Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Percentage Accurate: 99.9% → 100.0%

Time: 13.3s

Alternatives: 14

Speedup: 1.2×

• 27.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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 = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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 = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma y 5.0 (* x (+ t (* (+ y z) 2.0)))))

C

double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (x * (t + ((y + z) * 2.0))));
}

Julia

function code(x, y, z, t)
	return fma(y, 5.0, Float64(x * Float64(t + Float64(Float64(y + z) * 2.0))))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

   3. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

   4. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

   5. associate-+l+ 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

   6. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

   7. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

   8. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

   9. distribute-rgt-out 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

   10. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \]
6. Add Preprocessing

Alternative 2: 78.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.9e+32)
     t_2
     (if (<= y -3.9e-29)
       t_1
       (if (<= y -3.8e-29)
         (* y 5.0)
         (if (<= y -1e-80)
           t_1
           (if (<= y -2.2e-94)
             t_2
             (if (<= y 2.95e+58)
               t_1
               (if (<= y 2e+107)
                 t_2
                 (if (<= y 1.18e+123)
                   (* x (* (+ y z) 2.0))
                   (if (<= y 3.2e+128) (* x (+ t (* y 2.0))) t_2)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.9e+32) {
		tmp = t_2;
	} else if (y <= -3.9e-29) {
		tmp = t_1;
	} else if (y <= -3.8e-29) {
		tmp = y * 5.0;
	} else if (y <= -1e-80) {
		tmp = t_1;
	} else if (y <= -2.2e-94) {
		tmp = t_2;
	} else if (y <= 2.95e+58) {
		tmp = t_1;
	} else if (y <= 2e+107) {
		tmp = t_2;
	} else if (y <= 1.18e+123) {
		tmp = x * ((y + z) * 2.0);
	} else if (y <= 3.2e+128) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.9d+32)) then
        tmp = t_2
    else if (y <= (-3.9d-29)) then
        tmp = t_1
    else if (y <= (-3.8d-29)) then
        tmp = y * 5.0d0
    else if (y <= (-1d-80)) then
        tmp = t_1
    else if (y <= (-2.2d-94)) then
        tmp = t_2
    else if (y <= 2.95d+58) then
        tmp = t_1
    else if (y <= 2d+107) then
        tmp = t_2
    else if (y <= 1.18d+123) then
        tmp = x * ((y + z) * 2.0d0)
    else if (y <= 3.2d+128) then
        tmp = x * (t + (y * 2.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.9e+32) {
		tmp = t_2;
	} else if (y <= -3.9e-29) {
		tmp = t_1;
	} else if (y <= -3.8e-29) {
		tmp = y * 5.0;
	} else if (y <= -1e-80) {
		tmp = t_1;
	} else if (y <= -2.2e-94) {
		tmp = t_2;
	} else if (y <= 2.95e+58) {
		tmp = t_1;
	} else if (y <= 2e+107) {
		tmp = t_2;
	} else if (y <= 1.18e+123) {
		tmp = x * ((y + z) * 2.0);
	} else if (y <= 3.2e+128) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -2.9e+32:
		tmp = t_2
	elif y <= -3.9e-29:
		tmp = t_1
	elif y <= -3.8e-29:
		tmp = y * 5.0
	elif y <= -1e-80:
		tmp = t_1
	elif y <= -2.2e-94:
		tmp = t_2
	elif y <= 2.95e+58:
		tmp = t_1
	elif y <= 2e+107:
		tmp = t_2
	elif y <= 1.18e+123:
		tmp = x * ((y + z) * 2.0)
	elif y <= 3.2e+128:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -2.9e+32)
		tmp = t_2;
	elseif (y <= -3.9e-29)
		tmp = t_1;
	elseif (y <= -3.8e-29)
		tmp = Float64(y * 5.0);
	elseif (y <= -1e-80)
		tmp = t_1;
	elseif (y <= -2.2e-94)
		tmp = t_2;
	elseif (y <= 2.95e+58)
		tmp = t_1;
	elseif (y <= 2e+107)
		tmp = t_2;
	elseif (y <= 1.18e+123)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (y <= 3.2e+128)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -2.9e+32)
		tmp = t_2;
	elseif (y <= -3.9e-29)
		tmp = t_1;
	elseif (y <= -3.8e-29)
		tmp = y * 5.0;
	elseif (y <= -1e-80)
		tmp = t_1;
	elseif (y <= -2.2e-94)
		tmp = t_2;
	elseif (y <= 2.95e+58)
		tmp = t_1;
	elseif (y <= 2e+107)
		tmp = t_2;
	elseif (y <= 1.18e+123)
		tmp = x * ((y + z) * 2.0);
	elseif (y <= 3.2e+128)
		tmp = x * (t + (y * 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+32], t$95$2, If[LessEqual[y, -3.9e-29], t$95$1, If[LessEqual[y, -3.8e-29], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -1e-80], t$95$1, If[LessEqual[y, -2.2e-94], t$95$2, If[LessEqual[y, 2.95e+58], t$95$1, If[LessEqual[y, 2e+107], t$95$2, If[LessEqual[y, 1.18e+123], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+128], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.90000000000000003e32 or -9.99999999999999961e-81 < y < -2.20000000000000001e-94 or 2.94999999999999986e58 < y < 1.9999999999999999e107 or 3.19999999999999986e128 < y

