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

Percentage Accurate: 84.3% → 97.0%

Time: 8.6s

Alternatives: 14

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: 84.3% 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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.6%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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 96.5

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

4. Applied rewrites 96.5%

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

5. Final simplification 96.5%

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

Alternative 2: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - t} \cdot x\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+158}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- z t)) x)))
   (if (<= z -7.6e+158)
     (* (/ (- z y) z) x)
     (if (<= z -7.8e-8) t_1 (if (<= z 3.5e-92) (/ (* x y) (- t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (z - t)) * x;
	double tmp;
	if (z <= -7.6e+158) {
		tmp = ((z - y) / z) * x;
	} else if (z <= -7.8e-8) {
		tmp = t_1;
	} else if (z <= 3.5e-92) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / (z - t)) * x
    if (z <= (-7.6d+158)) then
        tmp = ((z - y) / z) * x
    else if (z <= (-7.8d-8)) then
        tmp = t_1
    else if (z <= 3.5d-92) then
        tmp = (x * y) / (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 = (z / (z - t)) * x;
	double tmp;
	if (z <= -7.6e+158) {
		tmp = ((z - y) / z) * x;
	} else if (z <= -7.8e-8) {
		tmp = t_1;
	} else if (z <= 3.5e-92) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / (z - t)) * x
	tmp = 0
	if z <= -7.6e+158:
		tmp = ((z - y) / z) * x
	elif z <= -7.8e-8:
		tmp = t_1
	elif z <= 3.5e-92:
		tmp = (x * y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / Float64(z - t)) * x)
	tmp = 0.0
	if (z <= -7.6e+158)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= -7.8e-8)
		tmp = t_1;
	elseif (z <= 3.5e-92)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / (z - t)) * x;
	tmp = 0.0;
	if (z <= -7.6e+158)
		tmp = ((z - y) / z) * x;
	elseif (z <= -7.8e-8)
		tmp = t_1;
	elseif (z <= 3.5e-92)
		tmp = (x * y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -7.6e+158], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, -7.8e-8], t$95$1, If[LessEqual[z, 3.5e-92], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999997e158

   1. Initial program 58.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 100.0

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

   4. Applied rewrites 100.0%

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

   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-in N/A

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

      5. div-add N/A

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

      6. neg-mul-1 N/A

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

      7. remove-double-neg N/A

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

      8. *-inverses N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 96.8

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

   7. Applied rewrites 96.8%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 96.8

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

   10. Applied rewrites 96.8%

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

   if -7.5999999999999997e158 < z < -7.7999999999999997e-8 or 3.5e-92 < z

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 79.7

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

   5. Applied rewrites 79.7%

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

   if -7.7999999999999997e-8 < z < 3.5e-92

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 82.0

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

   5. Applied rewrites 82.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+158}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - t} \cdot x\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- z t)) x)))
   (if (<= z -7.6e+158)
     (fma (/ y (- z)) x x)
     (if (<= z -7.8e-8) t_1 (if (<= z 3.5e-92) (/ (* x y) (- t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (z - t)) * x;
	double tmp;
	if (z <= -7.6e+158) {
		tmp = fma((y / -z), x, x);
	} else if (z <= -7.8e-8) {
		tmp = t_1;
	} else if (z <= 3.5e-92) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / Float64(z - t)) * x)
	tmp = 0.0
	if (z <= -7.6e+158)
		tmp = fma(Float64(y / Float64(-z)), x, x);
	elseif (z <= -7.8e-8)
		tmp = t_1;
	elseif (z <= 3.5e-92)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -7.6e+158], N[(N[(y / (-z)), $MachinePrecision] * x + x), $MachinePrecision], If[LessEqual[z, -7.8e-8], t$95$1, If[LessEqual[z, 3.5e-92], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999997e158

   1. Initial program 58.1%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. div-add N/A

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

      6. distribute-rgt-in N/A

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

      7. mul-1-neg N/A

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

      8. distribute-frac-neg N/A

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

      9. *-inverses N/A

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

      10. metadata-eval N/A

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

      11. neg-mul-1 N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

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

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

      16. distribute-lft-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. mul-1-neg N/A

