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

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

Alternatives: 9

Speedup: 0.1×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. sub-neg 99.7%

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

   2. +-commutative 99.7%

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

   3. associate-+l+ 99.7%

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

   4. associate-/l* 99.9%

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

   5. distribute-frac-neg 99.9%

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

   6. associate-/r/ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. fma-def 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate-/l* 100.0%

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

   12. associate-/r/ 100.0%

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

   13. *-commutative 100.0%

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

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(z, y \cdot \color{blue}{-0.5}, t + \frac{1}{8} \cdot x\right) \]

   15. +-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(z, y \cdot -0.5, \color{blue}{\frac{1}{8} \cdot x + t}\right) \]

   16. fma-def 100.0%

       \[\leadsto \mathsf{fma}\left(z, y \cdot -0.5, \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, t\right)}\right) \]

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. metadata-eval 99.7%

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

   2. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0 99.7%

   \[\leadsto \color{blue}{\left(t + 0.125 \cdot x\right) - 0.5 \cdot \left(y \cdot z\right)} \]
6. Step-by-step derivation

   1. associate--l+ 99.7%

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

   2. cancel-sign-sub-inv 99.7%

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

   3. metadata-eval 99.7%

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

   4. +-commutative 99.7%

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

   5. *-commutative 99.7%

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

   6. associate-*l* 100.0%

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

   7. metadata-eval 100.0%

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

   8. distribute-rgt-neg-in 100.0%

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

   9. fma-udef 100.0%

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

   10. distribute-rgt-neg-in 100.0%

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

   11. metadata-eval 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 3: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot -0.5\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-248}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-217}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* y -0.5))))
   (if (<= z -3.8e+67)
     t_1
     (if (<= z 3.3e-248)
       t
       (if (<= z 1.15e-217)
         (* 0.125 x)
         (if (<= z 9e-89)
           t
           (if (<= z 1.8e+43) (* 0.125 x) (if (<= z 3.6e+113) t t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y * -0.5);
	double tmp;
	if (z <= -3.8e+67) {
		tmp = t_1;
	} else if (z <= 3.3e-248) {
		tmp = t;
	} else if (z <= 1.15e-217) {
		tmp = 0.125 * x;
	} else if (z <= 9e-89) {
		tmp = t;
	} else if (z <= 1.8e+43) {
		tmp = 0.125 * x;
	} else if (z <= 3.6e+113) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y * (-0.5d0))
    if (z <= (-3.8d+67)) then
        tmp = t_1
    else if (z <= 3.3d-248) then
        tmp = t
    else if (z <= 1.15d-217) then
        tmp = 0.125d0 * x
    else if (z <= 9d-89) then
        tmp = t
    else if (z <= 1.8d+43) then
        tmp = 0.125d0 * x
    else if (z <= 3.6d+113) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y * -0.5);
	double tmp;
	if (z <= -3.8e+67) {
		tmp = t_1;
	} else if (z <= 3.3e-248) {
		tmp = t;
	} else if (z <= 1.15e-217) {
		tmp = 0.125 * x;
	} else if (z <= 9e-89) {
		tmp = t;
	} else if (z <= 1.8e+43) {
		tmp = 0.125 * x;
	} else if (z <= 3.6e+113) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y * -0.5)
	tmp = 0
	if z <= -3.8e+67:
		tmp = t_1
	elif z <= 3.3e-248:
		tmp = t
	elif z <= 1.15e-217:
		tmp = 0.125 * x
	elif z <= 9e-89:
		tmp = t
	elif z <= 1.8e+43:
		tmp = 0.125 * x
	elif z <= 3.6e+113:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y * -0.5))
	tmp = 0.0
	if (z <= -3.8e+67)
		tmp = t_1;
	elseif (z <= 3.3e-248)
		tmp = t;
	elseif (z <= 1.15e-217)
		tmp = Float64(0.125 * x);
	elseif (z <= 9e-89)
		tmp = t;
	elseif (z <= 1.8e+43)
		tmp = Float64(0.125 * x);
	elseif (z <= 3.6e+113)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y * -0.5);
	tmp = 0.0;
	if (z <= -3.8e+67)
		tmp = t_1;
	elseif (z <= 3.3e-248)
		tmp = t;
	elseif (z <= 1.15e-217)
		tmp = 0.125 * x;
	elseif (z <= 9e-89)
		tmp = t;
	elseif (z <= 1.8e+43)
		tmp = 0.125 * x;
	elseif (z <= 3.6e+113)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+67], t$95$1, If[LessEqual[z, 3.3e-248], t, If[LessEqual[z, 1.15e-217], N[(0.125 * x), $MachinePrecision], If[LessEqual[z, 9e-89], t, If[LessEqual[z, 1.8e+43], N[(0.125 * x), $MachinePrecision], If[LessEqual[z, 3.6e+113], t, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e67 or 3.59999999999999992e113 < z

