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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 9

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 99.9%

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

   2. fma-define 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-46}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-56} \lor \neg \left(y \leq 3 \cdot 10^{-76}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -8.8e+55)
     t_1
     (if (<= y -6.2e-46)
       (* y z)
       (if (or (<= y -7.2e-56) (not (<= y 3e-76))) t_1 t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -8.8e+55) {
		tmp = t_1;
	} else if (y <= -6.2e-46) {
		tmp = y * z;
	} else if ((y <= -7.2e-56) || !(y <= 3e-76)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y * y)
    if (y <= (-8.8d+55)) then
        tmp = t_1
    else if (y <= (-6.2d-46)) then
        tmp = y * z
    else if ((y <= (-7.2d-56)) .or. (.not. (y <= 3d-76))) then
        tmp = t_1
    else
        tmp = t
    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 <= -8.8e+55) {
		tmp = t_1;
	} else if (y <= -6.2e-46) {
		tmp = y * z;
	} else if ((y <= -7.2e-56) || !(y <= 3e-76)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -8.8e+55:
		tmp = t_1
	elif y <= -6.2e-46:
		tmp = y * z
	elif (y <= -7.2e-56) or not (y <= 3e-76):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -8.8e+55)
		tmp = t_1;
	elseif (y <= -6.2e-46)
		tmp = Float64(y * z);
	elseif ((y <= -7.2e-56) || !(y <= 3e-76))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * y);
	tmp = 0.0;
	if (y <= -8.8e+55)
		tmp = t_1;
	elseif (y <= -6.2e-46)
		tmp = y * z;
	elseif ((y <= -7.2e-56) || ~((y <= 3e-76)))
		tmp = t_1;
	else
		tmp = t;
	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, -8.8e+55], t$95$1, If[LessEqual[y, -6.2e-46], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, -7.2e-56], N[Not[LessEqual[y, 3e-76]], $MachinePrecision]], t$95$1, t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.80000000000000042e55 or -6.2000000000000002e-46 < y < -7.19999999999999956e-56 or 3.00000000000000024e-76 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.7%

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

      1. +-commutative 81.7%

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

      2. distribute-lft-in 81.7%

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

      3. unpow2 81.7%

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

      4. associate-*l* 85.3%

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

      5. associate-/l* 84.6%

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

      6. associate-*r* 76.2%

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

      7. distribute-lft-out 97.1%

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

      8. *-commutative 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in t around 0 79.4%

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

   7. Taylor expanded in y around inf 70.9%

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

   if -8.80000000000000042e55 < y < -6.2000000000000002e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in t around -inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. distribute-rgt-neg-in 90.8%

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

      3. fma-neg 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-undefine 90.8%

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

      6. *-commutative 90.8%

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

      7. associate-/l* 90.8%

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

      8. fma-undefine 90.8%

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

      9. *-commutative 90.8%

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

      10. fma-undefine 90.8%

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

      11. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in z around inf 49.6%

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

   if -7.19999999999999956e-56 < y < 3.00000000000000024e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-46}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-56} \lor \neg \left(y \leq 3 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -7.6e+54)
     t_1
     (if (<= y -9e-37)
       (* y z)
       (if (<= y -3.1e-56) t_1 (if (<= y 1.35e-73) t (* y (* x y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -7.6e+54) {
		tmp = t_1;
	} else if (y <= -9e-37) {
		tmp = y * z;
	} else if (y <= -3.1e-56) {
		tmp = t_1;
	} else if (y <= 1.35e-73) {
		tmp = t;
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * y)
    if (y <= (-7.6d+54)) then
        tmp = t_1
    else if (y <= (-9d-37)) then
        tmp = y * z
    else if (y <= (-3.1d-56)) then
        tmp = t_1
    else if (y <= 1.35d-73) then
        tmp = t
    else
        tmp = y * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -7.6e+54) {
		tmp = t_1;
	} else if (y <= -9e-37) {
		tmp = y * z;
	} else if (y <= -3.1e-56) {
		tmp = t_1;
	} else if (y <= 1.35e-73) {
		tmp = t;
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -7.6e+54:
		tmp = t_1
	elif y <= -9e-37:
		tmp = y * z
	elif y <= -3.1e-56:
		tmp = t_1
	elif y <= 1.35e-73:
		tmp = t
	else:
		tmp = y * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -7.6e+54)
		tmp = t_1;
	elseif (y <= -9e-37)
		tmp = Float64(y * z);
	elseif (y <= -3.1e-56)
		tmp = t_1;
	elseif (y <= 1.35e-73)
		tmp = t;
	else
		tmp = Float64(y * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * y);
	tmp = 0.0;
	if (y <= -7.6e+54)
		tmp = t_1;
	elseif (y <= -9e-37)
		tmp = y * z;
	elseif (y <= -3.1e-56)
		tmp = t_1;
	elseif (y <= 1.35e-73)
		tmp = t;
	else
		tmp = y * (x * y);
	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, -7.6e+54], t$95$1, If[LessEqual[y, -9e-37], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.1e-56], t$95$1, If[LessEqual[y, 1.35e-73], t, N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.6000000000000005e54 or -9.00000000000000081e-37 < y < -3.09999999999999987e-56

