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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(0.125 * x + N[(N[(y / -2.0), $MachinePrecision] * z + 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. sub-neg 100.0%

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

   2. associate-+l+ 100.0%

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

   3. fma-def 100.0%

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

   4. metadata-eval 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. distribute-lft-neg-out 100.0%

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

   7. associate-*l/ 100.0%

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

   8. fma-def 100.0%

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

   9. neg-mul-1 100.0%

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

   10. *-commutative 100.0%

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

   11. associate-/l* 100.0%

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

   12. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;y \cdot z \leq -3.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq -1 \cdot 10^{+60}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq -106000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq -6 \cdot 10^{-96}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 1.1 \cdot 10^{-256}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 1.2 \cdot 10^{-154}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 7.6 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) -0.5)))
   (if (<= (* y z) -3.8e+149)
     t_1
     (if (<= (* y z) -1e+60)
       (* 0.125 x)
       (if (<= (* y z) -106000.0)
         t_1
         (if (<= (* y z) -6e-96)
           (* 0.125 x)
           (if (<= (* y z) 1.1e-256)
             t
             (if (<= (* y z) 1.2e-154)
               (* 0.125 x)
               (if (<= (* y z) 7.6e+119) t t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * -0.5;
	double tmp;
	if ((y * z) <= -3.8e+149) {
		tmp = t_1;
	} else if ((y * z) <= -1e+60) {
		tmp = 0.125 * x;
	} else if ((y * z) <= -106000.0) {
		tmp = t_1;
	} else if ((y * z) <= -6e-96) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 1.1e-256) {
		tmp = t;
	} else if ((y * z) <= 1.2e-154) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 7.6e+119) {
		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 = (y * z) * (-0.5d0)
    if ((y * z) <= (-3.8d+149)) then
        tmp = t_1
    else if ((y * z) <= (-1d+60)) then
        tmp = 0.125d0 * x
    else if ((y * z) <= (-106000.0d0)) then
        tmp = t_1
    else if ((y * z) <= (-6d-96)) then
        tmp = 0.125d0 * x
    else if ((y * z) <= 1.1d-256) then
        tmp = t
    else if ((y * z) <= 1.2d-154) then
        tmp = 0.125d0 * x
    else if ((y * z) <= 7.6d+119) 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 = (y * z) * -0.5;
	double tmp;
	if ((y * z) <= -3.8e+149) {
		tmp = t_1;
	} else if ((y * z) <= -1e+60) {
		tmp = 0.125 * x;
	} else if ((y * z) <= -106000.0) {
		tmp = t_1;
	} else if ((y * z) <= -6e-96) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 1.1e-256) {
		tmp = t;
	} else if ((y * z) <= 1.2e-154) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 7.6e+119) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * -0.5
	tmp = 0
	if (y * z) <= -3.8e+149:
		tmp = t_1
	elif (y * z) <= -1e+60:
		tmp = 0.125 * x
	elif (y * z) <= -106000.0:
		tmp = t_1
	elif (y * z) <= -6e-96:
		tmp = 0.125 * x
	elif (y * z) <= 1.1e-256:
		tmp = t
	elif (y * z) <= 1.2e-154:
		tmp = 0.125 * x
	elif (y * z) <= 7.6e+119:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) * -0.5)
	tmp = 0.0
	if (Float64(y * z) <= -3.8e+149)
		tmp = t_1;
	elseif (Float64(y * z) <= -1e+60)
		tmp = Float64(0.125 * x);
	elseif (Float64(y * z) <= -106000.0)
		tmp = t_1;
	elseif (Float64(y * z) <= -6e-96)
		tmp = Float64(0.125 * x);
	elseif (Float64(y * z) <= 1.1e-256)
		tmp = t;
	elseif (Float64(y * z) <= 1.2e-154)
		tmp = Float64(0.125 * x);
	elseif (Float64(y * z) <= 7.6e+119)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) * -0.5;
	tmp = 0.0;
	if ((y * z) <= -3.8e+149)
		tmp = t_1;
	elseif ((y * z) <= -1e+60)
		tmp = 0.125 * x;
	elseif ((y * z) <= -106000.0)
		tmp = t_1;
	elseif ((y * z) <= -6e-96)
		tmp = 0.125 * x;
	elseif ((y * z) <= 1.1e-256)
		tmp = t;
	elseif ((y * z) <= 1.2e-154)
		tmp = 0.125 * x;
	elseif ((y * z) <= 7.6e+119)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -3.8e+149], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -1e+60], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], -106000.0], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -6e-96], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1.1e-256], t, If[LessEqual[N[(y * z), $MachinePrecision], 1.2e-154], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 7.6e+119], t, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -3.8000000000000001e149 or -9.9999999999999995e59 < (*.f64 y z) < -106000 or 7.59999999999999979e119 < (*.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.1%

