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

Percentage Accurate: 99.9% → 99.9%

Time: 6.0s

Alternatives: 9

Speedup: 1.0×

• 29.4% 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 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. Final simplification 99.9%

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

Alternative 2: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -4e+35)
     t_1
     (if (<= y -4000000.0)
       (* y z)
       (if (<= y -1.4e-14)
         t_1
         (if (<= y 2.3e-24)
           t
           (if (<= y 1.15e+28)
             t_1
             (if (<= y 6.6e+82) t (if (<= y 3.5e+103) (* y z) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -4e+35) {
		tmp = t_1;
	} else if (y <= -4000000.0) {
		tmp = y * z;
	} else if (y <= -1.4e-14) {
		tmp = t_1;
	} else if (y <= 2.3e-24) {
		tmp = t;
	} else if (y <= 1.15e+28) {
		tmp = t_1;
	} else if (y <= 6.6e+82) {
		tmp = t;
	} else if (y <= 3.5e+103) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * y)
    if (y <= (-4d+35)) then
        tmp = t_1
    else if (y <= (-4000000.0d0)) then
        tmp = y * z
    else if (y <= (-1.4d-14)) then
        tmp = t_1
    else if (y <= 2.3d-24) then
        tmp = t
    else if (y <= 1.15d+28) then
        tmp = t_1
    else if (y <= 6.6d+82) then
        tmp = t
    else if (y <= 3.5d+103) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -4e+35) {
		tmp = t_1;
	} else if (y <= -4000000.0) {
		tmp = y * z;
	} else if (y <= -1.4e-14) {
		tmp = t_1;
	} else if (y <= 2.3e-24) {
		tmp = t;
	} else if (y <= 1.15e+28) {
		tmp = t_1;
	} else if (y <= 6.6e+82) {
		tmp = t;
	} else if (y <= 3.5e+103) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -4e+35:
		tmp = t_1
	elif y <= -4000000.0:
		tmp = y * z
	elif y <= -1.4e-14:
		tmp = t_1
	elif y <= 2.3e-24:
		tmp = t
	elif y <= 1.15e+28:
		tmp = t_1
	elif y <= 6.6e+82:
		tmp = t
	elif y <= 3.5e+103:
		tmp = y * z
	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 <= -4e+35)
		tmp = t_1;
	elseif (y <= -4000000.0)
		tmp = Float64(y * z);
	elseif (y <= -1.4e-14)
		tmp = t_1;
	elseif (y <= 2.3e-24)
		tmp = t;
	elseif (y <= 1.15e+28)
		tmp = t_1;
	elseif (y <= 6.6e+82)
		tmp = t;
	elseif (y <= 3.5e+103)
		tmp = Float64(y * z);
	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 <= -4e+35)
		tmp = t_1;
	elseif (y <= -4000000.0)
		tmp = y * z;
	elseif (y <= -1.4e-14)
		tmp = t_1;
	elseif (y <= 2.3e-24)
		tmp = t;
	elseif (y <= 1.15e+28)
		tmp = t_1;
	elseif (y <= 6.6e+82)
		tmp = t;
	elseif (y <= 3.5e+103)
		tmp = y * z;
	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, -4e+35], t$95$1, If[LessEqual[y, -4000000.0], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.4e-14], t$95$1, If[LessEqual[y, 2.3e-24], t, If[LessEqual[y, 1.15e+28], t$95$1, If[LessEqual[y, 6.6e+82], t, If[LessEqual[y, 3.5e+103], N[(y * z), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999999e35 or -4e6 < y < -1.4e-14 or 2.3000000000000001e-24 < y < 1.14999999999999992e28 or 3.5e103 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.7%

      \[\leadsto \color{blue}{y \cdot z + \left(t + {y}^{2} \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 83.7%

         \[\leadsto \color{blue}{\left(y \cdot z + t\right) + {y}^{2} \cdot x} \]

      2. fma-def 83.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} + {y}^{2} \cdot x \]

      3. unpow2 83.7%

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

      4. associate-*r* 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in y around inf 67.5%

