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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 5

Speedup: 2.2×

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, 2.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. associate-/l* N/A

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

   5. *-commutative N/A

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

   6. distribute-lft-neg-in N/A

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

   7. +-commutative N/A

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

   8. accelerator-lowering-fma.f64 N/A

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

   9. div-inv N/A

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

   10. distribute-rgt-neg-in N/A

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

   11. metadata-eval N/A

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

   12. metadata-eval N/A

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

   13. metadata-eval N/A

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

   14. metadata-eval N/A

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

   15. *-lowering-*.f64 N/A

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

   16. metadata-eval N/A

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

   17. metadata-eval N/A

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

   18. +-commutative N/A

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

   19. accelerator-lowering-fma.f64 N/A

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

   20. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 49.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{1}{8}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ 1.0 8.0))))
   (if (<= t_1 -2e-57) (* 0.125 x) (if (<= t_1 2e+79) t (* 0.125 x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 / 8.0);
	double tmp;
	if (t_1 <= -2e-57) {
		tmp = 0.125 * x;
	} else if (t_1 <= 2e+79) {
		tmp = t;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 / 8.0d0)
    if (t_1 <= (-2d-57)) then
        tmp = 0.125d0 * x
    else if (t_1 <= 2d+79) then
        tmp = t
    else
        tmp = 0.125d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 / 8.0);
	double tmp;
	if (t_1 <= -2e-57) {
		tmp = 0.125 * x;
	} else if (t_1 <= 2e+79) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 / 8.0)
	tmp = 0
	if t_1 <= -2e-57:
		tmp = 0.125 * x
	elif t_1 <= 2e+79:
		tmp = t
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 / 8.0))
	tmp = 0.0
	if (t_1 <= -2e-57)
		tmp = Float64(0.125 * x);
	elseif (t_1 <= 2e+79)
		tmp = t;
	else
		tmp = Float64(0.125 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 / 8.0);
	tmp = 0.0;
	if (t_1 <= -2e-57)
		tmp = 0.125 * x;
	elseif (t_1 <= 2e+79)
		tmp = t;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 / 8.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-57], N[(0.125 * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+79], t, N[(0.125 * x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 8 binary64)) x) < -1.99999999999999991e-57 or 1.99999999999999993e79 < (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 8 binary64)) x)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x} \]
   4. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x + 0} \]

      2. accelerator-lowering-fma.f64 61.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, 0\right)} \]

   5. Simplified 61.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{1}{8}} \]

      3. *-lowering-*.f64 61.6

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

   7. Applied egg-rr 61.6%

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

   if -1.99999999999999991e-57 < (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 8 binary64)) x) < 1.99999999999999993e79

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 44.2%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{1}{8} \leq -2 \cdot 10^{-57}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \cdot \frac{1}{8} \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z \cdot -0.5, y, t\right)\\ \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot y \leq 4 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(0.125, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (* z -0.5) y t)))
   (if (<= (* z y) -2e+116) t_1 (if (<= (* z y) 4e-26) (fma 0.125 x t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z * -0.5), y, t);
	double tmp;
	if ((z * y) <= -2e+116) {
		tmp = t_1;
	} else if ((z * y) <= 4e-26) {
		tmp = fma(0.125, x, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z * -0.5), y, t)
	tmp = 0.0
	if (Float64(z * y) <= -2e+116)
		tmp = t_1;
	elseif (Float64(z * y) <= 4e-26)
		tmp = fma(0.125, x, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] * y + t), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -2e+116], t$95$1, If[LessEqual[N[(z * y), $MachinePrecision], 4e-26], N[(0.125 * x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.00000000000000003e116 or 4.0000000000000002e-26 < (*.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. +-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. div-inv N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. accelerator-lowering-fma.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(z \cdot \frac{-1}{2}, y, \color{blue}{t}\right) \]
   6. Step-by-step derivation

   7. Simplified 87.0%

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

   if -2.00000000000000003e116 < (*.f64 y z) < 4.0000000000000002e-26

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t + \frac{1}{8} \cdot x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x + t} \]

      2. accelerator-lowering-fma.f64 88.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, t\right)} \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot -0.5, y, t\right)\\ \mathbf{elif}\;z \cdot y \leq 4 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(0.125, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot -0.5, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.125, x, t\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z, t)
	return fma(0.125, x, t)
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{t + \frac{1}{8} \cdot x} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x + t} \]

   2. accelerator-lowering-fma.f64 61.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, t\right)} \]

5. Simplified 61.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, t\right)} \]
6. Add Preprocessing

Alternative 5: 33.0% accurate, 39.0× 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. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 32.8%

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

Developer Target 1: 100.0% accurate, 1.1× 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 2024195 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ (/ x 8) t) (* (/ z 2) y)))

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