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

Percentage Accurate: 99.9% → 99.9%

Time: 7.5s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-undefine 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

   \[\leadsto y \cdot \mathsf{fma}\left(y, x, z\right) + t \]
7. Add Preprocessing

Alternative 2: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -4200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* y x))))
   (if (<= y -4200000000.0)
     t_1
     (if (<= y -9.5e-80)
       (* y z)
       (if (<= y 2.2e-31) t (if (<= y 9.2e+50) (* y z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -4200000000.0) {
		tmp = t_1;
	} else if (y <= -9.5e-80) {
		tmp = y * z;
	} else if (y <= 2.2e-31) {
		tmp = t;
	} else if (y <= 9.2e+50) {
		tmp = 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 * (y * x)
    if (y <= (-4200000000.0d0)) then
        tmp = t_1
    else if (y <= (-9.5d-80)) then
        tmp = y * z
    else if (y <= 2.2d-31) then
        tmp = t
    else if (y <= 9.2d+50) then
        tmp = 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 * (y * x);
	double tmp;
	if (y <= -4200000000.0) {
		tmp = t_1;
	} else if (y <= -9.5e-80) {
		tmp = y * z;
	} else if (y <= 2.2e-31) {
		tmp = t;
	} else if (y <= 9.2e+50) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (y * x)
	tmp = 0
	if y <= -4200000000.0:
		tmp = t_1
	elif y <= -9.5e-80:
		tmp = y * z
	elif y <= 2.2e-31:
		tmp = t
	elif y <= 9.2e+50:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(y * x))
	tmp = 0.0
	if (y <= -4200000000.0)
		tmp = t_1;
	elseif (y <= -9.5e-80)
		tmp = Float64(y * z);
	elseif (y <= 2.2e-31)
		tmp = t;
	elseif (y <= 9.2e+50)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (y * x);
	tmp = 0.0;
	if (y <= -4200000000.0)
		tmp = t_1;
	elseif (y <= -9.5e-80)
		tmp = y * z;
	elseif (y <= 2.2e-31)
		tmp = t;
	elseif (y <= 9.2e+50)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4200000000.0], t$95$1, If[LessEqual[y, -9.5e-80], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.2e-31], t, If[LessEqual[y, 9.2e+50], N[(y * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e9 or 9.19999999999999987e50 < 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 86.5%

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

      1. associate-/l* 86.5%

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

      2. +-commutative 86.5%

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

      3. *-commutative 86.5%

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

      4. fma-undefine 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in t around 0 92.5%

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

   7. Taylor expanded in z around 0 69.8%

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

   if -4.2e9 < y < -9.5000000000000003e-80 or 2.2000000000000001e-31 < y < 9.19999999999999987e50

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. associate-/l* 80.1%

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

      2. +-commutative 80.1%

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

      3. *-commutative 80.1%

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

      4. fma-undefine 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around 0 76.6%

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

   7. Taylor expanded in y around 0 58.6%

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

   if -9.5000000000000003e-80 < y < 2.2000000000000001e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 66.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4200000000:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-40} \lor \neg \left(y \leq 1.56 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-40) (not (<= y 1.56e-18)))
   (* y (+ z (* y x)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-40) || !(y <= 1.56e-18)) {
		tmp = y * (z + (y * x));
	} 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 <= (-6.5d-40)) .or. (.not. (y <= 1.56d-18))) then
        tmp = y * (z + (y * x))
    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 <= -6.5e-40) || !(y <= 1.56e-18)) {
		tmp = y * (z + (y * x));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e-40) or not (y <= 1.56e-18):
		tmp = y * (z + (y * x))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-40) || !(y <= 1.56e-18))
		tmp = Float64(y * Float64(z + Float64(y * x)));
	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 <= -6.5e-40) || ~((y <= 1.56e-18)))
		tmp = y * (z + (y * x));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-40], N[Not[LessEqual[y, 1.56e-18]], $MachinePrecision]], N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999999e-40 or 1.55999999999999998e-18 < 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 85.7%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   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 t around 0 89.9%

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

   if -6.4999999999999999e-40 < y < 1.55999999999999998e-18

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-40} \lor \neg \left(y \leq 1.56 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000000000 \lor \neg \left(y \leq 9 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7000000000.0) (not (<= y 9e+84))) (* y (* y x)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7000000000.0) || !(y <= 9e+84)) {
		tmp = y * (y * x);
	} 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 <= (-7000000000.0d0)) .or. (.not. (y <= 9d+84))) then
        tmp = y * (y * x)
    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 <= -7000000000.0) || !(y <= 9e+84)) {
		tmp = y * (y * x);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7000000000.0) or not (y <= 9e+84):
		tmp = y * (y * x)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7000000000.0) || !(y <= 9e+84))
		tmp = Float64(y * Float64(y * x));
	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 <= -7000000000.0) || ~((y <= 9e+84)))
		tmp = y * (y * x);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7000000000.0], N[Not[LessEqual[y, 9e+84]], $MachinePrecision]], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e9 or 8.9999999999999994e84 < 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 88.0%

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

      1. associate-/l* 88.0%

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

      2. +-commutative 88.0%

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

      3. *-commutative 88.0%

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

      4. fma-undefine 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in t around 0 93.8%

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

   7. Taylor expanded in z around 0 73.9%

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

   if -7e9 < y < 8.9999999999999994e84

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000000000 \lor \neg \left(y \leq 9 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+189} \lor \neg \left(z \leq 1.05 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e+189) (not (<= z 1.05e-29))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e+189) || !(z <= 1.05e-29)) {
		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 <= (-2.1d+189)) .or. (.not. (z <= 1.05d-29))) 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 <= -2.1e+189) || !(z <= 1.05e-29)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e+189) or not (z <= 1.05e-29):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e+189) || !(z <= 1.05e-29))
		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 <= -2.1e+189) || ~((z <= 1.05e-29)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e+189], N[Not[LessEqual[z, 1.05e-29]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999992e189 or 1.04999999999999995e-29 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 89.1%

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

      1. associate-/l* 78.7%

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

      2. +-commutative 78.7%

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

      3. *-commutative 78.7%

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

      4. fma-undefine 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 78.4%

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

   7. Taylor expanded in y around 0 62.4%

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

   if -2.09999999999999992e189 < z < 1.04999999999999995e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 52.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+189} \lor \neg \left(z \leq 1.05 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (y * x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 7: 38.3% 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 40.6%

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))