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

Percentage Accurate: 99.9% → 99.9%

Time: 6.1s

Alternatives: 8

Speedup: 1.0×

• 29.1% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 79.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+146} \lor \neg \left(y \leq -9.2 \cdot 10^{+78} \lor \neg \left(y \leq -8.8 \cdot 10^{+46}\right) \land y \leq 1.1 \cdot 10^{+112}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+146)
         (not
          (or (<= y -9.2e+78) (and (not (<= y -8.8e+46)) (<= y 1.1e+112)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+146) || !((y <= -9.2e+78) || (!(y <= -8.8e+46) && (y <= 1.1e+112)))) {
		tmp = y * (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 <= (-7.5d+146)) .or. (.not. (y <= (-9.2d+78)) .or. (.not. (y <= (-8.8d+46))) .and. (y <= 1.1d+112))) then
        tmp = y * (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 <= -7.5e+146) || !((y <= -9.2e+78) || (!(y <= -8.8e+46) && (y <= 1.1e+112)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+146) or not ((y <= -9.2e+78) or (not (y <= -8.8e+46) and (y <= 1.1e+112))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+146) || !((y <= -9.2e+78) || (!(y <= -8.8e+46) && (y <= 1.1e+112))))
		tmp = Float64(y * 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 <= -7.5e+146) || ~(((y <= -9.2e+78) || (~((y <= -8.8e+46)) && (y <= 1.1e+112)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+146], N[Not[Or[LessEqual[y, -9.2e+78], And[N[Not[LessEqual[y, -8.8e+46]], $MachinePrecision], LessEqual[y, 1.1e+112]]]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999983e146 or -9.2000000000000008e78 < y < -8.8000000000000001e46 or 1.1e112 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      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. Taylor expanded in t around 0 97.9%

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

   5. Taylor expanded in z around 0 77.4%

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

      1. *-commutative 77.4%

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

   7. Simplified 77.4%

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

   if -7.49999999999999983e146 < y < -9.2000000000000008e78 or -8.8000000000000001e46 < y < 1.1e112

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 81.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+146} \lor \neg \left(y \leq -9.2 \cdot 10^{+78} \lor \neg \left(y \leq -8.8 \cdot 10^{+46}\right) \land y \leq 1.1 \cdot 10^{+112}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 3: 50.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+126}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+207}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e+47)
   (* y z)
   (if (<= z 7.5e+72)
     t
     (if (<= z 1.6e+126) (* y z) (if (<= z 4.5e+207) t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e+47) {
		tmp = y * z;
	} else if (z <= 7.5e+72) {
		tmp = t;
	} else if (z <= 1.6e+126) {
		tmp = y * z;
	} else if (z <= 4.5e+207) {
		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 <= (-1.02d+47)) then
        tmp = y * z
    else if (z <= 7.5d+72) then
        tmp = t
    else if (z <= 1.6d+126) then
        tmp = y * z
    else if (z <= 4.5d+207) 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 <= -1.02e+47) {
		tmp = y * z;
	} else if (z <= 7.5e+72) {
		tmp = t;
	} else if (z <= 1.6e+126) {
		tmp = y * z;
	} else if (z <= 4.5e+207) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e+47:
		tmp = y * z
	elif z <= 7.5e+72:
		tmp = t
	elif z <= 1.6e+126:
		tmp = y * z
	elif z <= 4.5e+207:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e+47)
		tmp = Float64(y * z);
	elseif (z <= 7.5e+72)
		tmp = t;
	elseif (z <= 1.6e+126)
		tmp = Float64(y * z);
	elseif (z <= 4.5e+207)
		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 <= -1.02e+47)
		tmp = y * z;
	elseif (z <= 7.5e+72)
		tmp = t;
	elseif (z <= 1.6e+126)
		tmp = y * z;
	elseif (z <= 4.5e+207)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e+47], N[(y * z), $MachinePrecision], If[LessEqual[z, 7.5e+72], t, If[LessEqual[z, 1.6e+126], N[(y * z), $MachinePrecision], If[LessEqual[z, 4.5e+207], t, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0199999999999999e47 or 7.50000000000000027e72 < z < 1.5999999999999999e126 or 4.50000000000000003e207 < z