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 77.9%

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

      1. +-commutative 77.9%

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

      2. distribute-lft-in 77.9%

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

      3. unpow2 77.9%

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

      4. associate-*l* 84.0%

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

      5. associate-/l* 82.5%

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

      6. associate-*r* 74.1%

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

      7. distribute-lft-out 98.3%

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

      8. *-commutative 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in t around 0 84.7%

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

   7. Taylor expanded in y around inf 76.3%

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

   if -7.6000000000000005e54 < y < -9.00000000000000081e-37

   1. Initial program 99.9%

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

   3. Taylor expanded in t around -inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. distribute-rgt-neg-in 90.8%

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

      3. fma-neg 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-undefine 90.8%

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

      6. *-commutative 90.8%

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

      7. associate-/l* 90.8%

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

      8. fma-undefine 90.8%

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

      9. *-commutative 90.8%

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

      10. fma-undefine 90.8%

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

      11. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in z around inf 49.6%

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

   if -3.09999999999999987e-56 < y < 1.34999999999999997e-73

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.3%

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

   if 1.34999999999999997e-73 < 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 89.6%

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

      1. mul-1-neg 89.6%

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

      2. distribute-rgt-neg-in 89.6%

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

      3. fma-neg 89.6%

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

      4. +-commutative 89.6%

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

      5. fma-undefine 89.6%

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

      6. *-commutative 89.6%

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

      7. associate-/l* 88.2%

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

      8. fma-undefine 88.2%

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

      9. *-commutative 88.2%

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

      10. fma-undefine 88.2%

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

      11. metadata-eval 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in t around 0 82.7%

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

   7. Taylor expanded in z around 0 70.3%

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

      1. *-commutative 70.3%

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

   9. Simplified 70.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+24} \lor \neg \left(y \leq 2.5 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e+24) (not (<= y 2.5e-6)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e+24) || !(y <= 2.5e-6)) {
		tmp = y * (z + (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 <= (-2.4d+24)) .or. (.not. (y <= 2.5d-6))) then
        tmp = y * (z + (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 <= -2.4e+24) || !(y <= 2.5e-6)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e+24) or not (y <= 2.5e-6):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e+24) || !(y <= 2.5e-6))
		tmp = Float64(y * Float64(z + 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 <= -2.4e+24) || ~((y <= 2.5e-6)))
		tmp = y * (z + (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e+24], N[Not[LessEqual[y, 2.5e-6]], $MachinePrecision]], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000001e24 or 2.5000000000000002e-6 < 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 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-in 91.7%

