Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.7% → 97.2%

Time: 9.6s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y - z}{t - z} \cdot x \end{array} \]

FPCore

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

C

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

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) / (t - z)) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.0%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 97.4

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

4. Applied rewrites 97.4%

   \[\leadsto \color{blue}{\frac{y - z}{t - z} \cdot x} \]
5. Add Preprocessing

Alternative 2: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+178}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.95e+109)
   (* x (/ (- z y) z))
   (if (<= z 3.3e+178) (* (- y z) (/ x (- t z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.95e+109) {
		tmp = x * ((z - y) / z);
	} else if (z <= 3.3e+178) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x * (z / (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 (z <= (-2.95d+109)) then
        tmp = x * ((z - y) / z)
    else if (z <= 3.3d+178) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.95e+109) {
		tmp = x * ((z - y) / z);
	} else if (z <= 3.3e+178) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.95e+109:
		tmp = x * ((z - y) / z)
	elif z <= 3.3e+178:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.95e+109)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= 3.3e+178)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.95e+109)
		tmp = x * ((z - y) / z);
	elseif (z <= 3.3e+178)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.95e+109], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+178], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9499999999999999e109

   1. Initial program 62.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. unsub-neg N/A

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

      8. remove-double-neg N/A

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

      9. lower--.f64 84.3

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

   7. Applied rewrites 84.3%

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

   if -2.9499999999999999e109 < z < 3.2999999999999998e178

   1. Initial program 89.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 93.6

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

   4. Applied rewrites 93.6%

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

   if 3.2999999999999998e178 < z

   1. Initial program 63.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. neg-sub0 N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{\color{blue}{0 - \left(t - z\right)}}\right) \]

      13. lift--.f64 N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(t - z\right)}}\right) \]

      14. sub-neg N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}}\right) \]

      15. +-commutative N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)}}\right) \]

      16. associate--r+ N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t}}\right) \]

      17. neg-sub0 N/A

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

      18. remove-double-neg N/A

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

      19. lower--.f64 54.6

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

   4. Applied rewrites 54.6%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 93.5

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

   7. Applied rewrites 93.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+178}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -6.8e+33) t_1 (if (<= y 3.4e+43) (* x (/ z (- z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -6.8e+33) {
		tmp = t_1;
	} else if (y <= 3.4e+43) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-6.8d+33)) then
        tmp = t_1
    else if (y <= 3.4d+43) then
        tmp = x * (z / (z - t))
    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 * (y / (t - z));
	double tmp;
	if (y <= -6.8e+33) {
		tmp = t_1;
	} else if (y <= 3.4e+43) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -6.8e+33:
		tmp = t_1
	elif y <= 3.4e+43:
		tmp = x * (z / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -6.8e+33)
		tmp = t_1;
	elseif (y <= 3.4e+43)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -6.8e+33)
		tmp = t_1;
	elseif (y <= 3.4e+43)
		tmp = x * (z / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+33], t$95$1, If[LessEqual[y, 3.4e+43], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999999e33 or 3.40000000000000012e43 < y

   1. Initial program 80.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if -6.7999999999999999e33 < y < 3.40000000000000012e43

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. neg-sub0 N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{\color{blue}{0 - \left(t - z\right)}}\right) \]

      13. lift--.f64 N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(t - z\right)}}\right) \]

      14. sub-neg N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}}\right) \]

      15. +-commutative N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)}}\right) \]

      16. associate--r+ N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t}}\right) \]

      17. neg-sub0 N/A

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

      18. remove-double-neg N/A

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

      19. lower--.f64 85.3

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

   4. Applied rewrites 85.3%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.7

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

   7. Applied rewrites 76.7%

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

Alternative 4: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.08e-35) t_1 (if (<= z 2.25e-66) (* x (/ y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.08e-35) {
		tmp = t_1;
	} else if (z <= 2.25e-66) {
		tmp = x * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.08d-35)) then
        tmp = t_1
    else if (z <= 2.25d-66) then
        tmp = x * (y / t)
    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 * (z / (z - t));
	double tmp;
	if (z <= -1.08e-35) {
		tmp = t_1;
	} else if (z <= 2.25e-66) {
		tmp = x * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.08e-35:
		tmp = t_1
	elif z <= 2.25e-66:
		tmp = x * (y / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.08e-35)
		tmp = t_1;
	elseif (z <= 2.25e-66)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.08e-35)
		tmp = t_1;
	elseif (z <= 2.25e-66)
		tmp = x * (y / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-35], t$95$1, If[LessEqual[z, 2.25e-66], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08000000000000003e-35 or 2.2499999999999999e-66 < z

