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

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 7

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 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. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(x \cdot y + z\right) \]
4. Add Preprocessing

Alternative 2: 89.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4200000000 \lor \neg \left(y \leq 3.7 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4200000000.0) (not (<= y 3.7e-53)))
   (* y (+ (* x y) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4200000000.0) || !(y <= 3.7e-53)) {
		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 <= (-4200000000.0d0)) .or. (.not. (y <= 3.7d-53))) 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 <= -4200000000.0) || !(y <= 3.7e-53)) {
		tmp = y * ((x * y) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4200000000.0) or not (y <= 3.7e-53):
		tmp = y * ((x * y) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4200000000.0) || !(y <= 3.7e-53))
		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 <= -4200000000.0) || ~((y <= 3.7e-53)))
		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, -4200000000.0], N[Not[LessEqual[y, 3.7e-53]], $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 < -4.2e9 or 3.69999999999999982e-53 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 93.3%

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

      1. associate-/l* 91.9%

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

      2. +-commutative 91.9%

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

      3. *-commutative 91.9%

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

      4. fma-undefine 91.9%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 91.9%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 92.0%

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

   if -4.2e9 < y < 3.69999999999999982e-53

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4200000000 \lor \neg \left(y \leq 3.7 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-5} \lor \neg \left(y \leq 1.02 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.8e-5) (not (<= y 1.02e-42))) (* x (* y y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e-5) || !(y <= 1.02e-42)) {
		tmp = x * (y * 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 <= (-2.8d-5)) .or. (.not. (y <= 1.02d-42))) then
        tmp = x * (y * 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 <= -2.8e-5) || !(y <= 1.02e-42)) {
		tmp = x * (y * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.8e-5) or not (y <= 1.02e-42):
		tmp = x * (y * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.8e-5) || !(y <= 1.02e-42))
		tmp = Float64(x * Float64(y * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.8e-5) || ~((y <= 1.02e-42)))
		tmp = x * (y * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.8e-5], N[Not[LessEqual[y, 1.02e-42]], $MachinePrecision]], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -2.79999999999999996e-5 or 1.0199999999999999e-42 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.3%

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

      1. +-commutative 81.3%

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

      2. unpow2 81.3%

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

      3. associate-/l* 85.6%

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

      4. distribute-lft-out 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in t around 0 84.9%

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

   7. Taylor expanded in y around inf 70.9%

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

   if -2.79999999999999996e-5 < y < 1.0199999999999999e-42

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-5} \lor \neg \left(y \leq 1.02 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+85)
   (* x (* y y))
   (if (<= y 1.2e+43) (+ t (* y z)) (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+85) {
		tmp = x * (y * y);
	} else if (y <= 1.2e+43) {
		tmp = t + (y * z);
	} else {
		tmp = 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 (y <= (-1.9d+85)) then
        tmp = x * (y * y)
    else if (y <= 1.2d+43) then
        tmp = t + (y * z)
    else
        tmp = 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 (y <= -1.9e+85) {
		tmp = x * (y * y);
	} else if (y <= 1.2e+43) {
		tmp = t + (y * z);
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+85:
		tmp = x * (y * y)
	elif y <= 1.2e+43:
		tmp = t + (y * z)
	else:
		tmp = y * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+85)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 1.2e+43)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(y * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e+85)
		tmp = x * (y * y);
	elseif (y <= 1.2e+43)
		tmp = t + (y * z);
	else
		tmp = y * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+85], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+43], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.89999999999999996e85

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. unpow2 82.6%

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

      3. associate-/l* 90.4%

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

      4. distribute-lft-out 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in t around 0 86.6%

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

   7. Taylor expanded in y around inf 82.8%

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

   if -1.89999999999999996e85 < y < 1.20000000000000012e43

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.6%

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

   if 1.20000000000000012e43 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.5%

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

      1. associate-/l* 90.4%

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

      2. +-commutative 90.4%

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

      3. *-commutative 90.4%

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

      4. fma-undefine 90.5%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 90.5%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 97.5%

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

   7. Taylor expanded in z around 0 81.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00055:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.00055) (* x (* y y)) (if (<= y 2.1e-42) t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.00055) {
		tmp = x * (y * y);
	} else if (y <= 2.1e-42) {
		tmp = t;
	} else {
		tmp = 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 (y <= (-0.00055d0)) then
        tmp = x * (y * y)
    else if (y <= 2.1d-42) then
        tmp = t
    else
        tmp = 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 (y <= -0.00055) {
		tmp = x * (y * y);
	} else if (y <= 2.1e-42) {
		tmp = t;
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.00055:
		tmp = x * (y * y)
	elif y <= 2.1e-42:
		tmp = t
	else:
		tmp = y * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.00055)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 2.1e-42)
		tmp = t;
	else
		tmp = Float64(y * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.00055)
		tmp = x * (y * y);
	elseif (y <= 2.1e-42)
		tmp = t;
	else
		tmp = y * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.00055], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-42], t, N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000033e-4

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. unpow2 83.5%

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

      3. associate-/l* 89.1%

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

      4. distribute-lft-out 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in t around 0 81.9%

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

   7. Taylor expanded in y around inf 70.8%

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

   if -5.50000000000000033e-4 < y < 2.10000000000000006e-42

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.6%

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

   if 2.10000000000000006e-42 < y

   1. Initial program 99.8%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 92.0%

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

      1. associate-/l* 90.5%

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

      2. +-commutative 90.5%

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

      3. *-commutative 90.5%

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

      4. fma-undefine 90.5%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 90.5%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 97.8%

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

   7. Taylor expanded in z around 0 75.6%

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

Alternative 6: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+139} \lor \neg \left(z \leq 3.4 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e+139) (not (<= z 3.4e+95))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+139) || !(z <= 3.4e+95)) {
		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 <= (-2.6d+139)) .or. (.not. (z <= 3.4d+95))) 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 <= -2.6e+139) || !(z <= 3.4e+95)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e+139) or not (z <= 3.4e+95):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e+139) || !(z <= 3.4e+95))
		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 <= -2.6e+139) || ~((z <= 3.4e+95)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e+139], N[Not[LessEqual[z, 3.4e+95]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000022e139 or 3.40000000000000022e95 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 98.7%

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

      1. associate-/l* 85.6%

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

      2. +-commutative 85.6%

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

      3. *-commutative 85.6%

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

      4. fma-undefine 85.6%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 85.6%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in z around inf 67.3%

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

   if -2.60000000000000022e139 < z < 3.40000000000000022e95

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 42.8%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+139} \lor \neg \left(z \leq 3.4 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.4% 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. Add Preprocessing

3. Taylor expanded in y around 0 36.7%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))