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

      3. fma-neg 91.7%

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

      4. +-commutative 91.7%

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

      5. fma-undefine 91.7%

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

      6. *-commutative 91.7%

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

      7. associate-/l* 90.8%

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

      8. fma-undefine 90.8%

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

      9. *-commutative 90.8%

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

      10. fma-undefine 90.8%

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

      11. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in t around 0 91.5%

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

   if -2.4000000000000001e24 < y < 2.5000000000000002e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+24} \lor \neg \left(y \leq 2.5 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+139} \lor \neg \left(z \leq 2.1 \cdot 10^{+63}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+139) (not (<= z 2.1e+63)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+139) || !(z <= 2.1e+63)) {
		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 <= (-1.8d+139)) .or. (.not. (z <= 2.1d+63))) 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 <= -1.8e+139) || !(z <= 2.1e+63)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+139) or not (z <= 2.1e+63):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+139) || !(z <= 2.1e+63))
		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 <= -1.8e+139) || ~((z <= 2.1e+63)))
		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, -1.8e+139], N[Not[LessEqual[z, 2.1e+63]], $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 < -1.79999999999999993e139 or 2.1000000000000002e63 < 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 90.0%

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

   if -1.79999999999999993e139 < z < 2.1000000000000002e63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.0%

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

      1. *-commutative 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+139} \lor \neg \left(z \leq 2.1 \cdot 10^{+63}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 30500:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.4e+51)
   (* x (* y y))
   (if (<= y 30500.0) (+ t (* y z)) (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e+51) {
		tmp = x * (y * y);
	} else if (y <= 30500.0) {
		tmp = t + (y * z);
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.4d+51)) then
        tmp = x * (y * y)
    else if (y <= 30500.0d0) then
        tmp = t + (y * z)
    else
        tmp = y * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e+51) {
		tmp = x * (y * y);
	} else if (y <= 30500.0) {
		tmp = t + (y * z);
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.4e+51:
		tmp = x * (y * y)
	elif y <= 30500.0:
		tmp = t + (y * z)
	else:
		tmp = y * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.4e+51)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 30500.0)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(y * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.4e+51)
		tmp = x * (y * y);
	elseif (y <= 30500.0)
		tmp = t + (y * z);
	else
		tmp = y * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.4e+51], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 30500.0], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.39999999999999983e51

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. distribute-lft-in 75.6%

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

      3. unpow2 75.6%

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

      4. associate-*l* 82.0%

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

      5. associate-/l* 82.0%

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

      6. associate-*r* 74.9%

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

      7. distribute-lft-out 99.9%

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

      8. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 85.9%

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

   7. Taylor expanded in y around inf 75.9%

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

   if -5.39999999999999983e51 < y < 30500

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.9%

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

   if 30500 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around -inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. distribute-rgt-neg-in 90.0%

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

      3. fma-neg 90.0%

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

      4. +-commutative 90.0%

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

      5. fma-undefine 90.0%

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

      6. *-commutative 90.0%

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

      7. associate-/l* 88.2%

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

      8. fma-undefine 88.2%

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

      9. *-commutative 88.2%

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

      10. fma-undefine 88.2%

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

      11. metadata-eval 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in t around 0 88.1%

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

   7. Taylor expanded in z around 0 78.9%

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

      1. *-commutative 78.9%

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

   9. Simplified 78.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 30500:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+129} \lor \neg \left(z \leq 7.6 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e+129) (not (<= z 7.6e+81))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e+129) || !(z <= 7.6e+81)) {
		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+129)) .or. (.not. (z <= 7.6d+81))) 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+129) || !(z <= 7.6e+81)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e+129) or not (z <= 7.6e+81):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e+129) || !(z <= 7.6e+81))
		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+129) || ~((z <= 7.6e+81)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e+129], N[Not[LessEqual[z, 7.6e+81]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999997e129 or 7.599999999999999e81 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around -inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. distribute-rgt-neg-in 89.6%

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

      3. fma-neg 89.6%

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

      4. +-commutative 89.6%

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

      5. fma-undefine 89.6%

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

      6. *-commutative 89.6%

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

      7. associate-/l* 89.5%

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

      8. fma-undefine 89.5%

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

      9. *-commutative 89.5%

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

      10. fma-undefine 89.5%

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

      11. metadata-eval 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in z around inf 67.7%

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

   if -2.09999999999999997e129 < z < 7.599999999999999e81

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 45.1%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+129} \lor \neg \left(z \leq 7.6 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 9: 38.2% 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 38.2%

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

4. Final simplification 38.2%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))