   1. Initial program 73.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. neg-sub0 N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{\color{blue}{0 - \left(t - z\right)}}\right) \]

      13. lift--.f64 N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(t - z\right)}}\right) \]

      14. sub-neg N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}}\right) \]

      15. +-commutative N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)}}\right) \]

      16. associate--r+ N/A

          \[\leadsto \left(y - z\right) \cdot \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{1}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t}}\right) \]

      17. neg-sub0 N/A

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

      18. remove-double-neg N/A

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

      19. lower--.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 72.0

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

   7. Applied rewrites 72.0%

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

   if -1.08000000000000003e-35 < z < 2.2499999999999999e-66

   1. Initial program 92.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 94.3

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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 72.9

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

   7. Applied rewrites 72.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.6e+14) (* x 1.0) (if (<= z 1.3e+59) (* x (/ y t)) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e+14) {
		tmp = x * 1.0;
	} else if (z <= 1.3e+59) {
		tmp = x * (y / t);
	} else {
		tmp = x * 1.0;
	}
	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 <= (-8.6d+14)) then
        tmp = x * 1.0d0
    else if (z <= 1.3d+59) then
        tmp = x * (y / t)
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e+14) {
		tmp = x * 1.0;
	} else if (z <= 1.3e+59) {
		tmp = x * (y / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.6e+14:
		tmp = x * 1.0
	elif z <= 1.3e+59:
		tmp = x * (y / t)
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.6e+14)
		tmp = Float64(x * 1.0);
	elseif (z <= 1.3e+59)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.6e+14)
		tmp = x * 1.0;
	elseif (z <= 1.3e+59)
		tmp = x * (y / t);
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.6e+14], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 1.3e+59], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6e14 or 1.3e59 < z

   1. Initial program 68.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 59.5%

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

   if -8.6e14 < z < 1.3e59

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 65.4

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

   7. Applied rewrites 65.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+14) (* x 1.0) (if (<= z 1.55e+58) (* y (/ x t)) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+14) {
		tmp = x * 1.0;
	} else if (z <= 1.55e+58) {
		tmp = y * (x / t);
	} else {
		tmp = x * 1.0;
	}
	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 <= (-5.2d+14)) then
        tmp = x * 1.0d0
    else if (z <= 1.55d+58) then
        tmp = y * (x / t)
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+14) {
		tmp = x * 1.0;
	} else if (z <= 1.55e+58) {
		tmp = y * (x / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+14:
		tmp = x * 1.0
	elif z <= 1.55e+58:
		tmp = y * (x / t)
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+14)
		tmp = Float64(x * 1.0);
	elseif (z <= 1.55e+58)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+14)
		tmp = x * 1.0;
	elseif (z <= 1.55e+58)
		tmp = y * (x / t);
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+14], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 1.55e+58], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e14 or 1.55e58 < z

   1. Initial program 68.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 59.5%

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

   if -5.2e14 < z < 1.55e58

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 61.7

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

   5. Applied rewrites 61.7%

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

   7. Applied rewrites 64.2%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x 1.0))

C

double code(double x, double y, double z, double t) {
	return x * 1.0;
}

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 * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * 1.0;
}

Python

def code(x, y, z, t):
	return x * 1.0

Julia

function code(x, y, z, t)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * 1.0), $MachinePrecision]

Derivation

1. Initial program 82.0%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 97.4

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

4. Applied rewrites 97.4%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 31.7%

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

8. Final simplification 31.7%

   \[\leadsto x \cdot 1 \]
9. Add Preprocessing

Developer Target 1: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024233 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

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