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

      1. *-commutative 80.1%

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

   4. Simplified 80.1%

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

   if -3.8000000000000001e149 < (*.f64 y z) < -9.9999999999999995e59 or -106000 < (*.f64 y z) < -6e-96 or 1.10000000000000005e-256 < (*.f64 y z) < 1.19999999999999993e-154

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.1%

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

   if -6e-96 < (*.f64 y z) < 1.10000000000000005e-256 or 1.19999999999999993e-154 < (*.f64 y z) < 7.59999999999999979e119

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 58.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -3.8 \cdot 10^{+149}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq -1 \cdot 10^{+60}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq -106000:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq -6 \cdot 10^{-96}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 1.1 \cdot 10^{-256}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 1.2 \cdot 10^{-154}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 7.6 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \end{array} \]

Alternative 3: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -3.9 \cdot 10^{+149} \lor \neg \left(y \cdot z \leq -1.8 \cdot 10^{+61} \lor \neg \left(y \cdot z \leq -102000\right) \land y \cdot z \leq 1.85 \cdot 10^{+130}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -3.9e+149)
         (not
          (or (<= (* y z) -1.8e+61)
              (and (not (<= (* y z) -102000.0)) (<= (* y z) 1.85e+130)))))
   (- 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) <= -3.9e+149) || !(((y * z) <= -1.8e+61) || (!((y * z) <= -102000.0) && ((y * z) <= 1.85e+130)))) {
		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) <= (-3.9d+149)) .or. (.not. ((y * z) <= (-1.8d+61)) .or. (.not. ((y * z) <= (-102000.0d0))) .and. ((y * z) <= 1.85d+130))) 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) <= -3.9e+149) || !(((y * z) <= -1.8e+61) || (!((y * z) <= -102000.0) && ((y * z) <= 1.85e+130)))) {
		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) <= -3.9e+149) or not (((y * z) <= -1.8e+61) or (not ((y * z) <= -102000.0) and ((y * z) <= 1.85e+130))):
		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) <= -3.9e+149) || !((Float64(y * z) <= -1.8e+61) || (!(Float64(y * z) <= -102000.0) && (Float64(y * z) <= 1.85e+130))))
		tmp = Float64(t - Float64(Float64(y * 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) <= -3.9e+149) || ~((((y * z) <= -1.8e+61) || (~(((y * z) <= -102000.0)) && ((y * z) <= 1.85e+130)))))
		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], -3.9e+149], N[Not[Or[LessEqual[N[(y * z), $MachinePrecision], -1.8e+61], And[N[Not[LessEqual[N[(y * z), $MachinePrecision], -102000.0]], $MachinePrecision], LessEqual[N[(y * z), $MachinePrecision], 1.85e+130]]]], $MachinePrecision]], N[(t - N[(N[(y * z), $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) < -3.8999999999999999e149 or -1.80000000000000005e61 < (*.f64 y z) < -102000 or 1.8500000000000001e130 < (*.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.9%

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

   if -3.8999999999999999e149 < (*.f64 y z) < -1.80000000000000005e61 or -102000 < (*.f64 y z) < 1.8500000000000001e130

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -3.9 \cdot 10^{+149} \lor \neg \left(y \cdot z \leq -1.8 \cdot 10^{+61} \lor \neg \left(y \cdot z \leq -102000\right) \land y \cdot z \leq 1.85 \cdot 10^{+130}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 4: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -9.5 \cdot 10^{+155} \lor \neg \left(y \cdot z \leq -1.95 \cdot 10^{+27}\right) \land \left(y \cdot z \leq -160000 \lor \neg \left(y \cdot z \leq 1.32 \cdot 10^{+178}\right)\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -9.5e+155)
         (and (not (<= (* y z) -1.95e+27))
              (or (<= (* y z) -160000.0) (not (<= (* y z) 1.32e+178)))))
   (* (* y z) -0.5)
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -9.5e+155) || (!((y * z) <= -1.95e+27) && (((y * z) <= -160000.0) || !((y * z) <= 1.32e+178)))) {
		tmp = (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) <= (-9.5d+155)) .or. (.not. ((y * z) <= (-1.95d+27))) .and. ((y * z) <= (-160000.0d0)) .or. (.not. ((y * z) <= 1.32d+178))) then
        tmp = (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) <= -9.5e+155) || (!((y * z) <= -1.95e+27) && (((y * z) <= -160000.0) || !((y * z) <= 1.32e+178)))) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -9.5e+155) or (not ((y * z) <= -1.95e+27) and (((y * z) <= -160000.0) or not ((y * z) <= 1.32e+178))):
		tmp = (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) <= -9.5e+155) || (!(Float64(y * z) <= -1.95e+27) && ((Float64(y * z) <= -160000.0) || !(Float64(y * z) <= 1.32e+178))))
		tmp = Float64(Float64(y * 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) <= -9.5e+155) || (~(((y * z) <= -1.95e+27)) && (((y * z) <= -160000.0) || ~(((y * z) <= 1.32e+178)))))
		tmp = (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], -9.5e+155], And[N[Not[LessEqual[N[(y * z), $MachinePrecision], -1.95e+27]], $MachinePrecision], Or[LessEqual[N[(y * z), $MachinePrecision], -160000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1.32e+178]], $MachinePrecision]]]], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -9.5000000000000006e155 or -1.9499999999999999e27 < (*.f64 y z) < -1.6e5 or 1.3200000000000001e178 < (*.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. *-commutative 90.7%