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

      1. unpow2 67.5%

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

      2. associate-*r* 72.9%

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

   7. Simplified 72.9%

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

   if -3.9999999999999999e35 < y < -4e6 or 6.5999999999999997e82 < y < 3.5e103

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{y \cdot z + \left(t + {y}^{2} \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(y \cdot z + t\right) + {y}^{2} \cdot x} \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} + {y}^{2} \cdot x \]

      3. unpow2 100.0%

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

      4. associate-*r* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 68.6%

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

   if -1.4e-14 < y < 2.3000000000000001e-24 or 1.14999999999999992e28 < y < 6.5999999999999997e82

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+123} \lor \neg \left(y \leq -6.8 \cdot 10^{+64} \lor \neg \left(y \leq -4 \cdot 10^{+37}\right) \land y \leq 2.4 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e+123)
         (not (or (<= y -6.8e+64) (and (not (<= y -4e+37)) (<= y 2.4e+109)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+123) || !((y <= -6.8e+64) || (!(y <= -4e+37) && (y <= 2.4e+109)))) {
		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 <= (-7.2d+123)) .or. (.not. (y <= (-6.8d+64)) .or. (.not. (y <= (-4d+37))) .and. (y <= 2.4d+109))) 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 <= -7.2e+123) || !((y <= -6.8e+64) || (!(y <= -4e+37) && (y <= 2.4e+109)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e+123) or not ((y <= -6.8e+64) or (not (y <= -4e+37) and (y <= 2.4e+109))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e+123) || !((y <= -6.8e+64) || (!(y <= -4e+37) && (y <= 2.4e+109))))
		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 <= -7.2e+123) || ~(((y <= -6.8e+64) || (~((y <= -4e+37)) && (y <= 2.4e+109)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e+123], N[Not[Or[LessEqual[y, -6.8e+64], And[N[Not[LessEqual[y, -4e+37]], $MachinePrecision], LessEqual[y, 2.4e+109]]]], $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 < -7.19999999999999996e123 or -6.8000000000000003e64 < y < -3.99999999999999982e37 or 2.39999999999999987e109 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{y \cdot z + \left(t + {y}^{2} \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 77.6%

         \[\leadsto \color{blue}{\left(y \cdot z + t\right) + {y}^{2} \cdot x} \]

      2. fma-def 77.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} + {y}^{2} \cdot x \]

      3. unpow2 77.6%

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

      4. associate-*r* 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. unpow2 76.1%

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

      2. associate-*r* 83.5%

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

   7. Simplified 83.5%

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

   if -7.19999999999999996e123 < y < -6.8000000000000003e64 or -3.99999999999999982e37 < y < 2.39999999999999987e109

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+123} \lor \neg \left(y \leq -6.8 \cdot 10^{+64} \lor \neg \left(y \leq -4 \cdot 10^{+37}\right) \land y \leq 2.4 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+63} \lor \neg \left(z \leq 4.4 \cdot 10^{-18}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.05e+158)
   (* y (+ z (* x y)))
   (if (or (<= z -7.4e+63) (not (<= z 4.4e-18)))
     (+ t (* y z))
     (+ t (* y (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e+158) {
		tmp = y * (z + (x * y));
	} else if ((z <= -7.4e+63) || !(z <= 4.4e-18)) {
		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 <= (-2.05d+158)) then
        tmp = y * (z + (x * y))
    else if ((z <= (-7.4d+63)) .or. (.not. (z <= 4.4d-18))) 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 <= -2.05e+158) {
		tmp = y * (z + (x * y));
	} else if ((z <= -7.4e+63) || !(z <= 4.4e-18)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.05e+158:
		tmp = y * (z + (x * y))
	elif (z <= -7.4e+63) or not (z <= 4.4e-18):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.05e+158)
		tmp = Float64(y * Float64(z + Float64(x * y)));
	elseif ((z <= -7.4e+63) || !(z <= 4.4e-18))
		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 <= -2.05e+158)
		tmp = y * (z + (x * y));
	elseif ((z <= -7.4e+63) || ~((z <= 4.4e-18)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.05e+158], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.4e+63], N[Not[LessEqual[z, 4.4e-18]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05000000000000002e158

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.3%

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

   if -2.05000000000000002e158 < z < -7.39999999999999937e63 or 4.3999999999999997e-18 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.4%