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      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. Taylor expanded in t around 0 75.4%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -1.0199999999999999e47 < z < 7.50000000000000027e72 or 1.5999999999999999e126 < z < 4.50000000000000003e207

   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 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 48.6%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+126}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+207}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-14} \lor \neg \left(y \leq 4.5 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e-14) (not (<= y 4.5e+59)))
   (* y (+ (* x y) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-14) || !(y <= 4.5e+59)) {
		tmp = y * ((x * y) + z);
	} 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 <= (-2.9d-14)) .or. (.not. (y <= 4.5d+59))) then
        tmp = y * ((x * y) + z)
    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 <= -2.9e-14) || !(y <= 4.5e+59)) {
		tmp = y * ((x * y) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e-14) or not (y <= 4.5e+59):
		tmp = y * ((x * y) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e-14) || !(y <= 4.5e+59))
		tmp = Float64(y * Float64(Float64(x * y) + z));
	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 <= -2.9e-14) || ~((y <= 4.5e+59)))
		tmp = y * ((x * y) + z);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e-14], N[Not[LessEqual[y, 4.5e+59]], $MachinePrecision]], N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000003e-14 or 4.49999999999999959e59 < y

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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. Taylor expanded in t around 0 88.5%

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

   if -2.9000000000000003e-14 < y < 4.49999999999999959e59

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-14} \lor \neg \left(y \leq 4.5 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+70} \lor \neg \left(z \leq 3.9 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+70) (not (<= z 3.9e+79)))
   (+ t (* y z))
   (+ t (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+70) || !(z <= 3.9e+79)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (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 ((z <= (-3.1d+70)) .or. (.not. (z <= 3.9d+79))) then
        tmp = t + (y * z)
    else
        tmp = t + (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 ((z <= -3.1e+70) || !(z <= 3.9e+79)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (x * (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+70) or not (z <= 3.9e+79):
		tmp = t + (y * z)
	else:
		tmp = t + (x * (y * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+70) || !(z <= 3.9e+79))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(x * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+70) || ~((z <= 3.9e+79)))
		tmp = t + (y * z);
	else
		tmp = t + (x * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+70], N[Not[LessEqual[z, 3.9e+79]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000003e70 or 3.8999999999999997e79 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.6%

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

   if -3.1000000000000003e70 < z < 3.8999999999999997e79

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-rgt-in 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in x around inf 92.0%

      \[\leadsto \color{blue}{x \cdot {y}^{2}} + t \]
   5. Step-by-step derivation

      1. unpow2 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+70} \lor \neg \left(z \leq 3.9 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 6: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+72} \lor \neg \left(z \leq 2.95 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e+72) (not (<= z 2.95e+79)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+72) || !(z <= 2.95e+79)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * 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 ((z <= (-4.1d+72)) .or. (.not. (z <= 2.95d+79))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+72) || !(z <= 2.95e+79)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e+72) or not (z <= 2.95e+79):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e+72) || !(z <= 2.95e+79))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e+72) || ~((z <= 2.95e+79)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e+72], N[Not[LessEqual[z, 2.95e+79]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999963e72 or 2.95e79 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.6%

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

   if -4.09999999999999963e72 < z < 2.95e79

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 96.8%

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

      1. *-commutative 96.8%

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

   4. Simplified 96.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+72} \lor \neg \left(z \leq 2.95 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 7: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-20} \lor \neg \left(y \leq 1.3 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.15e-20) (not (<= y 1.3e+71))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e-20) || !(y <= 1.3e+71)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.15d-20)) .or. (.not. (y <= 1.3d+71))) then
        tmp = y * (x * y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e-20) || !(y <= 1.3e+71)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.15e-20) or not (y <= 1.3e+71):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.15e-20) || !(y <= 1.3e+71))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.15e-20) || ~((y <= 1.3e+71)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.15e-20], N[Not[LessEqual[y, 1.3e+71]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000006e-20 or 1.29999999999999996e71 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      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. Taylor expanded in t around 0 89.7%

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

   5. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   7. Simplified 67.7%

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

   if -2.15000000000000006e-20 < y < 1.29999999999999996e71

   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 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 67.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-20} \lor \neg \left(y \leq 1.3 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 39.6% 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. 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 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 40.2%

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

5. Final simplification 40.2%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))