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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

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, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (0.125 * x) + (t - (y * (0.5 * 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 = (0.125d0 * x) + (t - (y * (0.5d0 * z)))
end function

Java

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

Python

def code(x, y, z, t):
	return (0.125 * x) + (t - (y * (0.5 * z)))

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (0.125 * x) + (t - (y * (0.5 * z)));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

   4. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

   5. sub-neg 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

   6. +-commutative 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

   7. associate--r+ 100.0%

      \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   8. neg-sub0 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. distribute-rgt-neg-in 100.0%

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

   11. metadata-eval 100.0%

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

   12. remove-double-neg 100.0%

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

   13. associate-*l/ 100.0%

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

3. Simplified 100.0%

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

   1. associate-+l- 100.0%

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

   2. div-inv 100.0%

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

   3. associate-*l* 100.0%

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

   4. metadata-eval 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;y \cdot z \leq -1.6 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq -5 \cdot 10^{-318}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) -0.5)))
   (if (<= (* y z) -1.6e+169)
     t_1
     (if (<= (* y z) -5e-318)
       t
       (if (<= (* y z) 2.4e-200)
         (* 0.125 x)
         (if (<= (* y z) 8.5e+27) 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) <= -1.6e+169) {
		tmp = t_1;
	} else if ((y * z) <= -5e-318) {
		tmp = t;
	} else if ((y * z) <= 2.4e-200) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 8.5e+27) {
		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) <= (-1.6d+169)) then
        tmp = t_1
    else if ((y * z) <= (-5d-318)) then
        tmp = t
    else if ((y * z) <= 2.4d-200) then
        tmp = 0.125d0 * x
    else if ((y * z) <= 8.5d+27) 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) <= -1.6e+169) {
		tmp = t_1;
	} else if ((y * z) <= -5e-318) {
		tmp = t;
	} else if ((y * z) <= 2.4e-200) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 8.5e+27) {
		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) <= -1.6e+169:
		tmp = t_1
	elif (y * z) <= -5e-318:
		tmp = t
	elif (y * z) <= 2.4e-200:
		tmp = 0.125 * x
	elif (y * z) <= 8.5e+27:
		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) <= -1.6e+169)
		tmp = t_1;
	elseif (Float64(y * z) <= -5e-318)
		tmp = t;
	elseif (Float64(y * z) <= 2.4e-200)
		tmp = Float64(0.125 * x);
	elseif (Float64(y * z) <= 8.5e+27)
		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) <= -1.6e+169)
		tmp = t_1;
	elseif ((y * z) <= -5e-318)
		tmp = t;
	elseif ((y * z) <= 2.4e-200)
		tmp = 0.125 * x;
	elseif ((y * z) <= 8.5e+27)
		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], -1.6e+169], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -5e-318], t, If[LessEqual[N[(y * z), $MachinePrecision], 2.4e-200], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 8.5e+27], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1.5999999999999999e169 or 8.5e27 < (*.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   if -1.5999999999999999e169 < (*.f64 y z) < -4.9999987e-318 or 2.40000000000000002e-200 < (*.f64 y z) < 8.5e27

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 55.7%

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

   if -4.9999987e-318 < (*.f64 y z) < 2.40000000000000002e-200

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 68.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.6 \cdot 10^{+169}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq -5 \cdot 10^{-318}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \end{array} \]

Alternative 3: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;t - t_1\\ \mathbf{elif}\;y \cdot z \leq 1.86 \cdot 10^{+28}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (* y z))))
   (if (<= (* y z) -4.2e-23)
     (- t t_1)
     (if (<= (* y z) 1.86e+28) (+ (* 0.125 x) t) (- (* 0.125 x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * (y * z);
	double tmp;
	if ((y * z) <= -4.2e-23) {
		tmp = t - t_1;
	} else if ((y * z) <= 1.86e+28) {
		tmp = (0.125 * x) + t;
	} 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 = 0.5d0 * (y * z)
    if ((y * z) <= (-4.2d-23)) then
        tmp = t - t_1
    else if ((y * z) <= 1.86d+28) then
        tmp = (0.125d0 * x) + t
    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 = 0.5 * (y * z);
	double tmp;
	if ((y * z) <= -4.2e-23) {
		tmp = t - t_1;
	} else if ((y * z) <= 1.86e+28) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = (0.125 * x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * (y * z)
	tmp = 0
	if (y * z) <= -4.2e-23:
		tmp = t - t_1
	elif (y * z) <= 1.86e+28:
		tmp = (0.125 * x) + t
	else:
		tmp = (0.125 * x) - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(y * z))
	tmp = 0.0
	if (Float64(y * z) <= -4.2e-23)
		tmp = Float64(t - t_1);
	elseif (Float64(y * z) <= 1.86e+28)
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = Float64(Float64(0.125 * x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * (y * z);
	tmp = 0.0;
	if ((y * z) <= -4.2e-23)
		tmp = t - t_1;
	elseif ((y * z) <= 1.86e+28)
		tmp = (0.125 * x) + t;
	else
		tmp = (0.125 * x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -4.2e-23], N[(t - t$95$1), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1.86e+28], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.2000000000000002e-23