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

   if -7.39999999999999937e63 < z < 4.3999999999999997e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.1%

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

      1. unpow2 90.1%

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

      2. associate-*r* 96.6%

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

   4. Simplified 96.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+63} \lor \neg \left(z \leq 4.4 \cdot 10^{-18}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 5: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-133}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -2.2e-11)
     t_1
     (if (<= y 4.6e-133)
       (+ t (* y z))
       (if (<= y 8.4e+74) (+ t (* x (* y y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -2.2e-11) {
		tmp = t_1;
	} else if (y <= 4.6e-133) {
		tmp = t + (y * z);
	} else if (y <= 8.4e+74) {
		tmp = t + (x * (y * 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 = y * (z + (x * y))
    if (y <= (-2.2d-11)) then
        tmp = t_1
    else if (y <= 4.6d-133) then
        tmp = t + (y * z)
    else if (y <= 8.4d+74) then
        tmp = t + (x * (y * 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 = y * (z + (x * y));
	double tmp;
	if (y <= -2.2e-11) {
		tmp = t_1;
	} else if (y <= 4.6e-133) {
		tmp = t + (y * z);
	} else if (y <= 8.4e+74) {
		tmp = t + (x * (y * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -2.2e-11:
		tmp = t_1
	elif y <= 4.6e-133:
		tmp = t + (y * z)
	elif y <= 8.4e+74:
		tmp = t + (x * (y * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -2.2e-11)
		tmp = t_1;
	elseif (y <= 4.6e-133)
		tmp = Float64(t + Float64(y * z));
	elseif (y <= 8.4e+74)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -2.2e-11)
		tmp = t_1;
	elseif (y <= 4.6e-133)
		tmp = t + (y * z);
	elseif (y <= 8.4e+74)
		tmp = t + (x * (y * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-11], t$95$1, If[LessEqual[y, 4.6e-133], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+74], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000002e-11 or 8.3999999999999995e74 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 90.9%

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

   if -2.2000000000000002e-11 < y < 4.6000000000000001e-133

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.4%

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

   if 4.6000000000000001e-133 < y < 8.3999999999999995e74

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 85.4%

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

      1. unpow2 85.4%

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

      2. associate-*r* 85.3%

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

   4. Simplified 85.3%

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

      1. flip-+ 47.3%

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

      2. div-sub 47.3%

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

      3. pow2 47.3%

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

   6. Applied egg-rr 47.3%

      \[\leadsto \color{blue}{\frac{{\left(y \cdot \left(y \cdot x\right)\right)}^{2}}{y \cdot \left(y \cdot x\right) - t} - \frac{t \cdot t}{y \cdot \left(y \cdot x\right) - t}} \]
   7. Step-by-step derivation

      1. div-sub 47.3%

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

      2. unpow2 47.3%

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

      3. associate-*r* 47.3%

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

      4. *-commutative 47.3%

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

      5. associate-*r* 47.3%

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

      6. *-commutative 47.3%

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

      7. swap-sqr 31.5%

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

      8. unpow2 31.5%

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

      9. unpow2 31.5%

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

      10. pow-sqr 31.5%

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

      11. metadata-eval 31.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot {y}^{\color{blue}{4}} - t \cdot t}{y \cdot \left(y \cdot x\right) - t} \]

   8. Simplified 31.5%

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

      1. *-commutative 31.5%

         \[\leadsto \frac{\color{blue}{{y}^{4} \cdot \left(x \cdot x\right)} - t \cdot t}{y \cdot \left(y \cdot x\right) - t} \]

      2. metadata-eval 31.5%

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

      3. metadata-eval 31.5%

         \[\leadsto \frac{{y}^{\left(\color{blue}{\sqrt{4}} + 2\right)} \cdot \left(x \cdot x\right) - t \cdot t}{y \cdot \left(y \cdot x\right) - t} \]

      4. metadata-eval 31.5%

         \[\leadsto \frac{{y}^{\left(\sqrt{4} + \color{blue}{\sqrt{4}}\right)} \cdot \left(x \cdot x\right) - t \cdot t}{y \cdot \left(y \cdot x\right) - t} \]

