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

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• 28.3% 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 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. Final simplification 100.0%

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

Alternative 2: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-14} \lor \neg \left(y \leq -7 \cdot 10^{-41}\right) \land y \leq 1.05 \cdot 10^{+50}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+171)
   (* y (* x y))
   (if (or (<= y -2.5e-14) (and (not (<= y -7e-41)) (<= y 1.05e+50)))
     (+ t (* y z))
     (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+171) {
		tmp = y * (x * y);
	} else if ((y <= -2.5e-14) || (!(y <= -7e-41) && (y <= 1.05e+50))) {
		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 <= (-1d+171)) then
        tmp = y * (x * y)
    else if ((y <= (-2.5d-14)) .or. (.not. (y <= (-7d-41))) .and. (y <= 1.05d+50)) 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 <= -1e+171) {
		tmp = y * (x * y);
	} else if ((y <= -2.5e-14) || (!(y <= -7e-41) && (y <= 1.05e+50))) {
		tmp = t + (y * z);
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1e+171:
		tmp = y * (x * y)
	elif (y <= -2.5e-14) or (not (y <= -7e-41) and (y <= 1.05e+50)):
		tmp = t + (y * z)
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+171)
		tmp = Float64(y * Float64(x * y));
	elseif ((y <= -2.5e-14) || (!(y <= -7e-41) && (y <= 1.05e+50)))
		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 <= -1e+171)
		tmp = y * (x * y);
	elseif ((y <= -2.5e-14) || (~((y <= -7e-41)) && (y <= 1.05e+50)))
		tmp = t + (y * z);
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e+171], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.5e-14], And[N[Not[LessEqual[y, -7e-41]], $MachinePrecision], LessEqual[y, 1.05e+50]]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999954e170

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.8%

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

   3. Taylor expanded in y around inf 90.9%

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

   if -9.99999999999999954e170 < y < -2.5000000000000001e-14 or -6.9999999999999999e-41 < y < 1.05e50

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.9%

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

   if -2.5000000000000001e-14 < y < -6.9999999999999999e-41 or 1.05e50 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 82.4%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. +-commutative 82.7%

         \[\leadsto \color{blue}{{y}^{2} \cdot x + t} \]

      2. *-commutative 82.7%

         \[\leadsto \color{blue}{x \cdot {y}^{2}} + t \]

      3. unpow2 82.7%

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

      4. associate-*r* 82.4%

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

      5. *-commutative 82.4%

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

      6. fma-udef 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around inf 76.2%

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

      1. unpow2 76.2%

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

      2. *-commutative 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-14} \lor \neg \left(y \leq -7 \cdot 10^{-41}\right) \land y \leq 1.05 \cdot 10^{+50}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 3: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -9.2e+162)
     t_1
     (if (<= y -5.9e+53) (* y z) (if (<= y 4.0) t t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -9.2e+162) {
		tmp = t_1;
	} else if (y <= -5.9e+53) {
		tmp = y * z;
	} else if (y <= 4.0) {
		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 = x * (y * y)
    if (y <= (-9.2d+162)) then
        tmp = t_1
    else if (y <= (-5.9d+53)) then
        tmp = y * z
    else if (y <= 4.0d0) 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 = x * (y * y);
	double tmp;
	if (y <= -9.2e+162) {
		tmp = t_1;
	} else if (y <= -5.9e+53) {
		tmp = y * z;
	} else if (y <= 4.0) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -9.2e+162:
		tmp = t_1
	elif y <= -5.9e+53:
		tmp = y * z
	elif y <= 4.0:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -9.2e+162)
		tmp = t_1;
	elseif (y <= -5.9e+53)
		tmp = Float64(y * z);
	elseif (y <= 4.0)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * y);
	tmp = 0.0;
	if (y <= -9.2e+162)
		tmp = t_1;
	elseif (y <= -5.9e+53)
		tmp = y * z;
	elseif (y <= 4.0)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+162], t$95$1, If[LessEqual[y, -5.9e+53], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.0], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999975e162 or 4 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.9%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. +-commutative 81.3%

         \[\leadsto \color{blue}{{y}^{2} \cdot x + t} \]

      2. *-commutative 81.3%

         \[\leadsto \color{blue}{x \cdot {y}^{2}} + t \]

