Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 6.6s

Alternatives: 8

Speedup: 1.0×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z, t)
	return fma(fma(x, y, z), y, t)
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3200000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-175}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-239}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -3200000000000.0)
     t_1
     (if (<= y -2.4e-175)
       t
       (if (<= y -1.15e-239) (* y z) (if (<= y 5.1e+81) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -3200000000000.0) {
		tmp = t_1;
	} else if (y <= -2.4e-175) {
		tmp = t;
	} else if (y <= -1.15e-239) {
		tmp = y * z;
	} else if (y <= 5.1e+81) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * y)
    if (y <= (-3200000000000.0d0)) then
        tmp = t_1
    else if (y <= (-2.4d-175)) then
        tmp = t
    else if (y <= (-1.15d-239)) then
        tmp = y * z
    else if (y <= 5.1d+81) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -3200000000000.0) {
		tmp = t_1;
	} else if (y <= -2.4e-175) {
		tmp = t;
	} else if (y <= -1.15e-239) {
		tmp = y * z;
	} else if (y <= 5.1e+81) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -3200000000000.0:
		tmp = t_1
	elif y <= -2.4e-175:
		tmp = t
	elif y <= -1.15e-239:
		tmp = y * z
	elif y <= 5.1e+81:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -3200000000000.0)
		tmp = t_1;
	elseif (y <= -2.4e-175)
		tmp = t;
	elseif (y <= -1.15e-239)
		tmp = Float64(y * z);
	elseif (y <= 5.1e+81)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -3200000000000.0)
		tmp = t_1;
	elseif (y <= -2.4e-175)
		tmp = t;
	elseif (y <= -1.15e-239)
		tmp = y * z;
	elseif (y <= 5.1e+81)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3200000000000.0], t$95$1, If[LessEqual[y, -2.4e-175], t, If[LessEqual[y, -1.15e-239], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.1e+81], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e12 or 5.1000000000000003e81 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 91.2%

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

   3. Taylor expanded in y around inf 63.5%

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

   if -3.2e12 < y < -2.4e-175 or -1.1499999999999999e-239 < y < 5.1000000000000003e81

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.1%

      \[\leadsto \color{blue}{t} \]

   if -2.4e-175 < y < -1.1499999999999999e-239

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 69.1%

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

   3. Taylor expanded in y around 0 69.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3200000000000:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-175}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-239}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4200000000000:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-175}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-240}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4200000000000.0)
   (* y (* x y))
   (if (<= y -2.4e-175)
     t
     (if (<= y -9.5e-240) (* y z) (if (<= y 5.1e+81) t (* x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4200000000000.0) {
		tmp = y * (x * y);
	} else if (y <= -2.4e-175) {
		tmp = t;
	} else if (y <= -9.5e-240) {
		tmp = y * z;
	} else if (y <= 5.1e+81) {
		tmp = t;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4200000000000.0d0)) then
        tmp = y * (x * y)
    else if (y <= (-2.4d-175)) then
        tmp = t
    else if (y <= (-9.5d-240)) then
        tmp = y * z
    else if (y <= 5.1d+81) then
        tmp = t
    else
        tmp = x * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4200000000000.0) {
		tmp = y * (x * y);
	} else if (y <= -2.4e-175) {
		tmp = t;
	} else if (y <= -9.5e-240) {
		tmp = y * z;
	} else if (y <= 5.1e+81) {
		tmp = t;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4200000000000.0:
		tmp = y * (x * y)
	elif y <= -2.4e-175:
		tmp = t
	elif y <= -9.5e-240:
		tmp = y * z
	elif y <= 5.1e+81:
		tmp = t
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4200000000000.0)
		tmp = Float64(y * Float64(x * y));
	elseif (y <= -2.4e-175)
		tmp = t;
	elseif (y <= -9.5e-240)
		tmp = Float64(y * z);
	elseif (y <= 5.1e+81)
		tmp = t;
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4200000000000.0)
		tmp = y * (x * y);
	elseif (y <= -2.4e-175)
		tmp = t;
	elseif (y <= -9.5e-240)
		tmp = y * z;
	elseif (y <= 5.1e+81)
		tmp = t;
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4200000000000.0], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-175], t, If[LessEqual[y, -9.5e-240], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.1e+81], t, N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e12

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 86.6%

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

   3. Taylor expanded in y around inf 60.4%

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

   if -4.2e12 < y < -2.4e-175 or -9.5000000000000005e-240 < y < 5.1000000000000003e81

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.1%

      \[\leadsto \color{blue}{t} \]

   if -2.4e-175 < y < -9.5000000000000005e-240

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 69.1%

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

   3. Taylor expanded in y around 0 69.0%

      \[\leadsto \color{blue}{z} \cdot y \]

   if 5.1000000000000003e81 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.6%

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

      1. flip-+ 7.7%

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

      2. clear-num 7.7%

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

      3. *-commutative 7.7%

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

      4. associate-*l* 3.5%

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

      5. pow2 3.5%

         \[\leadsto \frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{\color{blue}{{\left(\left(y \cdot x\right) \cdot y\right)}^{2}} - t \cdot t}} \]

      6. *-commutative 3.5%

         \[\leadsto \frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{{\left(\color{blue}{\left(x \cdot y\right)} \cdot y\right)}^{2} - t \cdot t}} \]

      7. associate-*l* 3.4%

         \[\leadsto \frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{{\color{blue}{\left(x \cdot \left(y \cdot y\right)\right)}}^{2} - t \cdot t}} \]

   4. Applied egg-rr 3.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{{\left(x \cdot \left(y \cdot y\right)\right)}^{2} - t \cdot t}}} \]

   5. Taylor expanded in x around inf 72.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{{y}^{2} \cdot x}}} \]
   6. Step-by-step derivation

