×

• Unsound rule application detected in e-graph. Results may not be sound.

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{\frac{1}{x - z}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.35e+73) (* y (* t (- x z))) (/ (* t y) (/ 1.0 (- x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e+73) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (t * y) / (1.0 / (x - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 (t <= 1.35d+73) then
        tmp = y * (t * (x - z))
    else
        tmp = (t * y) / (1.0d0 / (x - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e+73) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (t * y) / (1.0 / (x - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.35e+73:
		tmp = y * (t * (x - z))
	else:
		tmp = (t * y) / (1.0 / (x - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.35e+73)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(t * y) / Float64(1.0 / Float64(x - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.35e+73)
		tmp = y * (t * (x - z));
	else
		tmp = (t * y) / (1.0 / (x - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.35e+73], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * y), $MachinePrecision] / N[(1.0 / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.35e73

   1. Initial program 87.5%

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

      1. distribute-rgt-out-- 89.6%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   if 1.35e73 < t

   1. Initial program 93.6%

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

      1. distribute-rgt-out-- 93.6%

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

   3. Simplified 93.6%

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

      1. add-cbrt-cube 72.9%

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

      2. pow3 72.9%

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

   5. Applied egg-rr 72.9%

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

      1. rem-cbrt-cube 93.6%

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

      2. flip-- 63.5%

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

      3. associate-*r/ 61.4%

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

   7. Applied egg-rr 61.4%

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

      1. associate-/l* 63.4%

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

      2. difference-of-squares 65.6%

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

      3. associate-/r* 93.4%

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

      4. *-inverses 93.4%

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

   9. Simplified 93.4%

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

       1. associate-*l/ 97.7%

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

   11. Applied egg-rr 97.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{\frac{1}{x - z}}\\ \end{array} \]

Alternative 2: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := -z \cdot \left(t \cdot y\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-81} \lor \neg \left(z \leq 0.012\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z (* t y)))))
   (if (<= z -1.1e+90)
     t_1
     (if (<= z -1e+68)
       (* y (* t x))
       (if (or (<= z -3.45e-81) (not (<= z 0.012))) t_1 (* x (* t y)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -(z * (t * y));
	double tmp;
	if (z <= -1.1e+90) {
		tmp = t_1;
	} else if (z <= -1e+68) {
		tmp = y * (t * x);
	} else if ((z <= -3.45e-81) || !(z <= 0.012)) {
		tmp = t_1;
	} else {
		tmp = x * (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(z * (t * y))
    if (z <= (-1.1d+90)) then
        tmp = t_1
    else if (z <= (-1d+68)) then
        tmp = y * (t * x)
    else if ((z <= (-3.45d-81)) .or. (.not. (z <= 0.012d0))) then
        tmp = t_1
    else
        tmp = x * (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -(z * (t * y));
	double tmp;
	if (z <= -1.1e+90) {
		tmp = t_1;
	} else if (z <= -1e+68) {
		tmp = y * (t * x);
	} else if ((z <= -3.45e-81) || !(z <= 0.012)) {
		tmp = t_1;
	} else {
		tmp = x * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -(z * (t * y))
	tmp = 0
	if z <= -1.1e+90:
		tmp = t_1
	elif z <= -1e+68:
		tmp = y * (t * x)
	elif (z <= -3.45e-81) or not (z <= 0.012):
		tmp = t_1
	else:
		tmp = x * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(-Float64(z * Float64(t * y)))
	tmp = 0.0
	if (z <= -1.1e+90)
		tmp = t_1;
	elseif (z <= -1e+68)
		tmp = Float64(y * Float64(t * x));
	elseif ((z <= -3.45e-81) || !(z <= 0.012))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -(z * (t * y));
	tmp = 0.0;
	if (z <= -1.1e+90)
		tmp = t_1;
	elseif (z <= -1e+68)
		tmp = y * (t * x);
	elseif ((z <= -3.45e-81) || ~((z <= 0.012)))
		tmp = t_1;
	else
		tmp = x * (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -1.1e+90], t$95$1, If[LessEqual[z, -1e+68], N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.45e-81], N[Not[LessEqual[z, 0.012]], $MachinePrecision]], t$95$1, N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999995e90 or -9.99999999999999953e67 < z < -3.4500000000000001e-81 or 0.012 < z

   1. Initial program 86.6%

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

      1. distribute-rgt-out-- 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-rgt-neg-out 76.0%

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

   6. Simplified 76.0%

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

      1. distribute-rgt-neg-out 76.0%

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

      2. distribute-lft-neg-out 76.0%

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

      3. *-commutative 76.0%

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

      4. add-sqr-sqrt 27.5%

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

      5. sqrt-unprod 20.9%

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

      6. sqr-neg 20.9%

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

      7. sqrt-unprod 3.3%

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

      8. add-sqr-sqrt 4.1%

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

      9. associate-*l* 4.2%

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

      10. add-sqr-sqrt 3.4%

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

      11. sqrt-unprod 21.9%

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

      12. sqr-neg 21.9%

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

      13. sqrt-unprod 30.7%

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

      14. add-sqr-sqrt 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -1.09999999999999995e90 < z < -9.99999999999999953e67