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 60.9%

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

      1. associate-*r* 61.6%

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

   7. Simplified 61.6%

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

   if -3.8000000000000002e67 < z < 3.3000000000000002e-248 or 1.15000000000000002e-217 < z < 8.9999999999999998e-89 or 1.80000000000000005e43 < z < 3.59999999999999992e113

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 48.9%

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

   if 3.3000000000000002e-248 < z < 1.15000000000000002e-217 or 8.9999999999999998e-89 < z < 1.80000000000000005e43

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 37.9%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-248}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-217}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot 0.5\\ t_2 := t - t_1\\ t_3 := 0.125 \cdot x - t_1\\ \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \cdot y \leq -1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* z y) 0.5)) (t_2 (- t t_1)) (t_3 (- (* 0.125 x) t_1)))
   (if (<= (* z y) -2e+128)
     t_3
     (if (<= (* z y) -1e+46)
       t_2
       (if (<= (* z y) -5e+38)
         t_3
         (if (<= (* z y) 5e+31) (+ t (* 0.125 x)) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * 0.5;
	double t_2 = t - t_1;
	double t_3 = (0.125 * x) - t_1;
	double tmp;
	if ((z * y) <= -2e+128) {
		tmp = t_3;
	} else if ((z * y) <= -1e+46) {
		tmp = t_2;
	} else if ((z * y) <= -5e+38) {
		tmp = t_3;
	} else if ((z * y) <= 5e+31) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (z * y) * 0.5d0
    t_2 = t - t_1
    t_3 = (0.125d0 * x) - t_1
    if ((z * y) <= (-2d+128)) then
        tmp = t_3
    else if ((z * y) <= (-1d+46)) then
        tmp = t_2
    else if ((z * y) <= (-5d+38)) then
        tmp = t_3
    else if ((z * y) <= 5d+31) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * 0.5;
	double t_2 = t - t_1;
	double t_3 = (0.125 * x) - t_1;
	double tmp;
	if ((z * y) <= -2e+128) {
		tmp = t_3;
	} else if ((z * y) <= -1e+46) {
		tmp = t_2;
	} else if ((z * y) <= -5e+38) {
		tmp = t_3;
	} else if ((z * y) <= 5e+31) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) * 0.5
	t_2 = t - t_1
	t_3 = (0.125 * x) - t_1
	tmp = 0
	if (z * y) <= -2e+128:
		tmp = t_3
	elif (z * y) <= -1e+46:
		tmp = t_2
	elif (z * y) <= -5e+38:
		tmp = t_3
	elif (z * y) <= 5e+31:
		tmp = t + (0.125 * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) * 0.5)
	t_2 = Float64(t - t_1)
	t_3 = Float64(Float64(0.125 * x) - t_1)
	tmp = 0.0
	if (Float64(z * y) <= -2e+128)
		tmp = t_3;
	elseif (Float64(z * y) <= -1e+46)
		tmp = t_2;
	elseif (Float64(z * y) <= -5e+38)
		tmp = t_3;
	elseif (Float64(z * y) <= 5e+31)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) * 0.5;
	t_2 = t - t_1;
	t_3 = (0.125 * x) - t_1;
	tmp = 0.0;
	if ((z * y) <= -2e+128)
		tmp = t_3;
	elseif ((z * y) <= -1e+46)
		tmp = t_2;
	elseif ((z * y) <= -5e+38)
		tmp = t_3;
	elseif ((z * y) <= 5e+31)
		tmp = t + (0.125 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$2 = N[(t - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -2e+128], t$95$3, If[LessEqual[N[(z * y), $MachinePrecision], -1e+46], t$95$2, If[LessEqual[N[(z * y), $MachinePrecision], -5e+38], t$95$3, If[LessEqual[N[(z * y), $MachinePrecision], 5e+31], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2.0000000000000002e128 or -9.9999999999999999e45 < (*.f64 y z) < -4.9999999999999997e38

