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

Percentage Accurate: 99.9% → 99.9%

Time: 7.8s

Alternatives: 7

Speedup: 1.0×

• 29.6% 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-define 100.0%

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

   2. fma-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.0152:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -1.6e+127)
     t_1
     (if (<= y -8.8e-27) (* y z) (if (<= y 0.0152) t t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -1.6e+127) {
		tmp = t_1;
	} else if (y <= -8.8e-27) {
		tmp = y * z;
	} else if (y <= 0.0152) {
		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 <= (-1.6d+127)) then
        tmp = t_1
    else if (y <= (-8.8d-27)) then
        tmp = y * z
    else if (y <= 0.0152d0) 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 <= -1.6e+127) {
		tmp = t_1;
	} else if (y <= -8.8e-27) {
		tmp = y * z;
	} else if (y <= 0.0152) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -1.6e+127:
		tmp = t_1
	elif y <= -8.8e-27:
		tmp = y * z
	elif y <= 0.0152:
		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 <= -1.6e+127)
		tmp = t_1;
	elseif (y <= -8.8e-27)
		tmp = Float64(y * z);
	elseif (y <= 0.0152)
		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 <= -1.6e+127)
		tmp = t_1;
	elseif (y <= -8.8e-27)
		tmp = y * z;
	elseif (y <= 0.0152)
		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, -1.6e+127], t$95$1, If[LessEqual[y, -8.8e-27], N[(y * z), $MachinePrecision], If[LessEqual[y, 0.0152], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999988e127 or 0.0152 < 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 69.9%

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

      1. +-commutative 69.9%

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

      2. distribute-lft-in 69.9%

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

      3. unpow2 69.9%

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

      4. associate-*l* 79.5%

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

      5. associate-/l* 79.5%

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

      6. associate-*r* 73.8%

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

      7. distribute-lft-out 96.5%

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

      8. *-commutative 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in t around 0 82.8%

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

   7. Taylor expanded in y around inf 72.7%

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

   if -1.59999999999999988e127 < y < -8.79999999999999948e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-/l* 92.7%

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

      3. fma-define 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in y around inf 92.7%

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

      1. associate-*l* 92.7%

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

      2. fma-define 92.7%

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

      3. distribute-rgt-in 92.7%

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

      4. *-commutative 92.7%

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

      5. lft-mult-inverse 92.7%

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

   8. Applied egg-rr 92.7%

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

   9. Taylor expanded in z around inf 59.1%

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

   if -8.79999999999999948e-27 < y < 0.0152

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.9%

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

Alternative 3: 89.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+59} \lor \neg \left(z \leq 7.4 \cdot 10^{+64}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+59) (not (<= z 7.4e+64)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+59) || !(z <= 7.4e+64)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.1d+59)) .or. (.not. (z <= 7.4d+64))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+59) || !(z <= 7.4e+64)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+59) or not (z <= 7.4e+64):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+59) || !(z <= 7.4e+64))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+59) || ~((z <= 7.4e+64)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+59], N[Not[LessEqual[z, 7.4e+64]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000015e59 or 7.39999999999999966e64 < 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 86.7%

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

   if -3.10000000000000015e59 < z < 7.39999999999999966e64

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.1%

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

      1. *-commutative 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+59} \lor \neg \left(z \leq 7.4 \cdot 10^{+64}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+127} \lor \neg \left(y \leq 1.1 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.05e+127) (not (<= y 1.1e+63))) (* x (* y y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e+127) || !(y <= 1.1e+63)) {
		tmp = x * (y * 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 <= (-2.05d+127)) .or. (.not. (y <= 1.1d+63))) then
        tmp = x * (y * 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 <= -2.05e+127) || !(y <= 1.1e+63)) {
		tmp = x * (y * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.05e+127) or not (y <= 1.1e+63):
		tmp = x * (y * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.05e+127) || !(y <= 1.1e+63))
		tmp = Float64(x * Float64(y * 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 <= -2.05e+127) || ~((y <= 1.1e+63)))
		tmp = x * (y * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.05e+127], N[Not[LessEqual[y, 1.1e+63]], $MachinePrecision]], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.04999999999999991e127 or 1.0999999999999999e63 < 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 68.4%

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

      1. +-commutative 68.4%

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

      2. distribute-lft-in 68.4%

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

      3. unpow2 68.4%

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

      4. associate-*l* 79.5%

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

      5. associate-/l* 79.5%

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

      6. associate-*r* 72.9%

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

      7. distribute-lft-out 98.9%

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

      8. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in t around 0 87.2%

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

   7. Taylor expanded in y around inf 76.9%

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

   if -2.04999999999999991e127 < y < 1.0999999999999999e63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+127} \lor \neg \left(y \leq 1.1 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+89} \lor \neg \left(z \leq 1.32 \cdot 10^{+56}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e+89) (not (<= z 1.32e+56))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e+89) || !(z <= 1.32e+56)) {
		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 <= (-1.5d+89)) .or. (.not. (z <= 1.32d+56))) 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 <= -1.5e+89) || !(z <= 1.32e+56)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e+89) or not (z <= 1.32e+56):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e+89) || !(z <= 1.32e+56))
		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 <= -1.5e+89) || ~((z <= 1.32e+56)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e+89], N[Not[LessEqual[z, 1.32e+56]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000006e89 or 1.32e56 < 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 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.9%

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

      1. associate-*l* 99.9%

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

      2. fma-define 99.9%

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

      3. distribute-rgt-in 99.9%

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

      4. *-commutative 99.9%

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

      5. lft-mult-inverse 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in z around inf 66.1%

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

   if -1.50000000000000006e89 < z < 1.32e56

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 46.3%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+89} \lor \neg \left(z \leq 1.32 \cdot 10^{+56}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(z + x \cdot y\right) \]
4. 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 36.9%

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

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))