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 90.4%

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

   if -4.2000000000000002e-23 < (*.f64 y z) < 1.86000000000000009e28

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 95.7%

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

   if 1.86000000000000009e28 < (*.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 83.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 1.86 \cdot 10^{+28}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 87.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5.2 \cdot 10^{-13} \lor \neg \left(y \cdot z \leq 180000000000\right):\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -5.2e-13) (not (<= (* y z) 180000000000.0)))
   (- t (* 0.5 (* y z)))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -5.2e-13) || !((y * z) <= 180000000000.0)) {
		tmp = t - (0.5 * (y * z));
	} else {
		tmp = (0.125 * x) + 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 (((y * z) <= (-5.2d-13)) .or. (.not. ((y * z) <= 180000000000.0d0))) then
        tmp = t - (0.5d0 * (y * z))
    else
        tmp = (0.125d0 * x) + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -5.2e-13) || !((y * z) <= 180000000000.0)) {
		tmp = t - (0.5 * (y * z));
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -5.2e-13) or not ((y * z) <= 180000000000.0):
		tmp = t - (0.5 * (y * z))
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -5.2e-13) || !(Float64(y * z) <= 180000000000.0))
		tmp = Float64(t - Float64(0.5 * Float64(y * z)));
	else
		tmp = Float64(Float64(0.125 * x) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -5.2e-13) || ~(((y * z) <= 180000000000.0)))
		tmp = t - (0.5 * (y * z));
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -5.2e-13], N[Not[LessEqual[N[(y * z), $MachinePrecision], 180000000000.0]], $MachinePrecision]], N[(t - N[(0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.2000000000000001e-13 or 1.8e11 < (*.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 85.6%

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

   if -5.2000000000000001e-13 < (*.f64 y z) < 1.8e11

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.3%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5.2 \cdot 10^{-13} \lor \neg \left(y \cdot z \leq 180000000000\right):\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 5: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -7.8 \cdot 10^{+192} \lor \neg \left(y \cdot z \leq 4.7 \cdot 10^{+226}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -7.8e+192) (not (<= (* y z) 4.7e+226)))
   (* (* y z) -0.5)
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -7.8e+192) || !((y * z) <= 4.7e+226)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = (0.125 * x) + 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 (((y * z) <= (-7.8d+192)) .or. (.not. ((y * z) <= 4.7d+226))) then
        tmp = (y * z) * (-0.5d0)
    else
        tmp = (0.125d0 * x) + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -7.8e+192) || !((y * z) <= 4.7e+226)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -7.8e+192) or not ((y * z) <= 4.7e+226):
		tmp = (y * z) * -0.5
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -7.8e+192) || !(Float64(y * z) <= 4.7e+226))
		tmp = Float64(Float64(y * z) * -0.5);
	else
		tmp = Float64(Float64(0.125 * x) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -7.8e+192) || ~(((y * z) <= 4.7e+226)))
		tmp = (y * z) * -0.5;
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -7.8e+192], N[Not[LessEqual[N[(y * z), $MachinePrecision], 4.7e+226]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -7.7999999999999996e192 or 4.69999999999999991e226 < (*.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. *-commutative 92.4%

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

   6. Simplified 92.4%

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

   if -7.7999999999999996e192 < (*.f64 y z) < 4.69999999999999991e226

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 82.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -7.8 \cdot 10^{+192} \lor \neg \left(y \cdot z \leq 4.7 \cdot 10^{+226}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t + ((0.125 * x) - (z * (y / 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) - (z * (y / 2.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

   4. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

   5. sub-neg 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

   6. +-commutative 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

   7. associate--r+ 100.0%

      \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   8. neg-sub0 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. distribute-rgt-neg-in 100.0%

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

   11. metadata-eval 100.0%

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

   12. remove-double-neg 100.0%

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

   13. associate-*l/ 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 7: 49.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 260000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.8e+21) t (if (<= t 260000000.0) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.8e+21) {
		tmp = t;
	} else if (t <= 260000000.0) {
		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 (t <= (-7.8d+21)) then
        tmp = t
    else if (t <= 260000000.0d0) 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 (t <= -7.8e+21) {
		tmp = t;
	} else if (t <= 260000000.0) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.8e+21:
		tmp = t
	elif t <= 260000000.0:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.8e+21)
		tmp = t;
	elseif (t <= 260000000.0)
		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 (t <= -7.8e+21)
		tmp = t;
	elseif (t <= 260000000.0)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.8e+21], t, If[LessEqual[t, 260000000.0], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -7.8e21 or 2.6e8 < t

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 61.7%

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

   if -7.8e21 < t < 2.6e8

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 52.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 260000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 32.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

public static double code(double x, double y, double z, double t) {
	return t;
}

Python

def code(x, y, z, t):
	return t

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

   4. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

   5. sub-neg 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

   6. +-commutative 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

   7. associate--r+ 100.0%

      \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   8. neg-sub0 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. distribute-rgt-neg-in 100.0%

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

   11. metadata-eval 100.0%

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

   12. remove-double-neg 100.0%

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

   13. associate-*l/ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in t around inf 37.5%

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

5. Final simplification 37.5%

   \[\leadsto t \]

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 2023194 
(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))