   1. Initial program 78.3%

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

      1. distribute-rgt-out-- 89.4%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

   if -3.4500000000000001e-81 < z < 0.012

   1. Initial program 91.4%

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

      1. distribute-rgt-out-- 91.5%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around inf 74.5%

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

      1. add-log-exp 29.4%

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

      2. associate-*r* 29.4%

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

      3. exp-prod 28.6%

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

   6. Applied egg-rr 28.6%

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

      1. log-pow 30.5%

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

      2. rem-log-exp 79.6%

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

   8. Simplified 79.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+90}:\\ \;\;\;\;-z \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-81} \lor \neg \left(z \leq 0.012\right):\\ \;\;\;\;-z \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := -z \cdot \left(t \cdot y\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 0.0032:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z (* t y)))))
   (if (<= z -1.1e+90)
     t_1
     (if (<= z -7.6e+67)
       (* y (* t x))
       (if (<= z -3.3e-81)
         (* t (* y (- z)))
         (if (<= z 0.0032) (* x (* t y)) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -(z * (t * y));
	double tmp;
	if (z <= -1.1e+90) {
		tmp = t_1;
	} else if (z <= -7.6e+67) {
		tmp = y * (t * x);
	} else if (z <= -3.3e-81) {
		tmp = t * (y * -z);
	} else if (z <= 0.0032) {
		tmp = x * (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(z * (t * y))
    if (z <= (-1.1d+90)) then
        tmp = t_1
    else if (z <= (-7.6d+67)) then
        tmp = y * (t * x)
    else if (z <= (-3.3d-81)) then
        tmp = t * (y * -z)
    else if (z <= 0.0032d0) then
        tmp = x * (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -(z * (t * y));
	double tmp;
	if (z <= -1.1e+90) {
		tmp = t_1;
	} else if (z <= -7.6e+67) {
		tmp = y * (t * x);
	} else if (z <= -3.3e-81) {
		tmp = t * (y * -z);
	} else if (z <= 0.0032) {
		tmp = x * (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -(z * (t * y))
	tmp = 0
	if z <= -1.1e+90:
		tmp = t_1
	elif z <= -7.6e+67:
		tmp = y * (t * x)
	elif z <= -3.3e-81:
		tmp = t * (y * -z)
	elif z <= 0.0032:
		tmp = x * (t * y)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(-Float64(z * Float64(t * y)))
	tmp = 0.0
	if (z <= -1.1e+90)
		tmp = t_1;
	elseif (z <= -7.6e+67)
		tmp = Float64(y * Float64(t * x));
	elseif (z <= -3.3e-81)
		tmp = Float64(t * Float64(y * Float64(-z)));
	elseif (z <= 0.0032)
		tmp = Float64(x * Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -(z * (t * y));
	tmp = 0.0;
	if (z <= -1.1e+90)
		tmp = t_1;
	elseif (z <= -7.6e+67)
		tmp = y * (t * x);
	elseif (z <= -3.3e-81)
		tmp = t * (y * -z);
	elseif (z <= 0.0032)
		tmp = x * (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -1.1e+90], t$95$1, If[LessEqual[z, -7.6e+67], N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-81], N[(t * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0032], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.09999999999999995e90 or 0.00320000000000000015 < z

   1. Initial program 83.0%

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

      1. distribute-rgt-out-- 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-out 76.1%

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

   6. Simplified 76.1%

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

      1. distribute-rgt-neg-out 76.1%

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

      2. distribute-lft-neg-out 76.1%

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

      3. *-commutative 76.1%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 23.1%

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

      6. sqr-neg 23.1%

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

      7. sqrt-unprod 0.5%

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

      8. add-sqr-sqrt 1.5%

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

      9. associate-*l* 1.7%

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

      10. add-sqr-sqrt 0.6%

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

      11. sqrt-unprod 24.4%

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

      12. sqr-neg 24.4%

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

      13. sqrt-unprod 39.6%

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

      14. add-sqr-sqrt 81.3%

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

   8. Applied egg-rr 81.3%

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

   if -1.09999999999999995e90 < z < -7.60000000000000041e67

   1. Initial program 78.3%

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

      1. distribute-rgt-out-- 89.4%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

   if -7.60000000000000041e67 < z < -3.29999999999999987e-81

   1. Initial program 99.3%

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

      1. distribute-rgt-out-- 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-rgt-neg-out 75.4%

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

   6. Simplified 75.4%

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

   if -3.29999999999999987e-81 < z < 0.00320000000000000015

   1. Initial program 91.4%

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

      1. distribute-rgt-out-- 91.5%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around inf 74.5%

