Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y, z \cdot -0.5, t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma 0.125 x (fma y (* z -0.5) t)))

C

double code(double x, double y, double z, double t) {
	return fma(0.125, x, fma(y, (z * -0.5), t));
}

Julia

function code(x, y, z, t)
	return fma(0.125, x, fma(y, Float64(z * -0.5), t))
end

Wolfram

code[x_, y_, z_, t_] := N[(0.125 * x + N[(y * N[(z * -0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

   2. fma-neg 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\left(\frac{y \cdot z}{2} - t\right)\right)} \]

   3. metadata-eval 100.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.125}, x, -\left(\frac{y \cdot z}{2} - t\right)\right) \]

   4. sub-neg 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, -\color{blue}{\left(\frac{y \cdot z}{2} + \left(-t\right)\right)}\right) \]

   5. distribute-neg-in 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{\left(-\frac{y \cdot z}{2}\right) + \left(-\left(-t\right)\right)}\right) \]

   6. distribute-frac-neg 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{\frac{-y \cdot z}{2}} + \left(-\left(-t\right)\right)\right) \]

   7. distribute-rgt-neg-out 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \frac{\color{blue}{y \cdot \left(-z\right)}}{2} + \left(-\left(-t\right)\right)\right) \]

   8. remove-double-neg 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \frac{y \cdot \left(-z\right)}{2} + \color{blue}{t}\right) \]

   9. associate-/l* 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{y \cdot \frac{-z}{2}} + t\right) \]

   10. fma-define 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{\mathsf{fma}\left(y, \frac{-z}{2}, t\right)}\right) \]

   11. neg-mul-1 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y, \frac{\color{blue}{-1 \cdot z}}{2}, t\right)\right) \]

   12. *-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y, \frac{\color{blue}{z \cdot -1}}{2}, t\right)\right) \]

   13. associate-/l* 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y, \color{blue}{z \cdot \frac{-1}{2}}, t\right)\right) \]

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y, z \cdot \color{blue}{-0.5}, t\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y, z \cdot -0.5, t\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 87.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + 0.125 \cdot x\\ t_2 := t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \cdot z \leq -4 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* 0.125 x))) (t_2 (- t (* y (* z 0.5)))))
   (if (<= (* y z) -4e+135)
     t_2
     (if (<= (* y z) -4e+47)
       t_1
       (if (<= (* y z) -5e-15)
         t_2
         (if (<= (* y z) 2e+29) t_1 (- (* 0.125 x) (* (* y z) 0.5))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (0.125 * x);
	double t_2 = t - (y * (z * 0.5));
	double tmp;
	if ((y * z) <= -4e+135) {
		tmp = t_2;
	} else if ((y * z) <= -4e+47) {
		tmp = t_1;
	} else if ((y * z) <= -5e-15) {
		tmp = t_2;
	} else if ((y * z) <= 2e+29) {
		tmp = t_1;
	} else {
		tmp = (0.125 * x) - ((y * z) * 0.5);
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t + (0.125d0 * x)
    t_2 = t - (y * (z * 0.5d0))
    if ((y * z) <= (-4d+135)) then
        tmp = t_2
    else if ((y * z) <= (-4d+47)) then
        tmp = t_1
    else if ((y * z) <= (-5d-15)) then
        tmp = t_2
    else if ((y * z) <= 2d+29) then
        tmp = t_1
    else
        tmp = (0.125d0 * x) - ((y * z) * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (0.125 * x);
	double t_2 = t - (y * (z * 0.5));
	double tmp;
	if ((y * z) <= -4e+135) {
		tmp = t_2;
	} else if ((y * z) <= -4e+47) {
		tmp = t_1;
	} else if ((y * z) <= -5e-15) {
		tmp = t_2;
	} else if ((y * z) <= 2e+29) {
		tmp = t_1;
	} else {
		tmp = (0.125 * x) - ((y * z) * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (0.125 * x)
	t_2 = t - (y * (z * 0.5))
	tmp = 0
	if (y * z) <= -4e+135:
		tmp = t_2
	elif (y * z) <= -4e+47:
		tmp = t_1
	elif (y * z) <= -5e-15:
		tmp = t_2
	elif (y * z) <= 2e+29:
		tmp = t_1
	else:
		tmp = (0.125 * x) - ((y * z) * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(0.125 * x))
	t_2 = Float64(t - Float64(y * Float64(z * 0.5)))
	tmp = 0.0
	if (Float64(y * z) <= -4e+135)
		tmp = t_2;
	elseif (Float64(y * z) <= -4e+47)
		tmp = t_1;
	elseif (Float64(y * z) <= -5e-15)
		tmp = t_2;
	elseif (Float64(y * z) <= 2e+29)
		tmp = t_1;
	else
		tmp = Float64(Float64(0.125 * x) - Float64(Float64(y * z) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (0.125 * x);
	t_2 = t - (y * (z * 0.5));
	tmp = 0.0;
	if ((y * z) <= -4e+135)
		tmp = t_2;
	elseif ((y * z) <= -4e+47)
		tmp = t_1;
	elseif ((y * z) <= -5e-15)
		tmp = t_2;
	elseif ((y * z) <= 2e+29)
		tmp = t_1;
	else
		tmp = (0.125 * x) - ((y * z) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -4e+135], t$95$2, If[LessEqual[N[(y * z), $MachinePrecision], -4e+47], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -5e-15], t$95$2, If[LessEqual[N[(y * z), $MachinePrecision], 2e+29], t$95$1, N[(N[(0.125 * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -3.99999999999999985e135 or -4.0000000000000002e47 < (*.f64 y z) < -4.99999999999999999e-15