      3. unpow2 81.3%

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

      4. associate-*r* 83.9%

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

      5. *-commutative 83.9%

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

      6. fma-udef 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around inf 72.9%

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

      1. unpow2 72.9%

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

      2. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -9.19999999999999975e162 < y < -5.8999999999999997e53

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 74.4%

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

   3. Taylor expanded in z around inf 61.6%

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

   if -5.8999999999999997e53 < y < 4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+53}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 4: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 175:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+157)
   (* y (* x y))
   (if (<= y -1.1e+54) (* y z) (if (<= y 175.0) t (* x (* y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+157) {
		tmp = y * (x * y);
	} else if (y <= -1.1e+54) {
		tmp = y * z;
	} else if (y <= 175.0) {
		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 <= (-4d+157)) then
        tmp = y * (x * y)
    else if (y <= (-1.1d+54)) then
        tmp = y * z
    else if (y <= 175.0d0) 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 <= -4e+157) {
		tmp = y * (x * y);
	} else if (y <= -1.1e+54) {
		tmp = y * z;
	} else if (y <= 175.0) {
		tmp = t;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+157:
		tmp = y * (x * y)
	elif y <= -1.1e+54:
		tmp = y * z
	elif y <= 175.0:
		tmp = t
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+157)
		tmp = Float64(y * Float64(x * y));
	elseif (y <= -1.1e+54)
		tmp = Float64(y * z);
	elseif (y <= 175.0)
		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 <= -4e+157)
		tmp = y * (x * y);
	elseif (y <= -1.1e+54)
		tmp = y * z;
	elseif (y <= 175.0)
		tmp = t;
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+157], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e+54], N[(y * z), $MachinePrecision], If[LessEqual[y, 175.0], t, N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.99999999999999993e157

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.3%

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

   3. Taylor expanded in y around inf 82.5%

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

   if -3.99999999999999993e157 < y < -1.09999999999999995e54

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.1%

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

   3. Taylor expanded in z around inf 62.8%

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

   if -1.09999999999999995e54 < y < 175

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.0%

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

   if 175 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.9%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. +-commutative 81.2%

         \[\leadsto \color{blue}{{y}^{2} \cdot x + t} \]

      2. *-commutative 81.2%

         \[\leadsto \color{blue}{x \cdot {y}^{2}} + t \]

      3. unpow2 81.2%

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

      4. associate-*r* 80.9%

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

      5. *-commutative 80.9%

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

      6. fma-udef 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around inf 69.6%

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

      1. unpow2 69.6%

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

      2. *-commutative 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 175:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 5: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-41} \lor \neg \left(y \leq 11.5\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e-41) (not (<= y 11.5))) (* y (+ z (* x y))) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-41) || !(y <= 11.5)) {
		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 <= (-6d-41)) .or. (.not. (y <= 11.5d0))) 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 <= -6e-41) || !(y <= 11.5)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e-41) or not (y <= 11.5):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e-41) || !(y <= 11.5))
		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 <= -6e-41) || ~((y <= 11.5)))
		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, -6e-41], N[Not[LessEqual[y, 11.5]], $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 < -5.99999999999999978e-41 or 11.5 < 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 -5.99999999999999978e-41 < y < 11.5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-41} \lor \neg \left(y \leq 11.5\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 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 7: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3e+76) (* y z) (if (<= z 7e+129) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3e+76) {
		tmp = y * z;
	} else if (z <= 7e+129) {
		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 <= (-3d+76)) then
        tmp = y * z
    else if (z <= 7d+129) 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 <= -3e+76) {
		tmp = y * z;
	} else if (z <= 7e+129) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3e+76:
		tmp = y * z
	elif z <= 7e+129:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3e+76)
		tmp = Float64(y * z);
	elseif (z <= 7e+129)
		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 <= -3e+76)
		tmp = y * z;
	elseif (z <= 7e+129)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3e+76], N[(y * z), $MachinePrecision], If[LessEqual[z, 7e+129], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999998e76 or 6.9999999999999997e129 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.8%

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

   3. Taylor expanded in z around inf 64.1%

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

   if -2.9999999999999998e76 < z < 6.9999999999999997e129

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 55.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 8: 39.0% 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 43.6%

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

3. Final simplification 43.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))