      1. unpow2 72.4%

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

      2. associate-*l* 66.8%

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

   7. Simplified 66.8%

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

      1. remove-double-div 66.8%

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

      2. associate-*r* 72.4%

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

   9. Applied egg-rr 72.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4200000000000:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-175}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-240}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.058:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+223}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.058)
   (* y z)
   (if (<= z 6.5e+71)
     t
     (if (<= z 6.2e+194) (* y z) (if (<= z 1.15e+223) t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.058) {
		tmp = y * z;
	} else if (z <= 6.5e+71) {
		tmp = t;
	} else if (z <= 6.2e+194) {
		tmp = y * z;
	} else if (z <= 1.15e+223) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.058d0)) then
        tmp = y * z
    else if (z <= 6.5d+71) then
        tmp = t
    else if (z <= 6.2d+194) then
        tmp = y * z
    else if (z <= 1.15d+223) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.058) {
		tmp = y * z;
	} else if (z <= 6.5e+71) {
		tmp = t;
	} else if (z <= 6.2e+194) {
		tmp = y * z;
	} else if (z <= 1.15e+223) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.058:
		tmp = y * z
	elif z <= 6.5e+71:
		tmp = t
	elif z <= 6.2e+194:
		tmp = y * z
	elif z <= 1.15e+223:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.058)
		tmp = Float64(y * z);
	elseif (z <= 6.5e+71)
		tmp = t;
	elseif (z <= 6.2e+194)
		tmp = Float64(y * z);
	elseif (z <= 1.15e+223)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.058)
		tmp = y * z;
	elseif (z <= 6.5e+71)
		tmp = t;
	elseif (z <= 6.2e+194)
		tmp = y * z;
	elseif (z <= 1.15e+223)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.058], N[(y * z), $MachinePrecision], If[LessEqual[z, 6.5e+71], t, If[LessEqual[z, 6.2e+194], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.15e+223], t, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0580000000000000029 or 6.49999999999999954e71 < z < 6.1999999999999999e194 or 1.15000000000000002e223 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 84.0%

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

   3. Taylor expanded in y around 0 66.6%

      \[\leadsto \color{blue}{z} \cdot y \]

   if -0.0580000000000000029 < z < 6.49999999999999954e71 or 6.1999999999999999e194 < z < 1.15000000000000002e223

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 60.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.058:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+223}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1750000000000 \lor \neg \left(y \leq 5.1 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1750000000000.0) (not (<= y 5.1e+81)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1750000000000.0) || !(y <= 5.1e+81)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1750000000000.0d0)) .or. (.not. (y <= 5.1d+81))) then
        tmp = y * (z + (x * y))
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1750000000000.0) || !(y <= 5.1e+81)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1750000000000.0) or not (y <= 5.1e+81):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1750000000000.0) || !(y <= 5.1e+81))
		tmp = Float64(y * Float64(z + Float64(x * y)));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1750000000000.0) || ~((y <= 5.1e+81)))
		tmp = y * (z + (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1750000000000.0], N[Not[LessEqual[y, 5.1e+81]], $MachinePrecision]], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e12 or 5.1000000000000003e81 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 91.2%

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

   if -1.75e12 < y < 5.1000000000000003e81

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1750000000000 \lor \neg \left(y \leq 5.1 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+192}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e+168)
   (* y (* x y))
   (if (<= y 3.8e+192) (+ t (* y z)) (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+168) {
		tmp = y * (x * y);
	} else if (y <= 3.8e+192) {
		tmp = t + (y * z);
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.3d+168)) then
        tmp = y * (x * y)
    else if (y <= 3.8d+192) then
        tmp = t + (y * z)
    else
        tmp = x * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+168) {
		tmp = y * (x * y);
	} else if (y <= 3.8e+192) {
		tmp = t + (y * z);
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e+168:
		tmp = y * (x * y)
	elif y <= 3.8e+192:
		tmp = t + (y * z)
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e+168)
		tmp = Float64(y * Float64(x * y));
	elseif (y <= 3.8e+192)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e+168)
		tmp = y * (x * y);
	elseif (y <= 3.8e+192)
		tmp = t + (y * z);
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e+168], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+192], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2999999999999999e168

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

   3. Taylor expanded in y around inf 85.7%

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

   if -3.2999999999999999e168 < y < 3.7999999999999999e192

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.0%

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

   if 3.7999999999999999e192 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 88.4%

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

      1. flip-+ 4.2%

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

      2. clear-num 4.2%

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

      3. *-commutative 4.2%

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

      4. associate-*l* 0.1%

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

      5. pow2 0.1%

         \[\leadsto \frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{\color{blue}{{\left(\left(y \cdot x\right) \cdot y\right)}^{2}} - t \cdot t}} \]

      6. *-commutative 0.1%

         \[\leadsto \frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{{\left(\color{blue}{\left(x \cdot y\right)} \cdot y\right)}^{2} - t \cdot t}} \]

      7. associate-*l* 0.0%

         \[\leadsto \frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{{\color{blue}{\left(x \cdot \left(y \cdot y\right)\right)}}^{2} - t \cdot t}} \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \left(y \cdot y\right) - t}{{\left(x \cdot \left(y \cdot y\right)\right)}^{2} - t \cdot t}}} \]

   5. Taylor expanded in x around inf 92.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{{y}^{2} \cdot x}}} \]
   6. Step-by-step derivation

      1. unpow2 92.2%

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

      2. associate-*l* 88.4%

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

   7. Simplified 88.4%

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

      1. remove-double-div 88.4%

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

      2. associate-*r* 92.2%

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

   9. Applied egg-rr 92.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+192}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 8: 39.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 40.1%

   \[\leadsto \color{blue}{t} \]

3. Final simplification 40.1%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))