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

      20. distribute-neg-frac2 N/A

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

      21. mul-1-neg N/A

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

      22. lower-/.f64 N/A

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

      23. mul-1-neg N/A

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

      24. lower-neg.f64 96.8

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

   5. Applied rewrites 96.8%

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

   if -7.5999999999999997e158 < z < -7.7999999999999997e-8 or 3.5e-92 < z

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 79.7

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

   5. Applied rewrites 79.7%

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

   if -7.7999999999999997e-8 < z < 3.5e-92

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 82.0

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

   5. Applied rewrites 82.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 370000000000:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ y (- z)) x x)))
   (if (<= z -4.4e-5)
     t_1
     (if (<= z 1.7e-254)
       (/ (* x y) (- t z))
       (if (<= z 370000000000.0) (* (/ (- y z) t) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / -z), x, x);
	double tmp;
	if (z <= -4.4e-5) {
		tmp = t_1;
	} else if (z <= 1.7e-254) {
		tmp = (x * y) / (t - z);
	} else if (z <= 370000000000.0) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / Float64(-z)), x, x)
	tmp = 0.0
	if (z <= -4.4e-5)
		tmp = t_1;
	elseif (z <= 1.7e-254)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 370000000000.0)
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / (-z)), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[z, -4.4e-5], t$95$1, If[LessEqual[z, 1.7e-254], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 370000000000.0], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3999999999999999e-5 or 3.7e11 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. div-add N/A

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

      6. distribute-rgt-in N/A

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

      7. mul-1-neg N/A

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

      8. distribute-frac-neg N/A

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

      9. *-inverses N/A

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

      10. metadata-eval N/A

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

      11. neg-mul-1 N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

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

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

      16. distribute-lft-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. mul-1-neg N/A

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

      20. distribute-neg-frac2 N/A

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

      21. mul-1-neg N/A

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

      22. lower-/.f64 N/A

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

      23. mul-1-neg N/A

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

      24. lower-neg.f64 78.0

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

   5. Applied rewrites 78.0%

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

   if -4.3999999999999999e-5 < z < 1.69999999999999996e-254

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if 1.69999999999999996e-254 < z < 3.7e11

   1. Initial program 88.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 94.4

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

   4. Applied rewrites 94.4%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 76.7

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

   7. Applied rewrites 76.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 370000000000:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+120}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e+120)
   (* (/ (- z y) z) x)
   (if (<= z 7.5e+109) (* (/ x (- z t)) (- z y)) (* (/ z (- z t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+120) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 7.5e+109) {
		tmp = (x / (z - t)) * (z - y);
	} else {
		tmp = (z / (z - t)) * x;
	}
	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 <= (-1.55d+120)) then
        tmp = ((z - y) / z) * x
    else if (z <= 7.5d+109) then
        tmp = (x / (z - t)) * (z - y)
    else
        tmp = (z / (z - t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+120) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 7.5e+109) {
		tmp = (x / (z - t)) * (z - y);
	} else {
		tmp = (z / (z - t)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+120:
		tmp = ((z - y) / z) * x
	elif z <= 7.5e+109:
		tmp = (x / (z - t)) * (z - y)
	else:
		tmp = (z / (z - t)) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e+120)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= 7.5e+109)
		tmp = Float64(Float64(x / Float64(z - t)) * Float64(z - y));
	else
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.55e+120)
		tmp = ((z - y) / z) * x;
	elseif (z <= 7.5e+109)
		tmp = (x / (z - t)) * (z - y);
	else
		tmp = (z / (z - t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e+120], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 7.5e+109], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999987e120

   1. Initial program 61.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 100.0

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

   4. Applied rewrites 100.0%

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

   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-in N/A

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

      5. div-add N/A

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

      6. neg-mul-1 N/A

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

      7. remove-double-neg N/A

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

      8. *-inverses N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 95.0

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

   7. Applied rewrites 95.0%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 95.0

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

   10. Applied rewrites 95.0%

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

   if -1.54999999999999987e120 < z < 7.50000000000000018e109

   1. Initial program 93.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 90.8

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

   4. Applied rewrites 90.8%

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

   if 7.50000000000000018e109 < z

   1. Initial program 70.4%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 92.2

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

   5. Applied rewrites 92.2%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+120}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e+68)
   (* (/ (- y z) t) x)
   (if (<= t 1.5e+56) (fma (/ y (- z)) x x) (* (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+68) {
		tmp = ((y - z) / t) * x;
	} else if (t <= 1.5e+56) {
		tmp = fma((y / -z), x, x);
	} else {
		tmp = (x / t) * (y - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e+68)
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	elseif (t <= 1.5e+56)
		tmp = fma(Float64(y / Float64(-z)), x, x);
	else
		tmp = Float64(Float64(x / t) * Float64(y - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e+68], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.5e+56], N[(N[(y / (-z)), $MachinePrecision] * x + x), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999997e68

   1. Initial program 83.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -1.59999999999999997e68 < t < 1.50000000000000003e56

