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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 8

Speedup: 1.0×

• 29.0% 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

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

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;z \leq -0.026:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y z))))
   (if (<= z -0.026) t_1 (if (<= z 2.1e+14) (+ t (* y (* x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double tmp;
	if (z <= -0.026) {
		tmp = t_1;
	} else if (z <= 2.1e+14) {
		tmp = t + (y * (x * 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 = t + (y * z)
    if (z <= (-0.026d0)) then
        tmp = t_1
    else if (z <= 2.1d+14) then
        tmp = t + (y * (x * 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 = t + (y * z);
	double tmp;
	if (z <= -0.026) {
		tmp = t_1;
	} else if (z <= 2.1e+14) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (y * z)
	tmp = 0
	if z <= -0.026:
		tmp = t_1
	elif z <= 2.1e+14:
		tmp = t + (y * (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(y * z))
	tmp = 0.0
	if (z <= -0.026)
		tmp = t_1;
	elseif (z <= 2.1e+14)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (y * z);
	tmp = 0.0;
	if (z <= -0.026)
		tmp = t_1;
	elseif (z <= 2.1e+14)
		tmp = t + (y * (x * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.026], t$95$1, If[LessEqual[z, 2.1e+14], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0259999999999999988 or 2.1e14 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, y\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 85.2%

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

   if -0.0259999999999999988 < z < 2.1e14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, y\right), t\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y \cdot x\right), y\right), t\right) \]

      2. *-lowering-*.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 95.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot y + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.026:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0033:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -1.15e-18) t_1 (if (<= y 0.0033) (+ t (* y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.15e-18) {
		tmp = t_1;
	} else if (y <= 0.0033) {
		tmp = t + (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 * (z + (x * y))
    if (y <= (-1.15d-18)) then
        tmp = t_1
    else if (y <= 0.0033d0) then
        tmp = t + (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 * (z + (x * y));
	double tmp;
	if (y <= -1.15e-18) {
		tmp = t_1;
	} else if (y <= 0.0033) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -1.15e-18:
		tmp = t_1
	elif y <= 0.0033:
		tmp = t + (y * z)
	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 <= -1.15e-18)
		tmp = t_1;
	elseif (y <= 0.0033)
		tmp = Float64(t + Float64(y * z));
	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 <= -1.15e-18)
		tmp = t_1;
	elseif (y <= 0.0033)
		tmp = t + (y * z);
	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, -1.15e-18], t$95$1, If[LessEqual[y, 0.0033], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-18 or 0.0033 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. distribute-rgt-in N/A

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

      2. +-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. fma-define N/A

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

      6. associate-*l/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{z \cdot y}{y}, y, x \cdot {y}^{2}\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(z \cdot \frac{y}{y}, y, x \cdot {y}^{2}\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(z \cdot 1, y, x \cdot {y}^{2}\right) \]

      9. *-rgt-identity N/A

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

      10. fma-define N/A

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

      11. *-commutative N/A

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

      12. unpow2 N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(z + x \cdot y\right)}\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

      19. *-lowering-*.f64 90.2%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 90.2%

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

   if -1.15e-18 < y < 0.0033

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, y\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 89.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.0033:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+68}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= x -2.45e+65) t_1 (if (<= x 8.2e+68) (+ t (* y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (x <= -2.45e+65) {
		tmp = t_1;
	} else if (x <= 8.2e+68) {
		tmp = t + (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 (x <= (-2.45d+65)) then
        tmp = t_1
    else if (x <= 8.2d+68) then
        tmp = t + (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 (x <= -2.45e+65) {
		tmp = t_1;
	} else if (x <= 8.2e+68) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if x <= -2.45e+65:
		tmp = t_1
	elif x <= 8.2e+68:
		tmp = t + (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 (x <= -2.45e+65)
		tmp = t_1;
	elseif (x <= 8.2e+68)
		tmp = Float64(t + 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 (x <= -2.45e+65)
		tmp = t_1;
	elseif (x <= 8.2e+68)
		tmp = t + (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[x, -2.45e+65], t$95$1, If[LessEqual[x, 8.2e+68], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.44999999999999978e65 or 8.1999999999999998e68 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 70.0%

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

   if -2.44999999999999978e65 < x < 8.1999999999999998e68

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, y\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 84.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+68}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.000202:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -1.4e-16) t_1 (if (<= y 0.000202) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.4e-16) {
		tmp = t_1;
	} else if (y <= 0.000202) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * y)
    if (y <= (-1.4d-16)) then
        tmp = t_1
    else if (y <= 0.000202d0) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.4e-16) {
		tmp = t_1;
	} else if (y <= 0.000202) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -1.4e-16:
		tmp = t_1
	elif y <= 0.000202:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -1.4e-16)
		tmp = t_1;
	elseif (y <= 0.000202)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -1.4e-16)
		tmp = t_1;
	elseif (y <= 0.000202)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e-16], t$95$1, If[LessEqual[y, 0.000202], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-16 or 2.02000000000000004e-4 < 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

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

      1. unpow2 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 66.3%

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

   if -1.4000000000000001e-16 < y < 2.02000000000000004e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 63.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.000202:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.00118:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -1.1e-15) t_1 (if (<= y 0.00118) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -1.1e-15) {
		tmp = t_1;
	} else if (y <= 0.00118) {
		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 <= (-1.1d-15)) then
        tmp = t_1
    else if (y <= 0.00118d0) 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 <= -1.1e-15) {
		tmp = t_1;
	} else if (y <= 0.00118) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -1.1e-15:
		tmp = t_1
	elif y <= 0.00118:
		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 <= -1.1e-15)
		tmp = t_1;
	elseif (y <= 0.00118)
		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 <= -1.1e-15)
		tmp = t_1;
	elseif (y <= 0.00118)
		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, -1.1e-15], t$95$1, If[LessEqual[y, 0.00118], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.09999999999999993e-15 or 0.0011800000000000001 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(x \cdot y + z\right)\right), t\right) \]

      2. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{{\left(x \cdot y\right)}^{3} + {z}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}\right), t\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}{{\left(x \cdot y\right)}^{3} + {z}^{3}}}\right), t\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}{{\left(x \cdot y\right)}^{3} + {z}^{3}}}\right), t\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}{{\left(x \cdot y\right)}^{3} + {z}^{3}}\right)\right), t\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{1}{\frac{{\left(x \cdot y\right)}^{3} + {z}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}}\right)\right), t\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{1}{x \cdot y + z}\right)\right), t\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \left(x \cdot y + z\right)\right)\right), t\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(x \cdot y\right), z\right)\right)\right), t\right) \]

      10. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right)\right), t\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   7. Simplified 65.1%

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

   if -1.09999999999999993e-15 < y < 0.0011800000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 63.0%

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

Alternative 7: 51.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+22}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+22) (* y z) (if (<= z 1.85e+15) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+22) {
		tmp = y * z;
	} else if (z <= 1.85e+15) {
		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 <= (-1.65d+22)) then
        tmp = y * z
    else if (z <= 1.85d+15) 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 <= -1.65e+22) {
		tmp = y * z;
	} else if (z <= 1.85e+15) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+22:
		tmp = y * z
	elif z <= 1.85e+15:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+22)
		tmp = Float64(y * z);
	elseif (z <= 1.85e+15)
		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 <= -1.65e+22)
		tmp = y * z;
	elseif (z <= 1.85e+15)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+22], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.85e+15], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e22 or 1.85e15 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 61.7%

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

   if -1.6499999999999999e22 < z < 1.85e15

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 45.3%

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

Alternative 8: 38.8% 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

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 35.7%

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))