      5. pow-prod-up 31.5%

         \[\leadsto \frac{\color{blue}{\left({y}^{\left(\sqrt{4}\right)} \cdot {y}^{\left(\sqrt{4}\right)}\right)} \cdot \left(x \cdot x\right) - t \cdot t}{y \cdot \left(y \cdot x\right) - t} \]

      6. pow-prod-down 31.5%

         \[\leadsto \frac{\color{blue}{{\left(y \cdot y\right)}^{\left(\sqrt{4}\right)}} \cdot \left(x \cdot x\right) - t \cdot t}{y \cdot \left(y \cdot x\right) - t} \]

      7. metadata-eval 31.5%

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

      8. pow2 31.5%

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

      9. swap-sqr 47.3%

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

      10. associate-*r* 47.3%

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

      11. associate-*r* 47.3%

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

      12. flip-+ 85.3%

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

   10. Applied egg-rr 85.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-133}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 6: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+158}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\\ \mathbf{elif}\;\neg \left(z \leq -8.5 \cdot 10^{+59}\right) \land z \leq 3 \cdot 10^{+217}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+158)
   (* y z)
   (if (<= z -1.95e+90)
     t
     (if (and (not (<= z -8.5e+59)) (<= z 3e+217)) t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+158) {
		tmp = y * z;
	} else if (z <= -1.95e+90) {
		tmp = t;
	} else if (!(z <= -8.5e+59) && (z <= 3e+217)) {
		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 <= (-1.05d+158)) then
        tmp = y * z
    else if (z <= (-1.95d+90)) then
        tmp = t
    else if ((.not. (z <= (-8.5d+59))) .and. (z <= 3d+217)) 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 <= -1.05e+158) {
		tmp = y * z;
	} else if (z <= -1.95e+90) {
		tmp = t;
	} else if (!(z <= -8.5e+59) && (z <= 3e+217)) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+158:
		tmp = y * z
	elif z <= -1.95e+90:
		tmp = t
	elif not (z <= -8.5e+59) and (z <= 3e+217):
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+158)
		tmp = Float64(y * z);
	elseif (z <= -1.95e+90)
		tmp = t;
	elseif (!(z <= -8.5e+59) && (z <= 3e+217))
		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 <= -1.05e+158)
		tmp = y * z;
	elseif (z <= -1.95e+90)
		tmp = t;
	elseif (~((z <= -8.5e+59)) && (z <= 3e+217))
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+158], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.95e+90], t, If[And[N[Not[LessEqual[z, -8.5e+59]], $MachinePrecision], LessEqual[z, 3e+217]], t, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e158 or -1.9500000000000001e90 < z < -8.4999999999999999e59 or 2.99999999999999976e217 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{y \cdot z + \left(t + {y}^{2} \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 87.8%

         \[\leadsto \color{blue}{\left(y \cdot z + t\right) + {y}^{2} \cdot x} \]

      2. fma-def 87.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, t\right)} + {y}^{2} \cdot x \]

      3. unpow2 87.8%

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

      4. associate-*r* 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in z around inf 76.6%

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

   if -1.0499999999999999e158 < z < -1.9500000000000001e90 or -8.4999999999999999e59 < z < 2.99999999999999976e217

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 52.5%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+158}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\\ \mathbf{elif}\;\neg \left(z \leq -8.5 \cdot 10^{+59}\right) \land z \leq 3 \cdot 10^{+217}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-11} \lor \neg \left(y \leq 4.8 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e-11) (not (<= y 4.8e-24)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-11) || !(y <= 4.8e-24)) {
		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 <= (-3.8d-11)) .or. (.not. (y <= 4.8d-24))) 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 <= -3.8e-11) || !(y <= 4.8e-24)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e-11) or not (y <= 4.8e-24):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e-11) || !(y <= 4.8e-24))
		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 <= -3.8e-11) || ~((y <= 4.8e-24)))
		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, -3.8e-11], N[Not[LessEqual[y, 4.8e-24]], $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 < -3.7999999999999998e-11 or 4.7999999999999996e-24 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 85.7%

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

   if -3.7999999999999998e-11 < y < 4.7999999999999996e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-11} \lor \neg \left(y \leq 4.8 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 8: 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 9: 37.9% 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 43.4%

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

3. Final simplification 43.4%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))