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

Percentage Accurate: 99.9% → 99.9%

Time: 5.8s

Alternatives: 7

Speedup: 1.0×

• 30.3% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-28} \lor \neg \left(y \leq 1.1 \cdot 10^{-63} \lor \neg \left(y \leq 4.5\right) \land y \leq 2.9 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-28)
         (not (or (<= y 1.1e-63) (and (not (<= y 4.5)) (<= y 2.9e+81)))))
   (* y (+ (* x y) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-28) || !((y <= 1.1e-63) || (!(y <= 4.5) && (y <= 2.9e+81)))) {
		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 <= (-1.4d-28)) .or. (.not. (y <= 1.1d-63) .or. (.not. (y <= 4.5d0)) .and. (y <= 2.9d+81))) 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 <= -1.4e-28) || !((y <= 1.1e-63) || (!(y <= 4.5) && (y <= 2.9e+81)))) {
		tmp = y * ((x * y) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-28) or not ((y <= 1.1e-63) or (not (y <= 4.5) and (y <= 2.9e+81))):
		tmp = y * ((x * y) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-28) || !((y <= 1.1e-63) || (!(y <= 4.5) && (y <= 2.9e+81))))
		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 <= -1.4e-28) || ~(((y <= 1.1e-63) || (~((y <= 4.5)) && (y <= 2.9e+81)))))
		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, -1.4e-28], N[Not[Or[LessEqual[y, 1.1e-63], And[N[Not[LessEqual[y, 4.5]], $MachinePrecision], LessEqual[y, 2.9e+81]]]], $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 < -1.3999999999999999e-28 or 1.1e-63 < y < 4.5 or 2.9e81 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.5%

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

   if -1.3999999999999999e-28 < y < 1.1e-63 or 4.5 < y < 2.9e81

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-28} \lor \neg \left(y \leq 1.1 \cdot 10^{-63} \lor \neg \left(y \leq 4.5\right) \land y \leq 2.9 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 3: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-28} \lor \neg \left(y \leq 9.6 \cdot 10^{-63}\right) \land \left(y \leq 1.12 \lor \neg \left(y \leq 6.1 \cdot 10^{+65}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.7e-28)
         (and (not (<= y 9.6e-63)) (or (<= y 1.12) (not (<= y 6.1e+65)))))
   (* y (* x y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.7e-28) || (!(y <= 9.6e-63) && ((y <= 1.12) || !(y <= 6.1e+65)))) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.7d-28)) .or. (.not. (y <= 9.6d-63)) .and. (y <= 1.12d0) .or. (.not. (y <= 6.1d+65))) then
        tmp = y * (x * y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.7e-28) || (!(y <= 9.6e-63) && ((y <= 1.12) || !(y <= 6.1e+65)))) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.7e-28) or (not (y <= 9.6e-63) and ((y <= 1.12) or not (y <= 6.1e+65))):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.7e-28) || (!(y <= 9.6e-63) && ((y <= 1.12) || !(y <= 6.1e+65))))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.7e-28) || (~((y <= 9.6e-63)) && ((y <= 1.12) || ~((y <= 6.1e+65)))))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.7e-28], And[N[Not[LessEqual[y, 9.6e-63]], $MachinePrecision], Or[LessEqual[y, 1.12], N[Not[LessEqual[y, 6.1e+65]], $MachinePrecision]]]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e-28 or 9.6000000000000002e-63 < y < 1.1200000000000001 or 6.09999999999999965e65 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.9%

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

   3. Taylor expanded in z around 0 74.4%

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

   if -1.7e-28 < y < 9.6000000000000002e-63 or 1.1200000000000001 < y < 6.09999999999999965e65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.6%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-28} \lor \neg \left(y \leq 9.6 \cdot 10^{-63}\right) \land \left(y \leq 1.12 \lor \neg \left(y \leq 6.1 \cdot 10^{+65}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+63)
   (* y (+ (* x y) z))
   (if (<= z 1.5e+108) (+ t (* y (* x y))) (+ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+63) {
		tmp = y * ((x * y) + z);
	} else if (z <= 1.5e+108) {
		tmp = t + (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 (z <= (-2.7d+63)) then
        tmp = y * ((x * y) + z)
    else if (z <= 1.5d+108) then
        tmp = t + (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 (z <= -2.7e+63) {
		tmp = y * ((x * y) + z);
	} else if (z <= 1.5e+108) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+63:
		tmp = y * ((x * y) + z)
	elif z <= 1.5e+108:
		tmp = t + (y * (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+63)
		tmp = Float64(y * Float64(Float64(x * y) + z));
	elseif (z <= 1.5e+108)
		tmp = Float64(t + 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 (z <= -2.7e+63)
		tmp = y * ((x * y) + z);
	elseif (z <= 1.5e+108)
		tmp = t + (y * (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+63], N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+108], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000017e63

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 86.2%

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

   if -2.70000000000000017e63 < z < 1.49999999999999992e108

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

   4. Simplified 93.6%

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

   if 1.49999999999999992e108 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+49} \lor \neg \left(y \leq 5.5 \cdot 10^{+88}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+49) (not (<= y 5.5e+88))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+49) || !(y <= 5.5e+88)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.5d+49)) .or. (.not. (y <= 5.5d+88))) then
        tmp = y * (x * y)
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+49) || !(y <= 5.5e+88)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+49) or not (y <= 5.5e+88):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+49) || !(y <= 5.5e+88))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+49) || ~((y <= 5.5e+88)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+49], N[Not[LessEqual[y, 5.5e+88]], $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 < -7.4999999999999995e49 or 5.5e88 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.7%

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

   3. Taylor expanded in z around 0 80.2%

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

   if -7.4999999999999995e49 < y < 5.5e88

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+49} \lor \neg \left(y \leq 5.5 \cdot 10^{+88}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 51.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+101}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+58) (* y z) (if (<= z 4e+101) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+58) {
		tmp = y * z;
	} else if (z <= 4e+101) {
		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 <= (-2.2d+58)) then
        tmp = y * z
    else if (z <= 4d+101) 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 <= -2.2e+58) {
		tmp = y * z;
	} else if (z <= 4e+101) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+58:
		tmp = y * z
	elif z <= 4e+101:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+58)
		tmp = Float64(y * z);
	elseif (z <= 4e+101)
		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 <= -2.2e+58)
		tmp = y * z;
	elseif (z <= 4e+101)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+58], N[(y * z), $MachinePrecision], If[LessEqual[z, 4e+101], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e58 or 3.9999999999999999e101 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 84.3%

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

   3. Taylor expanded in z around inf 64.9%

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

   if -2.2000000000000001e58 < z < 3.9999999999999999e101

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 46.5%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+101}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 38.4% 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. Taylor expanded in y around 0 36.5%

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

3. Final simplification 36.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))