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

Percentage Accurate: 83.7% → 97.1%

Time: 8.3s

Alternatives: 9

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: 83.7% 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: 97.1% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.2%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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. Final simplification 95.6%

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

Alternative 2: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{-y}{z}, x\right)\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y) z) x)))
   (if (<= z -5.3e-21)
     t_1
     (if (<= z -5.8e-275)
       (* (/ x (- t z)) y)
       (if (<= z 2.8e+68) (/ (* x y) (- t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, (-y / z), x);
	double tmp;
	if (z <= -5.3e-21) {
		tmp = t_1;
	} else if (z <= -5.8e-275) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 2.8e+68) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, Float64(Float64(-y) / z), x)
	tmp = 0.0
	if (z <= -5.3e-21)
		tmp = t_1;
	elseif (z <= -5.8e-275)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (z <= 2.8e+68)
		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[(x * N[((-y) / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.3e-21], t$95$1, If[LessEqual[z, -5.8e-275], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 2.8e+68], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2999999999999999e-21 or 2.8e68 < z

   1. Initial program 75.6%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

      11. distribute-neg-frac2 N/A

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

      12. *-commutative N/A

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

      13. distribute-lft-out-- N/A

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

      14. mul-1-neg N/A

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

      15. associate-/l* N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 81.8%

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

   if -5.2999999999999999e-21 < z < -5.800000000000001e-275

   1. Initial program 88.9%

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

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

      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 82.6

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

   5. Applied rewrites 82.6%

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

   if -5.800000000000001e-275 < z < 2.8e68

   1. Initial program 95.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-y}{z}, x\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-y}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+14}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 370:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+14)
   (* 1.0 x)
   (if (<= z -1.55e-40)
     (/ (* (- z) x) t)
     (if (<= z 370.0) (* (/ x t) y) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+14) {
		tmp = 1.0 * x;
	} else if (z <= -1.55e-40) {
		tmp = (-z * x) / t;
	} else if (z <= 370.0) {
		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 <= (-2.3d+14)) then
        tmp = 1.0d0 * x
    else if (z <= (-1.55d-40)) then
        tmp = (-z * x) / t
    else if (z <= 370.0d0) 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 <= -2.3e+14) {
		tmp = 1.0 * x;
	} else if (z <= -1.55e-40) {
		tmp = (-z * x) / t;
	} else if (z <= 370.0) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+14:
		tmp = 1.0 * x
	elif z <= -1.55e-40:
		tmp = (-z * x) / t
	elif z <= 370.0:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+14)
		tmp = Float64(1.0 * x);
	elseif (z <= -1.55e-40)
		tmp = Float64(Float64(Float64(-z) * x) / t);
	elseif (z <= 370.0)
		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 <= -2.3e+14)
		tmp = 1.0 * x;
	elseif (z <= -1.55e-40)
		tmp = (-z * x) / t;
	elseif (z <= 370.0)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+14], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, -1.55e-40], N[(N[((-z) * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 370.0], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e14 or 370 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 60.5%

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

   if -2.3e14 < z < -1.55000000000000005e-40

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 61.0

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\left(-1 \cdot z\right) \cdot x}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 55.9%

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

   if -1.55000000000000005e-40 < z < 370

   1. Initial program 92.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 65.9

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

   5. Applied rewrites 65.9%

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

   7. Applied rewrites 67.4%

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

Alternative 4: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-22}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{-t} \cdot z\\ \mathbf{elif}\;z \leq 370:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e-22)
   (* 1.0 x)
   (if (<= z -1.55e-40)
     (* (/ x (- t)) z)
     (if (<= z 370.0) (* (/ x t) y) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-22) {
		tmp = 1.0 * x;
	} else if (z <= -1.55e-40) {
		tmp = (x / -t) * z;
	} else if (z <= 370.0) {
		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 <= (-1.3d-22)) then
        tmp = 1.0d0 * x
    else if (z <= (-1.55d-40)) then
        tmp = (x / -t) * z
    else if (z <= 370.0d0) 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 <= -1.3e-22) {
		tmp = 1.0 * x;
	} else if (z <= -1.55e-40) {
		tmp = (x / -t) * z;
	} else if (z <= 370.0) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e-22:
		tmp = 1.0 * x
	elif z <= -1.55e-40:
		tmp = (x / -t) * z
	elif z <= 370.0:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e-22)
		tmp = Float64(1.0 * x);
	elseif (z <= -1.55e-40)
		tmp = Float64(Float64(x / Float64(-t)) * z);
	elseif (z <= 370.0)
		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 <= -1.3e-22)
		tmp = 1.0 * x;
	elseif (z <= -1.55e-40)
		tmp = (x / -t) * z;
	elseif (z <= 370.0)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e-22], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, -1.55e-40], N[(N[(x / (-t)), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 370.0], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e-22 or 370 < z