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. div-add N/A

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

      6. distribute-rgt-in N/A

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

      7. mul-1-neg N/A

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

      8. distribute-frac-neg N/A

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

      9. *-inverses N/A

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

      10. metadata-eval N/A

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

      11. neg-mul-1 N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

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

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

      16. distribute-lft-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. mul-1-neg N/A

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

      20. distribute-neg-frac2 N/A

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

      21. mul-1-neg N/A

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

      22. lower-/.f64 N/A

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

      23. mul-1-neg N/A

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

      24. lower-neg.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if 1.50000000000000003e56 < t

   1. Initial program 80.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 69.9

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

   5. Applied rewrites 69.9%

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

   7. Applied rewrites 76.9%

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

Alternative 7: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ y (- z)) x x)))
   (if (<= z -4.5e-5) t_1 (if (<= z 1.6e-34) (/ (* x (- y z)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / -z), x, x);
	double tmp;
	if (z <= -4.5e-5) {
		tmp = t_1;
	} else if (z <= 1.6e-34) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / Float64(-z)), x, x)
	tmp = 0.0
	if (z <= -4.5e-5)
		tmp = t_1;
	elseif (z <= 1.6e-34)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / (-z)), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[z, -4.5e-5], t$95$1, If[LessEqual[z, 1.6e-34], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000028e-5 or 1.60000000000000001e-34 < z

   1. Initial program 76.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. div-add N/A

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

      6. distribute-rgt-in N/A

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

      7. mul-1-neg N/A

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

      8. distribute-frac-neg N/A

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

      9. *-inverses N/A

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

      10. metadata-eval N/A

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

      11. neg-mul-1 N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

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

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

      16. distribute-lft-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. mul-1-neg N/A

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

      20. distribute-neg-frac2 N/A

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

      21. mul-1-neg N/A

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

      22. lower-/.f64 N/A

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

      23. mul-1-neg N/A

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

      24. lower-neg.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -4.50000000000000028e-5 < z < 1.60000000000000001e-34

   1. Initial program 93.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+101}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 14200000000:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+101)
   (* 1.0 x)
   (if (<= z 14200000000.0) (/ (* x (- y z)) t) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+101) {
		tmp = 1.0 * x;
	} else if (z <= 14200000000.0) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-2.7d+101)) then
        tmp = 1.0d0 * x
    else if (z <= 14200000000.0d0) then
        tmp = (x * (y - z)) / t
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+101) {
		tmp = 1.0 * x;
	} else if (z <= 14200000000.0) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+101:
		tmp = 1.0 * x
	elif z <= 14200000000.0:
		tmp = (x * (y - z)) / t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+101)
		tmp = Float64(1.0 * x);
	elseif (z <= 14200000000.0)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e+101)
		tmp = 1.0 * x;
	elseif (z <= 14200000000.0)
		tmp = (x * (y - z)) / t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+101], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 14200000000.0], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000006e101 or 1.42e10 < z

   1. Initial program 71.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 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 68.8%

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

   if -2.70000000000000006e101 < z < 1.42e10

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 73.9

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

   5. Applied rewrites 73.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+101}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 14200000000:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.01:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{t - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.01)
   (* 1.0 x)
   (if (<= z 5.5e+102) (* (/ y (- t z)) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.01) {
		tmp = 1.0 * x;
	} else if (z <= 5.5e+102) {
		tmp = (y / (t - z)) * x;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-0.01d0)) then
        tmp = 1.0d0 * x
    else if (z <= 5.5d+102) then
        tmp = (y / (t - z)) * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.01) {
		tmp = 1.0 * x;
	} else if (z <= 5.5e+102) {
		tmp = (y / (t - z)) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.01:
		tmp = 1.0 * x
	elif z <= 5.5e+102:
		tmp = (y / (t - z)) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.01)
		tmp = Float64(1.0 * x);
	elseif (z <= 5.5e+102)
		tmp = Float64(Float64(y / Float64(t - z)) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.01)
		tmp = 1.0 * x;
	elseif (z <= 5.5e+102)
		tmp = (y / (t - z)) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.01], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 5.5e+102], N[(N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0100000000000000002 or 5.49999999999999981e102 < z

   1. Initial program 71.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. 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 71.7%

