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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

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: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot 0.5\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+98}:\\ \;\;\;\;t - t_1\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+119}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) 0.5)))
   (if (<= (* y z) -5e+98)
     (- t t_1)
     (if (<= (* y z) 5e+119) (+ t (* 0.125 x)) (- (* 0.125 x) 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) <= -5e+98) {
		tmp = t - t_1;
	} else if ((y * z) <= 5e+119) {
		tmp = t + (0.125 * x);
	} else {
		tmp = (0.125 * x) - 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) <= (-5d+98)) then
        tmp = t - t_1
    else if ((y * z) <= 5d+119) then
        tmp = t + (0.125d0 * x)
    else
        tmp = (0.125d0 * x) - 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) <= -5e+98) {
		tmp = t - t_1;
	} else if ((y * z) <= 5e+119) {
		tmp = t + (0.125 * x);
	} else {
		tmp = (0.125 * x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * 0.5
	tmp = 0
	if (y * z) <= -5e+98:
		tmp = t - t_1
	elif (y * z) <= 5e+119:
		tmp = t + (0.125 * x)
	else:
		tmp = (0.125 * x) - 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) <= -5e+98)
		tmp = Float64(t - t_1);
	elseif (Float64(y * z) <= 5e+119)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = Float64(Float64(0.125 * x) - 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) <= -5e+98)
		tmp = t - t_1;
	elseif ((y * z) <= 5e+119)
		tmp = t + (0.125 * x);
	else
		tmp = (0.125 * x) - 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], -5e+98], N[(t - t$95$1), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+119], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.9999999999999998e98

   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 88.4%

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

   if -4.9999999999999998e98 < (*.f64 y z) < 4.9999999999999999e119

   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 90.9%

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

   if 4.9999999999999999e119 < (*.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 t around 0 97.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+98}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+119}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]

Alternative 3: 87.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+98} \lor \neg \left(y \cdot z \leq 10^{+94}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -5e+98) (not (<= (* y z) 1e+94)))
   (- 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) <= -5e+98) || !((y * z) <= 1e+94)) {
		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) <= (-5d+98)) .or. (.not. ((y * z) <= 1d+94))) 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) <= -5e+98) || !((y * z) <= 1e+94)) {
		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) <= -5e+98) or not ((y * z) <= 1e+94):
		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) <= -5e+98) || !(Float64(y * z) <= 1e+94))
		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) <= -5e+98) || ~(((y * z) <= 1e+94)))
		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], -5e+98], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+94]], $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) < -4.9999999999999998e98 or 1e94 < (*.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 89.9%

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

   if -4.9999999999999998e98 < (*.f64 y z) < 1e94

   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 91.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+98} \lor \neg \left(y \cdot z \leq 10^{+94}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 4: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+170} \lor \neg \left(y \leq -1.25 \cdot 10^{+122} \lor \neg \left(y \leq -2.7 \cdot 10^{+91}\right) \land y \leq 1.75 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e+170)
         (not
          (or (<= y -1.25e+122) (and (not (<= y -2.7e+91)) (<= y 1.75e-39)))))
   (* y (* z -0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e+170) || !((y <= -1.25e+122) || (!(y <= -2.7e+91) && (y <= 1.75e-39)))) {
		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 <= (-2.5d+170)) .or. (.not. (y <= (-1.25d+122)) .or. (.not. (y <= (-2.7d+91))) .and. (y <= 1.75d-39))) 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 <= -2.5e+170) || !((y <= -1.25e+122) || (!(y <= -2.7e+91) && (y <= 1.75e-39)))) {
		tmp = y * (z * -0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e+170) or not ((y <= -1.25e+122) or (not (y <= -2.7e+91) and (y <= 1.75e-39))):
		tmp = y * (z * -0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e+170) || !((y <= -1.25e+122) || (!(y <= -2.7e+91) && (y <= 1.75e-39))))
		tmp = 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 <= -2.5e+170) || ~(((y <= -1.25e+122) || (~((y <= -2.7e+91)) && (y <= 1.75e-39)))))
		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[y, -2.5e+170], N[Not[Or[LessEqual[y, -1.25e+122], And[N[Not[LessEqual[y, -2.7e+91]], $MachinePrecision], LessEqual[y, 1.75e-39]]]], $MachinePrecision]], N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999988e170 or -1.24999999999999997e122 < y < -2.7e91 or 1.75e-39 < y