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

      1. add-log-exp 29.4%

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

      2. associate-*r* 29.4%

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

      3. exp-prod 28.6%

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

   6. Applied egg-rr 28.6%

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

      1. log-pow 30.5%

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

      2. rem-log-exp 79.6%

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

   8. Simplified 79.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+90}:\\ \;\;\;\;-z \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 0.0032:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 4: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{+48}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e+48) (* y (* t (- x z))) (* t (* y (- x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e+48) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 (t <= 1d+48) then
        tmp = y * (t * (x - z))
    else
        tmp = t * (y * (x - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e+48) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1e+48:
		tmp = y * (t * (x - z))
	else:
		tmp = t * (y * (x - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1e+48)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(t * Float64(y * Float64(x - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e+48)
		tmp = y * (t * (x - z));
	else
		tmp = t * (y * (x - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1e+48], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000004e48

   1. Initial program 87.4%

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

      1. distribute-rgt-out-- 89.4%

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

      2. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   if 1.00000000000000004e48 < t

   1. Initial program 93.9%

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

      1. distribute-rgt-out-- 93.9%

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

   3. Simplified 93.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{+48}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 5: 56.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-74) (* x (* t y)) (* t (* y x))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-74) {
		tmp = x * (t * y);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-1.2d-74)) then
        tmp = x * (t * y)
    else
        tmp = t * (y * x)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-74) {
		tmp = x * (t * y);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-74:
		tmp = x * (t * y)
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-74)
		tmp = Float64(x * Float64(t * y));
	else
		tmp = Float64(t * Float64(y * x));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-74)
		tmp = x * (t * y);
	else
		tmp = t * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-74], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1999999999999999e-74

   1. Initial program 82.2%

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

      1. distribute-rgt-out-- 84.7%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 46.3%

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

      1. add-log-exp 31.3%

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

      2. associate-*r* 31.3%

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

      3. exp-prod 30.6%

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

   6. Applied egg-rr 30.6%

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

      1. log-pow 33.4%

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

      2. rem-log-exp 52.5%

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

   8. Simplified 52.5%

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

   if -1.1999999999999999e-74 < y

   1. Initial program 92.3%

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

      1. distribute-rgt-out-- 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 56.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 6: 91.8% accurate, 1.3× speedup

Math

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

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* y (* t (- x z))))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 * (t * (x - z))
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return y * (t * (x - z))

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(y * Float64(t * Float64(x - z)))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = y * (t * (x - z));
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

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

   1. distribute-rgt-out-- 90.3%

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

   2. associate-*l* 89.4%

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

3. Simplified 89.4%

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

4. Final simplification 89.4%

   \[\leadsto y \cdot \left(t \cdot \left(x - z\right)\right) \]

Alternative 7: 54.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ x \cdot \left(t \cdot y\right) \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* x (* t y)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 * (t * y)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return x * (t * y)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(x * Float64(t * y))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = x * (t * y);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

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

   1. distribute-rgt-out-- 90.3%

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

   2. associate-*l* 89.4%

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

3. Simplified 89.4%

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

4. Taylor expanded in x around inf 51.8%

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

   1. add-log-exp 26.3%

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

   2. associate-*r* 26.3%

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

   3. exp-prod 25.9%

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

6. Applied egg-rr 25.9%

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

   1. log-pow 27.5%

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

   2. rem-log-exp 54.3%

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

8. Simplified 54.3%

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

9. Final simplification 54.3%

   \[\leadsto x \cdot \left(t \cdot y\right) \]

Developer target: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< t -9.231879582886777e-80)
   (* (* y t) (- x z))
   (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t < -9.231879582886777e-80) {
		tmp = (y * t) * (x - z);
	} else if (t < 2.543067051564877e+83) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (y * (x - z)) * t;
	}
	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 (t < (-9.231879582886777d-80)) then
        tmp = (y * t) * (x - z)
    else if (t < 2.543067051564877d+83) then
        tmp = y * (t * (x - z))
    else
        tmp = (y * (x - z)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t < -9.231879582886777e-80) {
		tmp = (y * t) * (x - z);
	} else if (t < 2.543067051564877e+83) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (y * (x - z)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t < -9.231879582886777e-80:
		tmp = (y * t) * (x - z)
	elif t < 2.543067051564877e+83:
		tmp = y * (t * (x - z))
	else:
		tmp = (y * (x - z)) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t < -9.231879582886777e-80)
		tmp = Float64(Float64(y * t) * Float64(x - z));
	elseif (t < 2.543067051564877e+83)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(y * Float64(x - z)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t < -9.231879582886777e-80)
		tmp = (y * t) * (x - z);
	elseif (t < 2.543067051564877e+83)
		tmp = y * (t * (x - z));
	else
		tmp = (y * (x - z)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[t, -9.231879582886777e-80], N[(N[(y * t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], If[Less[t, 2.543067051564877e+83], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

  (* (- (* x y) (* z y)) t))