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 91.3%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 91.3%

         \[\leadsto t - \color{blue}{\left(y \cdot z\right) \cdot 0.5} \]

      2. associate-*r* 91.3%

         \[\leadsto t - \color{blue}{y \cdot \left(z \cdot 0.5\right)} \]

      3. *-commutative 91.3%

         \[\leadsto t - y \cdot \color{blue}{\left(0.5 \cdot z\right)} \]

   7. Simplified 91.3%

      \[\leadsto \color{blue}{t - y \cdot \left(0.5 \cdot z\right)} \]

   if -3.99999999999999985e135 < (*.f64 y z) < -4.0000000000000002e47 or -4.99999999999999999e-15 < (*.f64 y z) < 1.99999999999999983e29

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 93.1%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]

   if 1.99999999999999983e29 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 92.9%

      \[\leadsto \color{blue}{0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+135}:\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{elif}\;y \cdot z \leq -4 \cdot 10^{+47}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+29}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+135} \lor \neg \left(y \cdot z \leq -1 \cdot 10^{+56}\right) \land \left(y \cdot z \leq -5 \cdot 10^{-15} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+21}\right)\right):\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -4e+135)
         (and (not (<= (* y z) -1e+56))
              (or (<= (* y z) -5e-15) (not (<= (* y z) 2e+21)))))
   (- t (* y (* z 0.5)))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -4e+135) || (!((y * z) <= -1e+56) && (((y * z) <= -5e-15) || !((y * z) <= 2e+21)))) {
		tmp = t - (y * (z * 0.5));
	} else {
		tmp = t + (0.125 * x);
	}
	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 * z) <= (-4d+135)) .or. (.not. ((y * z) <= (-1d+56))) .and. ((y * z) <= (-5d-15)) .or. (.not. ((y * z) <= 2d+21))) then
        tmp = t - (y * (z * 0.5d0))
    else
        tmp = t + (0.125d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -4e+135) || (!((y * z) <= -1e+56) && (((y * z) <= -5e-15) || !((y * z) <= 2e+21)))) {
		tmp = t - (y * (z * 0.5));
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -4e+135) or (not ((y * z) <= -1e+56) and (((y * z) <= -5e-15) or not ((y * z) <= 2e+21))):
		tmp = t - (y * (z * 0.5))
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -4e+135) || (!(Float64(y * z) <= -1e+56) && ((Float64(y * z) <= -5e-15) || !(Float64(y * z) <= 2e+21))))
		tmp = Float64(t - Float64(y * Float64(z * 0.5)));
	else
		tmp = Float64(t + Float64(0.125 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -4e+135) || (~(((y * z) <= -1e+56)) && (((y * z) <= -5e-15) || ~(((y * z) <= 2e+21)))))
		tmp = t - (y * (z * 0.5));
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -4e+135], And[N[Not[LessEqual[N[(y * z), $MachinePrecision], -1e+56]], $MachinePrecision], Or[LessEqual[N[(y * z), $MachinePrecision], -5e-15], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+21]], $MachinePrecision]]]], N[(t - N[(y * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -3.99999999999999985e135 or -1.00000000000000009e56 < (*.f64 y z) < -4.99999999999999999e-15 or 2e21 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.2%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 89.2%

         \[\leadsto t - \color{blue}{\left(y \cdot z\right) \cdot 0.5} \]