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

   4. Simplified 90.7%

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

   if -9.5000000000000006e155 < (*.f64 y z) < -1.9499999999999999e27 or -1.6e5 < (*.f64 y z) < 1.3200000000000001e178

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -9.5 \cdot 10^{+155} \lor \neg \left(y \cdot z \leq -1.95 \cdot 10^{+27}\right) \land \left(y \cdot z \leq -160000 \lor \neg \left(y \cdot z \leq 1.32 \cdot 10^{+178}\right)\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 5: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot 0.5\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+167}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+72} \lor \neg \left(x \leq 9500000000\right):\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) 0.5)))
   (if (<= x -3.8e+167)
     (- (* 0.125 x) t_1)
     (if (or (<= x -4e+72) (not (<= x 9500000000.0)))
       (+ t (* 0.125 x))
       (- t t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * 0.5;
	double tmp;
	if (x <= -3.8e+167) {
		tmp = (0.125 * x) - t_1;
	} else if ((x <= -4e+72) || !(x <= 9500000000.0)) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) * 0.5d0
    if (x <= (-3.8d+167)) then
        tmp = (0.125d0 * x) - t_1
    else if ((x <= (-4d+72)) .or. (.not. (x <= 9500000000.0d0))) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * 0.5;
	double tmp;
	if (x <= -3.8e+167) {
		tmp = (0.125 * x) - t_1;
	} else if ((x <= -4e+72) || !(x <= 9500000000.0)) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * 0.5
	tmp = 0
	if x <= -3.8e+167:
		tmp = (0.125 * x) - t_1
	elif (x <= -4e+72) or not (x <= 9500000000.0):
		tmp = t + (0.125 * x)
	else:
		tmp = t - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) * 0.5)
	tmp = 0.0
	if (x <= -3.8e+167)
		tmp = Float64(Float64(0.125 * x) - t_1);
	elseif ((x <= -4e+72) || !(x <= 9500000000.0))
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = Float64(t - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) * 0.5;
	tmp = 0.0;
	if (x <= -3.8e+167)
		tmp = (0.125 * x) - t_1;
	elseif ((x <= -4e+72) || ~((x <= 9500000000.0)))
		tmp = t + (0.125 * x);
	else
		tmp = t - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[x, -3.8e+167], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision], If[Or[LessEqual[x, -4e+72], N[Not[LessEqual[x, 9500000000.0]], $MachinePrecision]], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], N[(t - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.79999999999999994e167

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 86.0%

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

   if -3.79999999999999994e167 < x < -3.99999999999999978e72 or 9.5e9 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.2%

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

   if -3.99999999999999978e72 < x < 9.5e9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+167}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+72} \lor \neg \left(x \leq 9500000000\right):\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.2× speedup

Math

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

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(Float64(y * 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[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 7: 51.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+40}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.7e+40) (* 0.125 x) (if (<= x 1.8e+118) t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.7e+40) {
		tmp = 0.125 * x;
	} else if (x <= 1.8e+118) {
		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) :: tmp
    if (x <= (-4.7d+40)) then
        tmp = 0.125d0 * x
    else if (x <= 1.8d+118) 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 tmp;
	if (x <= -4.7e+40) {
		tmp = 0.125 * x;
	} else if (x <= 1.8e+118) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.7e+40:
		tmp = 0.125 * x
	elif x <= 1.8e+118:
		tmp = t
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.7e+40)
		tmp = Float64(0.125 * x);
	elseif (x <= 1.8e+118)
		tmp = t;
	else
		tmp = Float64(0.125 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.7e+40)
		tmp = 0.125 * x;
	elseif (x <= 1.8e+118)
		tmp = t;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.7e+40], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, 1.8e+118], t, N[(0.125 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7000000000000004e40 or 1.8e118 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.1%

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

   if -4.7000000000000004e40 < x < 1.8e118

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 49.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+40}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 8: 34.2% 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. Taylor expanded in t around inf 38.0%

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

3. Final simplification 38.0%

   \[\leadsto t \]

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 2023274 
(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))