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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

Alternatives: 7

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. associate-+l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

   8. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

3. Simplified 100.0%

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. fma-define N/A

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

   6. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(\frac{z}{-2}\right), \color{blue}{y}, \left(\frac{1}{8} \cdot x + t\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(z, -2\right), y, \left(\frac{1}{8} \cdot x + t\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(z, -2\right), y, \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), t\right)\right) \]

   9. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(z, -2\right), y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), t\right)\right) \]

6. Applied egg-rr 100.0%

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

Alternative 2: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot -0.5\\ \mathbf{if}\;z \cdot y \leq -1.2 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot y \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \cdot y \leq 9 \cdot 10^{-63}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \cdot y \leq 3.4 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* z y) -0.5)))
   (if (<= (* z y) -1.2e+141)
     t_1
     (if (<= (* z y) -1.7e+18)
       t
       (if (<= (* z y) 9e-63) (* 0.125 x) (if (<= (* z y) 3.4e+91) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * -0.5;
	double tmp;
	if ((z * y) <= -1.2e+141) {
		tmp = t_1;
	} else if ((z * y) <= -1.7e+18) {
		tmp = t;
	} else if ((z * y) <= 9e-63) {
		tmp = 0.125 * x;
	} else if ((z * y) <= 3.4e+91) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) * (-0.5d0)
    if ((z * y) <= (-1.2d+141)) then
        tmp = t_1
    else if ((z * y) <= (-1.7d+18)) then
        tmp = t
    else if ((z * y) <= 9d-63) then
        tmp = 0.125d0 * x
    else if ((z * y) <= 3.4d+91) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * -0.5;
	double tmp;
	if ((z * y) <= -1.2e+141) {
		tmp = t_1;
	} else if ((z * y) <= -1.7e+18) {
		tmp = t;
	} else if ((z * y) <= 9e-63) {
		tmp = 0.125 * x;
	} else if ((z * y) <= 3.4e+91) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) * -0.5
	tmp = 0
	if (z * y) <= -1.2e+141:
		tmp = t_1
	elif (z * y) <= -1.7e+18:
		tmp = t
	elif (z * y) <= 9e-63:
		tmp = 0.125 * x
	elif (z * y) <= 3.4e+91:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) * -0.5)
	tmp = 0.0
	if (Float64(z * y) <= -1.2e+141)
		tmp = t_1;
	elseif (Float64(z * y) <= -1.7e+18)
		tmp = t;
	elseif (Float64(z * y) <= 9e-63)
		tmp = Float64(0.125 * x);
	elseif (Float64(z * y) <= 3.4e+91)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) * -0.5;
	tmp = 0.0;
	if ((z * y) <= -1.2e+141)
		tmp = t_1;
	elseif ((z * y) <= -1.7e+18)
		tmp = t;
	elseif ((z * y) <= 9e-63)
		tmp = 0.125 * x;
	elseif ((z * y) <= 3.4e+91)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * -0.5), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -1.2e+141], t$95$1, If[LessEqual[N[(z * y), $MachinePrecision], -1.7e+18], t, If[LessEqual[N[(z * y), $MachinePrecision], 9e-63], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 3.4e+91], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1.19999999999999999e141 or 3.4000000000000001e91 < (*.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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{2}, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 83.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 83.8%

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

   if -1.19999999999999999e141 < (*.f64 y z) < -1.7e18 or 8.9999999999999999e-63 < (*.f64 y z) < 3.4000000000000001e91

   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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 55.6%

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

   if -1.7e18 < (*.f64 y z) < 8.9999999999999999e-63

   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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 53.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{8}, \color{blue}{x}\right) \]

   7. Simplified 53.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -1.2 \cdot 10^{+141}:\\ \;\;\;\;\left(z \cdot y\right) \cdot -0.5\\ \mathbf{elif}\;z \cdot y \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \cdot y \leq 9 \cdot 10^{-63}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \cdot y \leq 3.4 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(z \cdot y\right) \cdot -0.5\\ \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+89}:\\ \;\;\;\;t - x \cdot -0.125\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (* z y) -0.5))))
   (if (<= (* z y) -5e+159)
     t_1
     (if (<= (* z y) 5e+89) (- t (* x -0.125)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((z * y) * -0.5);
	double tmp;
	if ((z * y) <= -5e+159) {
		tmp = t_1;
	} else if ((z * y) <= 5e+89) {
		tmp = t - (x * -0.125);
	} 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 = t + ((z * y) * (-0.5d0))
    if ((z * y) <= (-5d+159)) then
        tmp = t_1
    else if ((z * y) <= 5d+89) then
        tmp = t - (x * (-0.125d0))
    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 = t + ((z * y) * -0.5);
	double tmp;
	if ((z * y) <= -5e+159) {
		tmp = t_1;
	} else if ((z * y) <= 5e+89) {
		tmp = t - (x * -0.125);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((z * y) * -0.5)
	tmp = 0
	if (z * y) <= -5e+159:
		tmp = t_1
	elif (z * y) <= 5e+89:
		tmp = t - (x * -0.125)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(z * y) * -0.5))
	tmp = 0.0
	if (Float64(z * y) <= -5e+159)
		tmp = t_1;
	elseif (Float64(z * y) <= 5e+89)
		tmp = Float64(t - Float64(x * -0.125));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((z * y) * -0.5);
	tmp = 0.0;
	if ((z * y) <= -5e+159)
		tmp = t_1;
	elseif ((z * y) <= 5e+89)
		tmp = t - (x * -0.125);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(z * y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -5e+159], t$95$1, If[LessEqual[N[(z * y), $MachinePrecision], 5e+89], N[(t - N[(x * -0.125), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000003e159 or 4.99999999999999983e89 < (*.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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{-1}{2}, \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 93.0%

