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

Percentage Accurate: 99.9% → 99.9%

Time: 6.2s

Alternatives: 7

Speedup: 1.0×

• 29.2% 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: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-145}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-8}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+73}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -9e-30)
     t_1
     (if (<= y -8.5e-145)
       (* y z)
       (if (<= y 6.2e-59)
         t
         (if (<= y 8.6e-8) (* y z) (if (<= y 3.5e+73) t t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -9e-30) {
		tmp = t_1;
	} else if (y <= -8.5e-145) {
		tmp = y * z;
	} else if (y <= 6.2e-59) {
		tmp = t;
	} else if (y <= 8.6e-8) {
		tmp = y * z;
	} else if (y <= 3.5e+73) {
		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 <= (-9d-30)) then
        tmp = t_1
    else if (y <= (-8.5d-145)) then
        tmp = y * z
    else if (y <= 6.2d-59) then
        tmp = t
    else if (y <= 8.6d-8) then
        tmp = y * z
    else if (y <= 3.5d+73) 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 <= -9e-30) {
		tmp = t_1;
	} else if (y <= -8.5e-145) {
		tmp = y * z;
	} else if (y <= 6.2e-59) {
		tmp = t;
	} else if (y <= 8.6e-8) {
		tmp = y * z;
	} else if (y <= 3.5e+73) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -9e-30:
		tmp = t_1
	elif y <= -8.5e-145:
		tmp = y * z
	elif y <= 6.2e-59:
		tmp = t
	elif y <= 8.6e-8:
		tmp = y * z
	elif y <= 3.5e+73:
		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 <= -9e-30)
		tmp = t_1;
	elseif (y <= -8.5e-145)
		tmp = Float64(y * z);
	elseif (y <= 6.2e-59)
		tmp = t;
	elseif (y <= 8.6e-8)
		tmp = Float64(y * z);
	elseif (y <= 3.5e+73)
		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 <= -9e-30)
		tmp = t_1;
	elseif (y <= -8.5e-145)
		tmp = y * z;
	elseif (y <= 6.2e-59)
		tmp = t;
	elseif (y <= 8.6e-8)
		tmp = y * z;
	elseif (y <= 3.5e+73)
		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, -9e-30], t$95$1, If[LessEqual[y, -8.5e-145], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.2e-59], t, If[LessEqual[y, 8.6e-8], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.5e+73], t, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999935e-30 or 3.50000000000000002e73 < y

   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. Taylor expanded in t around 0 93.1%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. *-commutative 67.4%

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

   7. Simplified 67.4%

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

   if -8.99999999999999935e-30 < y < -8.50000000000000043e-145 or 6.19999999999999998e-59 < y < 8.6000000000000002e-8

   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 t around 0 76.5%

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

   5. Taylor expanded in z around inf 64.3%

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

   if -8.50000000000000043e-145 < y < 6.19999999999999998e-59 or 8.6000000000000002e-8 < y < 3.50000000000000002e73

   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 y around 0 67.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-145}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-8}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+73}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-60} \lor \neg \left(y \leq 4 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-60) (not (<= y 4e+39)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-60) || !(y <= 4e+39)) {
		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 <= (-4.2d-60)) .or. (.not. (y <= 4d+39))) 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 <= -4.2e-60) || !(y <= 4e+39)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e-60) or not (y <= 4e+39):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e-60) || !(y <= 4e+39))
		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 <= -4.2e-60) || ~((y <= 4e+39)))
		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, -4.2e-60], N[Not[LessEqual[y, 4e+39]], $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 < -4.19999999999999982e-60 or 3.99999999999999976e39 < y

   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 t around 0 90.4%

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

   if -4.19999999999999982e-60 < y < 3.99999999999999976e39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-60} \lor \neg \left(y \leq 4 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 4: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+94} \lor \neg \left(y \leq 5.5 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.7e+94) (not (<= y 5.5e+75))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e+94) || !(y <= 5.5e+75)) {
		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 <= (-4.7d+94)) .or. (.not. (y <= 5.5d+75))) 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 <= -4.7e+94) || !(y <= 5.5e+75)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.7e+94) or not (y <= 5.5e+75):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.7e+94) || !(y <= 5.5e+75))
		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 <= -4.7e+94) || ~((y <= 5.5e+75)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.7e+94], N[Not[LessEqual[y, 5.5e+75]], $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 < -4.70000000000000017e94 or 5.5000000000000001e75 < y

   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. Taylor expanded in t around 0 98.8%

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

   5. Taylor expanded in z around 0 73.5%

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

      1. *-commutative 73.5%

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

   7. Simplified 73.5%

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

   if -4.70000000000000017e94 < y < 5.5000000000000001e75

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+94} \lor \neg \left(y \leq 5.5 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 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 6: 52.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+134} \lor \neg \left(z \leq 1.36 \cdot 10^{+70}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e+134) (not (<= z 1.36e+70))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+134) || !(z <= 1.36e+70)) {
		tmp = y * z;
	} 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 ((z <= (-3.9d+134)) .or. (.not. (z <= 1.36d+70))) then
        tmp = y * z
    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 ((z <= -3.9e+134) || !(z <= 1.36e+70)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e+134) or not (z <= 1.36e+70):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e+134) || !(z <= 1.36e+70))
		tmp = Float64(y * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e+134) || ~((z <= 1.36e+70)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e+134], N[Not[LessEqual[z, 1.36e+70]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999983e134 or 1.35999999999999995e70 < 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 85.2%

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

   5. Taylor expanded in z around inf 75.3%

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

   if -3.89999999999999983e134 < z < 1.35999999999999995e70

   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 46.1%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+134} \lor \neg \left(z \leq 1.36 \cdot 10^{+70}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 38.6% 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 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 y around 0 35.3%

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

5. Final simplification 35.3%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))