   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 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l* 59.7%

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

   4. Simplified 59.7%

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

   if -2.49999999999999988e170 < y < -1.24999999999999997e122 or -2.7e91 < y < 1.75e-39

   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 82.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+170} \lor \neg \left(y \leq -1.25 \cdot 10^{+122} \lor \neg \left(y \leq -2.7 \cdot 10^{+91}\right) \land y \leq 1.75 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 5: 49.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot -0.5\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* z -0.5))))
   (if (<= y -1.45e+66)
     t_1
     (if (<= y -3.2e-166) (* 0.125 x) (if (<= y 1.65e-39) 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 <= -1.45e+66) {
		tmp = t_1;
	} else if (y <= -3.2e-166) {
		tmp = 0.125 * x;
	} else if (y <= 1.65e-39) {
		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 <= (-1.45d+66)) then
        tmp = t_1
    else if (y <= (-3.2d-166)) then
        tmp = 0.125d0 * x
    else if (y <= 1.65d-39) 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 <= -1.45e+66) {
		tmp = t_1;
	} else if (y <= -3.2e-166) {
		tmp = 0.125 * x;
	} else if (y <= 1.65e-39) {
		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 <= -1.45e+66:
		tmp = t_1
	elif y <= -3.2e-166:
		tmp = 0.125 * x
	elif y <= 1.65e-39:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z * -0.5))
	tmp = 0.0
	if (y <= -1.45e+66)
		tmp = t_1;
	elseif (y <= -3.2e-166)
		tmp = Float64(0.125 * x);
	elseif (y <= 1.65e-39)
		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 <= -1.45e+66)
		tmp = t_1;
	elseif (y <= -3.2e-166)
		tmp = 0.125 * x;
	elseif (y <= 1.65e-39)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+66], t$95$1, If[LessEqual[y, -3.2e-166], N[(0.125 * x), $MachinePrecision], If[LessEqual[y, 1.65e-39], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.44999999999999993e66 or 1.64999999999999992e-39 < y

   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 58.9%

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

      1. *-commutative 58.9%

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

      2. associate-*l* 58.9%

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

   4. Simplified 58.9%

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

   if -1.44999999999999993e66 < y < -3.20000000000000001e-166

   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 39.7%

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

   if -3.20000000000000001e-166 < y < 1.64999999999999992e-39

   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 48.2%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \]

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: 48.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-29}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e-29) (* 0.125 x) (if (<= x 1.15e+89) t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e-29) {
		tmp = 0.125 * x;
	} else if (x <= 1.15e+89) {
		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 <= (-5.5d-29)) then
        tmp = 0.125d0 * x
    else if (x <= 1.15d+89) 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 <= -5.5e-29) {
		tmp = 0.125 * x;
	} else if (x <= 1.15e+89) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e-29:
		tmp = 0.125 * x
	elif x <= 1.15e+89:
		tmp = t
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e-29)
		tmp = Float64(0.125 * x);
	elseif (x <= 1.15e+89)
		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 <= -5.5e-29)
		tmp = 0.125 * x;
	elseif (x <= 1.15e+89)
		tmp = t;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e-29], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, 1.15e+89], t, N[(0.125 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999999e-29 or 1.1499999999999999e89 < 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 57.6%

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

   if -5.4999999999999999e-29 < x < 1.1499999999999999e89

   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 50.9%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-29}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 8: 32.7% 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 35.3%

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

3. Final simplification 35.3%

   \[\leadsto t \]

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 2023287 
(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))