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

   if -5.00000000000000003e159 < (*.f64 y z) < 4.99999999999999983e89

   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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. remove-double-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(-1 \cdot \left(\frac{1}{8} \cdot x\right)\right)\right) \]

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \left(\frac{1}{8} \cdot x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(\mathsf{neg}\left(\frac{1}{8}\right)\right) \cdot \color{blue}{x}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{1}{8}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{8}\right)\right)}\right)\right) \]

      9. metadata-eval 88.5%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \frac{-1}{8}\right)\right) \]

   7. Simplified 88.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+159}:\\ \;\;\;\;t + \left(z \cdot y\right) \cdot -0.5\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+89}:\\ \;\;\;\;t - x \cdot -0.125\\ \mathbf{else}:\\ \;\;\;\;t + \left(z \cdot y\right) \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot -0.5\\ \mathbf{if}\;z \cdot y \leq -2.6 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot y \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;t - x \cdot -0.125\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* z y) -0.5)))
   (if (<= (* z y) -2.6e+151)
     t_1
     (if (<= (* z y) 2.35e+91) (- t (* x -0.125)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * -0.5;
	double tmp;
	if ((z * y) <= -2.6e+151) {
		tmp = t_1;
	} else if ((z * y) <= 2.35e+91) {
		tmp = t - (x * -0.125);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) * (-0.5d0)
    if ((z * y) <= (-2.6d+151)) then
        tmp = t_1
    else if ((z * y) <= 2.35d+91) then
        tmp = t - (x * (-0.125d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * -0.5;
	double tmp;
	if ((z * y) <= -2.6e+151) {
		tmp = t_1;
	} else if ((z * y) <= 2.35e+91) {
		tmp = t - (x * -0.125);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) * -0.5
	tmp = 0
	if (z * y) <= -2.6e+151:
		tmp = t_1
	elif (z * y) <= 2.35e+91:
		tmp = t - (x * -0.125)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) * -0.5)
	tmp = 0.0
	if (Float64(z * y) <= -2.6e+151)
		tmp = t_1;
	elseif (Float64(z * y) <= 2.35e+91)
		tmp = Float64(t - Float64(x * -0.125));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) * -0.5;
	tmp = 0.0;
	if ((z * y) <= -2.6e+151)
		tmp = t_1;
	elseif ((z * y) <= 2.35e+91)
		tmp = t - (x * -0.125);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * -0.5), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -2.6e+151], t$95$1, If[LessEqual[N[(z * y), $MachinePrecision], 2.35e+91], N[(t - N[(x * -0.125), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.60000000000000013e151 or 2.3499999999999999e91 < (*.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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{2}, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 83.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 83.8%

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

   if -2.60000000000000013e151 < (*.f64 y z) < 2.3499999999999999e91

   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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. remove-double-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(-1 \cdot \left(\frac{1}{8} \cdot x\right)\right)\right) \]

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \left(\frac{1}{8} \cdot x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(\mathsf{neg}\left(\frac{1}{8}\right)\right) \cdot \color{blue}{x}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{1}{8}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{8}\right)\right)}\right)\right) \]

      9. metadata-eval 88.5%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \frac{-1}{8}\right)\right) \]

   7. Simplified 88.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2.6 \cdot 10^{+151}:\\ \;\;\;\;\left(z \cdot y\right) \cdot -0.5\\ \mathbf{elif}\;z \cdot y \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;t - x \cdot -0.125\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-59}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.85e-59) t (if (<= t 2.1e+46) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.85e-59) {
		tmp = t;
	} else if (t <= 2.1e+46) {
		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 <= (-1.85d-59)) then
        tmp = t
    else if (t <= 2.1d+46) 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 <= -1.85e-59) {
		tmp = t;
	} else if (t <= 2.1e+46) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.85e-59:
		tmp = t
	elif t <= 2.1e+46:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.85e-59)
		tmp = t;
	elseif (t <= 2.1e+46)
		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 <= -1.85e-59)
		tmp = t;
	elseif (t <= 2.1e+46)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.85e-59], t, If[LessEqual[t, 2.1e+46], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85e-59 or 2.1e46 < 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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 59.9%

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

   if -1.85e-59 < t < 2.1e46

   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 N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 52.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{8}, \color{blue}{x}\right) \]

   7. Simplified 52.1%

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

Alternative 6: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(0.125 * x), $MachinePrecision] + N[(t + N[(N[(z * y), $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. Step-by-step derivation

   1. sub-neg N/A

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

   2. associate-+l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

   8. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 32.8% 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 N/A

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

   2. associate-+l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{8} \cdot x\right), \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) + t\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{8}\right), x\right), \left(\color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)} + t\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(\left(\mathsf{neg}\left(\color{blue}{\frac{y \cdot z}{2}}\right)\right) + t\right)\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \left(t + \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right)}\right)\right) \]

   8. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \left(\frac{y \cdot z}{\color{blue}{\mathsf{neg}\left(2\right)}}\right)\right)\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{8}, x\right), \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), -2\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in t around inf

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

7. Simplified 34.0%

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

Developer Target 1: 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 2024152 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

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

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