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 98.1%

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

   if -2.0000000000000002e128 < (*.f64 y z) < -9.9999999999999999e45 or 5.00000000000000027e31 < (*.f64 y z)

   1. Initial program 98.9%

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

      1. metadata-eval 98.9%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 92.2%

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

   if -4.9999999999999997e38 < (*.f64 y z) < 5.00000000000000027e31

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+128}:\\ \;\;\;\;0.125 \cdot x - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{elif}\;z \cdot y \leq -1 \cdot 10^{+46}:\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{elif}\;z \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;0.125 \cdot x - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+43} \lor \neg \left(z \cdot y \leq 5 \cdot 10^{+31}\right):\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z y) -2e+43) (not (<= (* z y) 5e+31)))
   (- t (* (* z y) 0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -2e+43) || !((z * y) <= 5e+31)) {
		tmp = t - ((z * y) * 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 (((z * y) <= (-2d+43)) .or. (.not. ((z * y) <= 5d+31))) then
        tmp = t - ((z * y) * 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 (((z * y) <= -2e+43) || !((z * y) <= 5e+31)) {
		tmp = t - ((z * y) * 0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * y) <= -2e+43) or not ((z * y) <= 5e+31):
		tmp = t - ((z * y) * 0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * y) <= -2e+43) || !(Float64(z * y) <= 5e+31))
		tmp = Float64(t - Float64(Float64(z * y) * 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 (((z * y) <= -2e+43) || ~(((z * y) <= 5e+31)))
		tmp = t - ((z * y) * 0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * y), $MachinePrecision], -2e+43], N[Not[LessEqual[N[(z * y), $MachinePrecision], 5e+31]], $MachinePrecision]], N[(t - N[(N[(z * y), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.00000000000000003e43 or 5.00000000000000027e31 < (*.f64 y z)

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 90.5%

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

   if -2.00000000000000003e43 < (*.f64 y z) < 5.00000000000000027e31

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+43} \lor \neg \left(z \cdot y \leq 5 \cdot 10^{+31}\right):\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+69} \lor \neg \left(z \leq 2.4 \cdot 10^{+183}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.22e+69) (not (<= z 2.4e+183)))
   (* z (* y -0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.22e+69) || !(z <= 2.4e+183)) {
		tmp = z * (y * -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 ((z <= (-1.22d+69)) .or. (.not. (z <= 2.4d+183))) then
        tmp = z * (y * (-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 ((z <= -1.22e+69) || !(z <= 2.4e+183)) {
		tmp = z * (y * -0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.22e+69) or not (z <= 2.4e+183):
		tmp = z * (y * -0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.22e+69) || !(z <= 2.4e+183))
		tmp = Float64(z * Float64(y * -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 ((z <= -1.22e+69) || ~((z <= 2.4e+183)))
		tmp = z * (y * -0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.22e+69], N[Not[LessEqual[z, 2.4e+183]], $MachinePrecision]], N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e69 or 2.4000000000000002e183 < z

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.1%

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

      1. associate-*r* 64.9%

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

   7. Simplified 64.9%

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

   if -1.22e69 < z < 2.4000000000000002e183

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 80.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+69} \lor \neg \left(z \leq 2.4 \cdot 10^{+183}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+32} \lor \neg \left(x \leq 3.7 \cdot 10^{+121}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e+32) (not (<= x 3.7e+121))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e+32) || !(x <= 3.7e+121)) {
		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 <= (-8.5d+32)) .or. (.not. (x <= 3.7d+121))) 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 <= -8.5e+32) || !(x <= 3.7e+121)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.5e+32) or not (x <= 3.7e+121):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.5e+32) || !(x <= 3.7e+121))
		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 <= -8.5e+32) || ~((x <= 3.7e+121)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.5e+32], N[Not[LessEqual[x, 3.7e+121]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999998e32 or 3.70000000000000013e121 < x

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 60.0%

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

   if -8.4999999999999998e32 < x < 3.70000000000000013e121

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 48.1%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+32} \lor \neg \left(x \leq 3.7 \cdot 10^{+121}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 / (2.0d0 / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. metadata-eval 99.7%

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

   2. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 9: 33.3% 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 99.7%

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

   1. metadata-eval 99.7%

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

   2. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in t around inf 35.5%

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

6. Final simplification 35.5%

   \[\leadsto t \]
7. 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 2024020 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

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

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