      2. associate-*r* 89.2%

         \[\leadsto t - \color{blue}{y \cdot \left(z \cdot 0.5\right)} \]

      3. *-commutative 89.2%

         \[\leadsto t - y \cdot \color{blue}{\left(0.5 \cdot z\right)} \]

   7. Simplified 89.2%

      \[\leadsto \color{blue}{t - y \cdot \left(0.5 \cdot z\right)} \]

   if -3.99999999999999985e135 < (*.f64 y z) < -1.00000000000000009e56 or -4.99999999999999999e-15 < (*.f64 y z) < 2e21

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 93.1%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+135} \lor \neg \left(y \cdot z \leq -1 \cdot 10^{+56}\right) \land \left(y \cdot z \leq -5 \cdot 10^{-15} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+21}\right)\right):\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -3.6 \cdot 10^{-140}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq -8.6 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 6 \cdot 10^{+26}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (* y z))))
   (if (<= (* y z) -5e-15)
     t_1
     (if (<= (* y z) -3.6e-140)
       (* 0.125 x)
       (if (<= (* y z) -8.6e-244)
         t
         (if (<= (* y z) 6e+26) (* 0.125 x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (y * z);
	double tmp;
	if ((y * z) <= -5e-15) {
		tmp = t_1;
	} else if ((y * z) <= -3.6e-140) {
		tmp = 0.125 * x;
	} else if ((y * z) <= -8.6e-244) {
		tmp = t;
	} else if ((y * z) <= 6e+26) {
		tmp = 0.125 * x;
	} 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 = (-0.5d0) * (y * z)
    if ((y * z) <= (-5d-15)) then
        tmp = t_1
    else if ((y * z) <= (-3.6d-140)) then
        tmp = 0.125d0 * x
    else if ((y * z) <= (-8.6d-244)) then
        tmp = t
    else if ((y * z) <= 6d+26) then
        tmp = 0.125d0 * x
    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 = -0.5 * (y * z);
	double tmp;
	if ((y * z) <= -5e-15) {
		tmp = t_1;
	} else if ((y * z) <= -3.6e-140) {
		tmp = 0.125 * x;
	} else if ((y * z) <= -8.6e-244) {
		tmp = t;
	} else if ((y * z) <= 6e+26) {
		tmp = 0.125 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (y * z)
	tmp = 0
	if (y * z) <= -5e-15:
		tmp = t_1
	elif (y * z) <= -3.6e-140:
		tmp = 0.125 * x
	elif (y * z) <= -8.6e-244:
		tmp = t
	elif (y * z) <= 6e+26:
		tmp = 0.125 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(y * z))
	tmp = 0.0
	if (Float64(y * z) <= -5e-15)
		tmp = t_1;
	elseif (Float64(y * z) <= -3.6e-140)
		tmp = Float64(0.125 * x);
	elseif (Float64(y * z) <= -8.6e-244)
		tmp = t;
	elseif (Float64(y * z) <= 6e+26)
		tmp = Float64(0.125 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (y * z);
	tmp = 0.0;
	if ((y * z) <= -5e-15)
		tmp = t_1;
	elseif ((y * z) <= -3.6e-140)
		tmp = 0.125 * x;
	elseif ((y * z) <= -8.6e-244)
		tmp = t;
	elseif ((y * z) <= 6e+26)
		tmp = 0.125 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5e-15], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -3.6e-140], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], -8.6e-244], t, If[LessEqual[N[(y * z), $MachinePrecision], 6e+26], N[(0.125 * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.99999999999999999e-15 or 5.99999999999999994e26 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.9%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

   if -4.99999999999999999e-15 < (*.f64 y z) < -3.6e-140 or -8.59999999999999973e-244 < (*.f64 y z) < 5.99999999999999994e26