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

   if -0.0100000000000000002 < z < 5.49999999999999981e102

   1. Initial program 92.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 71.1

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

   5. Applied rewrites 71.1%

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

Alternative 10: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.01:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.01) (* 1.0 x) (if (<= z 9.8e+33) (* (/ x (- t z)) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.01) {
		tmp = 1.0 * x;
	} else if (z <= 9.8e+33) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-0.01d0)) then
        tmp = 1.0d0 * x
    else if (z <= 9.8d+33) then
        tmp = (x / (t - z)) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.01) {
		tmp = 1.0 * x;
	} else if (z <= 9.8e+33) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.01:
		tmp = 1.0 * x
	elif z <= 9.8e+33:
		tmp = (x / (t - z)) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.01)
		tmp = Float64(1.0 * x);
	elseif (z <= 9.8e+33)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.01)
		tmp = 1.0 * x;
	elseif (z <= 9.8e+33)
		tmp = (x / (t - z)) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.01], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 9.8e+33], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0100000000000000002 or 9.80000000000000027e33 < z

   1. Initial program 74.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

   if -0.0100000000000000002 < z < 9.80000000000000027e33

   1. Initial program 93.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 93.0

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 75.3

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

   7. Applied rewrites 75.3%

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

Alternative 11: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00016:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.00016) (* 1.0 x) (if (<= z 8.6e+33) (* (/ y t) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00016) {
		tmp = 1.0 * x;
	} else if (z <= 8.6e+33) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-0.00016d0)) then
        tmp = 1.0d0 * x
    else if (z <= 8.6d+33) then
        tmp = (y / t) * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00016) {
		tmp = 1.0 * x;
	} else if (z <= 8.6e+33) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.00016:
		tmp = 1.0 * x
	elif z <= 8.6e+33:
		tmp = (y / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.00016)
		tmp = Float64(1.0 * x);
	elseif (z <= 8.6e+33)
		tmp = Float64(Float64(y / t) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.00016)
		tmp = 1.0 * x;
	elseif (z <= 8.6e+33)
		tmp = (y / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.00016], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 8.6e+33], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000013e-4 or 8.60000000000000057e33 < z

   1. Initial program 74.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

   if -1.60000000000000013e-4 < z < 8.60000000000000057e33

   1. Initial program 93.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 93.0

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 68.5

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

   7. Applied rewrites 68.5%

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

Alternative 12: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00016:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.00016) (* 1.0 x) (if (<= z 5.2e+33) (/ (* x y) t) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00016) {
		tmp = 1.0 * x;
	} else if (z <= 5.2e+33) {
		tmp = (x * y) / t;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-0.00016d0)) then
        tmp = 1.0d0 * x
    else if (z <= 5.2d+33) then
        tmp = (x * y) / t
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00016) {
		tmp = 1.0 * x;
	} else if (z <= 5.2e+33) {
		tmp = (x * y) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.00016:
		tmp = 1.0 * x
	elif z <= 5.2e+33:
		tmp = (x * y) / t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.00016)
		tmp = Float64(1.0 * x);
	elseif (z <= 5.2e+33)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.00016)
		tmp = 1.0 * x;
	elseif (z <= 5.2e+33)
		tmp = (x * y) / t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.00016], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 5.2e+33], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000013e-4 or 5.1999999999999995e33 < z

   1. Initial program 74.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

   if -1.60000000000000013e-4 < z < 5.1999999999999995e33

   1. Initial program 93.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-commutative N/A

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

      3. lower-*.f64 66.9

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

   5. Applied rewrites 66.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00016:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00016:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.00016) (* 1.0 x) (if (<= z 8.6e+33) (* (/ x t) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00016) {
		tmp = 1.0 * x;
	} else if (z <= 8.6e+33) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-0.00016d0)) then
        tmp = 1.0d0 * x
    else if (z <= 8.6d+33) then
        tmp = (x / t) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00016) {
		tmp = 1.0 * x;
	} else if (z <= 8.6e+33) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.00016:
		tmp = 1.0 * x
	elif z <= 8.6e+33:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.00016)
		tmp = Float64(1.0 * x);
	elseif (z <= 8.6e+33)
		tmp = Float64(Float64(x / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.00016)
		tmp = 1.0 * x;
	elseif (z <= 8.6e+33)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.00016], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 8.6e+33], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000013e-4 or 8.60000000000000057e33 < z

   1. Initial program 74.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

   if -1.60000000000000013e-4 < z < 8.60000000000000057e33

   1. Initial program 93.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-commutative N/A

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

      3. lower-*.f64 66.9

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

   5. Applied rewrites 66.9%

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

   7. Applied rewrites 66.6%

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

Alternative 14: 35.3% accurate, 3.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.6%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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 96.5

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

4. Applied rewrites 96.5%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 40.2%

   \[\leadsto \color{blue}{1} \cdot x \]
8. Add Preprocessing

Developer Target 1: 96.9% 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 2024298 
(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)))