   1. Initial program 77.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 58.7%

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

   if -1.3e-22 < z < -1.55000000000000005e-40

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.9%

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

   if -1.55000000000000005e-40 < z < 370

   1. Initial program 92.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 65.9

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

   5. Applied rewrites 65.9%

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

   7. Applied rewrites 67.4%

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

Alternative 5: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{-y}{z}, x\right)\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 55:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y) z) x)))
   (if (<= z -5.3e-21) t_1 (if (<= z 55.0) (* (/ x (- t z)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, (-y / z), x);
	double tmp;
	if (z <= -5.3e-21) {
		tmp = t_1;
	} else if (z <= 55.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, Float64(Float64(-y) / z), x)
	tmp = 0.0
	if (z <= -5.3e-21)
		tmp = t_1;
	elseif (z <= 55.0)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-y) / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.3e-21], t$95$1, If[LessEqual[z, 55.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2999999999999999e-21 or 55 < z

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

      11. distribute-neg-frac2 N/A

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

      12. *-commutative N/A

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

      13. distribute-lft-out-- N/A

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

      14. mul-1-neg N/A

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

      15. associate-/l* N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 79.8%

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

   if -5.2999999999999999e-21 < z < 55

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   4. 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 80.2

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

   5. Applied rewrites 80.2%

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

Alternative 6: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 55:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (* x y) z))))
   (if (<= z -1.25e-26) t_1 (if (<= z 55.0) (* (/ x (- t z)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((x * y) / z);
	double tmp;
	if (z <= -1.25e-26) {
		tmp = t_1;
	} else if (z <= 55.0) {
		tmp = (x / (t - z)) * y;
	} 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 - ((x * y) / z)
    if (z <= (-1.25d-26)) then
        tmp = t_1
    else if (z <= 55.0d0) then
        tmp = (x / (t - z)) * y
    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 - ((x * y) / z);
	double tmp;
	if (z <= -1.25e-26) {
		tmp = t_1;
	} else if (z <= 55.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((x * y) / z)
	tmp = 0
	if z <= -1.25e-26:
		tmp = t_1
	elif z <= 55.0:
		tmp = (x / (t - z)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(x * y) / z))
	tmp = 0.0
	if (z <= -1.25e-26)
		tmp = t_1;
	elseif (z <= 55.0)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((x * y) / z);
	tmp = 0.0;
	if (z <= -1.25e-26)
		tmp = t_1;
	elseif (z <= 55.0)
		tmp = (x / (t - z)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e-26], t$95$1, If[LessEqual[z, 55.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000005e-26 or 55 < z

   1. Initial program 77.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. metadata-eval N/A

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

      8. distribute-rgt-in N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -1.25000000000000005e-26 < z < 55

   1. Initial program 92.2%

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

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

      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 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 55:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+63)
   (* 1.0 x)
   (if (<= z 8.5e+102) (* (/ x (- t z)) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+63) {
		tmp = 1.0 * x;
	} else if (z <= 8.5e+102) {
		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 <= (-1.65d+63)) then
        tmp = 1.0d0 * x
    else if (z <= 8.5d+102) 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 <= -1.65e+63) {
		tmp = 1.0 * x;
	} else if (z <= 8.5e+102) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+63:
		tmp = 1.0 * x
	elif z <= 8.5e+102:
		tmp = (x / (t - z)) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+63)
		tmp = Float64(1.0 * x);
	elseif (z <= 8.5e+102)
		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 <= -1.65e+63)
		tmp = 1.0 * x;
	elseif (z <= 8.5e+102)
		tmp = (x / (t - z)) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+63], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 8.5e+102], 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 < -1.6500000000000001e63 or 8.4999999999999996e102 < z

   1. Initial program 71.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 67.0%

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

   if -1.6500000000000001e63 < z < 8.4999999999999996e102

   1. Initial program 92.6%

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

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

      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 72.8

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

   5. Applied rewrites 72.8%

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

Alternative 8: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-27}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 370:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e-27) (* 1.0 x) (if (<= z 370.0) (* (/ x t) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-27) {
		tmp = 1.0 * x;
	} else if (z <= 370.0) {
		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 <= (-2.7d-27)) then
        tmp = 1.0d0 * x
    else if (z <= 370.0d0) 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 <= -2.7e-27) {
		tmp = 1.0 * x;
	} else if (z <= 370.0) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e-27:
		tmp = 1.0 * x
	elif z <= 370.0:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e-27)
		tmp = Float64(1.0 * x);
	elseif (z <= 370.0)
		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 <= -2.7e-27)
		tmp = 1.0 * x;
	elseif (z <= 370.0)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e-27], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 370.0], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999989e-27 or 370 < z

   1. Initial program 77.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 57.4%

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

   if -2.69999999999999989e-27 < z < 370

   1. Initial program 92.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 64.5

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

   5. Applied rewrites 64.5%

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

   7. Applied rewrites 65.9%

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

Alternative 9: 34.8% 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 85.2%

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

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

7. Applied rewrites 32.6%

   \[\leadsto \color{blue}{1} \cdot x \]
8. 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 2024332 
(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)))