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{0.125 \cdot x} \]

   if -3.6e-140 < (*.f64 y z) < -8.59999999999999973e-244

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 62.1%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq -3.6 \cdot 10^{-140}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq -8.6 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 6 \cdot 10^{+26}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.4 \cdot 10^{+214} \lor \neg \left(y \cdot z \leq 4.4 \cdot 10^{+123}\right):\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -2.4e+214) (not (<= (* y z) 4.4e+123)))
   (* -0.5 (* y z))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -2.4e+214) || !((y * z) <= 4.4e+123)) {
		tmp = -0.5 * (y * z);
	} else {
		tmp = t + (0.125 * x);
	}
	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 * z) <= (-2.4d+214)) .or. (.not. ((y * z) <= 4.4d+123))) then
        tmp = (-0.5d0) * (y * z)
    else
        tmp = t + (0.125d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -2.4e+214) || !((y * z) <= 4.4e+123)) {
		tmp = -0.5 * (y * z);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -2.4e+214) or not ((y * z) <= 4.4e+123):
		tmp = -0.5 * (y * z)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -2.4e+214) || !(Float64(y * z) <= 4.4e+123))
		tmp = Float64(-0.5 * Float64(y * z));
	else
		tmp = Float64(t + Float64(0.125 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -2.4e+214) || ~(((y * z) <= 4.4e+123)))
		tmp = -0.5 * (y * z);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2.4e+214], N[Not[LessEqual[N[(y * z), $MachinePrecision], 4.4e+123]], $MachinePrecision]], N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.4000000000000001e214 or 4.39999999999999984e123 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 88.4%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 88.4%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

   if -2.4000000000000001e214 < (*.f64 y z) < 4.39999999999999984e123

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 86.6%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.4 \cdot 10^{+214} \lor \neg \left(y \cdot z \leq 4.4 \cdot 10^{+123}\right):\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+67} \lor \neg \left(x \leq 7.5 \cdot 10^{+78}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e+67) (not (<= x 7.5e+78))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e+67) || !(x <= 7.5e+78)) {
		tmp = 0.125 * x;
	} 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 ((x <= (-1.35d+67)) .or. (.not. (x <= 7.5d+78))) then
        tmp = 0.125d0 * x
    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 ((x <= -1.35e+67) || !(x <= 7.5e+78)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.35e+67) or not (x <= 7.5e+78):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.35e+67) || !(x <= 7.5e+78))
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.35e+67) || ~((x <= 7.5e+78)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.35e+67], N[Not[LessEqual[x, 7.5e+78]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e67 or 7.49999999999999934e78 < x

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.7%

      \[\leadsto \color{blue}{0.125 \cdot x} \]

   if -1.35e67 < x < 7.49999999999999934e78

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.4%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+67} \lor \neg \left(x \leq 7.5 \cdot 10^{+78}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ t + \left(0.125 \cdot x - y \cdot \frac{z}{2}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ t (- (* 0.125 x) (* y (/ z 2.0)))))

C

double code(double x, double y, double z, double t) {
	return t + ((0.125 * x) - (y * (z / 2.0)));
}

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 + ((0.125d0 * x) - (y * (z / 2.0d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t + ((0.125 * x) - (y * (z / 2.0)));
}

Python

def code(x, y, z, t):
	return t + ((0.125 * x) - (y * (z / 2.0)))

Julia

function code(x, y, z, t)
	return Float64(t + Float64(Float64(0.125 * x) - Float64(y * Float64(z / 2.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t + ((0.125 * x) - (y * (z / 2.0)));
end

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(N[(0.125 * x), $MachinePrecision] - N[(y * N[(z / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

   2. *-commutative 100.0%

      \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

   3. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

   4. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

   5. *-commutative 100.0%

      \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

   6. associate-/l* 100.0%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto t + \left(0.125 \cdot x - y \cdot \frac{z}{2}\right) \]
6. Add Preprocessing

Alternative 8: 32.9% accurate, 13.0× 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 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

   2. *-commutative 100.0%

      \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

   3. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

   4. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

   5. *-commutative 100.0%

      \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

   6. associate-/l* 100.0%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 32.4%

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

Developer target: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (+ (/ x 8.0) t) (* (/ z 2.0) y)))

C

double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * 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 = ((x / 8.0d0) + t) - ((z / 2.0d0) * y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * y);
}

Python

def code(x, y, z, t):
	return ((x / 8.0) + t) - ((z / 2.0) * y)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / 8.0) + t) - Float64(Float64(z / 2.0) * y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / 8.0) + t) - ((z / 2.0) * y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / 8.0), $MachinePrecision] + t), $MachinePrecision] - N[(N[(z / 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024091 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))