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   5. Simplified 75.2%

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot x + 5\right)} \]

   if -2.90000000000000003e32 < y < -3.8999999999999998e-29 or -3.79999999999999976e-29 < y < -9.99999999999999961e-81 or -2.20000000000000001e-94 < y < 2.94999999999999986e58

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 99.8%

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

      1. fma-define 99.8%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 99.9%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 99.9%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 99.9%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in y around 0 75.9%

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

   if -3.8999999999999998e-29 < y < -3.79999999999999976e-29

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot 5} \]

   if 1.9999999999999999e107 < y < 1.18000000000000006e123

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 100.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. *-un-lft-identity 100.0%

         \[\leadsto x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right) + y \cdot 5 \]

      3. +-commutative 100.0%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      4. *-un-lft-identity 100.0%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      5. distribute-rgt-out 100.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right) + y \cdot 5 \]

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(y + z\right) \cdot x\right)} \cdot 2 + y \cdot 5 \]

      3. associate-*l* 100.0%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   8. Taylor expanded in x around inf 80.2%

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

      1. associate-*r* 80.2%

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

      2. *-commutative 80.2%

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

      3. +-commutative 80.2%

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

      4. associate-*r* 80.2%

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

   10. Simplified 80.2%

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

   if 1.18000000000000006e123 < y < 3.19999999999999986e128

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto x \cdot \left(\left(\color{blue}{y} + y\right) + t\right) + y \cdot 5 \]

   4. Taylor expanded in x around inf 94.6%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 2\right)\\ t_2 := x \cdot \left(z \cdot 2\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x 2.0))) (t_2 (* x (* z 2.0))))
   (if (<= x -4.8e+219)
     t_1
     (if (<= x -4.8e+178)
       t_2
       (if (<= x -4.5e+22)
         t_1
         (if (<= x 1.15e-76)
           (* y 5.0)
           (if (<= x 1.65e+39)
             (* x t)
             (if (<= x 8.5e+89)
               t_2
               (if (<= x 3.1e+129) t_1 (if (<= x 2e+153) (* x t) t_2))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 2.0);
	double t_2 = x * (z * 2.0);
	double tmp;
	if (x <= -4.8e+219) {
		tmp = t_1;
	} else if (x <= -4.8e+178) {
		tmp = t_2;
	} else if (x <= -4.5e+22) {
		tmp = t_1;
	} else if (x <= 1.15e-76) {
		tmp = y * 5.0;
	} else if (x <= 1.65e+39) {
		tmp = x * t;
	} else if (x <= 8.5e+89) {
		tmp = t_2;
	} else if (x <= 3.1e+129) {
		tmp = t_1;
	} else if (x <= 2e+153) {
		tmp = x * t;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = y * (x * 2.0d0)
    t_2 = x * (z * 2.0d0)
    if (x <= (-4.8d+219)) then
        tmp = t_1
    else if (x <= (-4.8d+178)) then
        tmp = t_2
    else if (x <= (-4.5d+22)) then
        tmp = t_1
    else if (x <= 1.15d-76) then
        tmp = y * 5.0d0
    else if (x <= 1.65d+39) then
        tmp = x * t
    else if (x <= 8.5d+89) then
        tmp = t_2
    else if (x <= 3.1d+129) then
        tmp = t_1
    else if (x <= 2d+153) then
        tmp = x * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 2.0);
	double t_2 = x * (z * 2.0);
	double tmp;
	if (x <= -4.8e+219) {
		tmp = t_1;
	} else if (x <= -4.8e+178) {
		tmp = t_2;
	} else if (x <= -4.5e+22) {
		tmp = t_1;
	} else if (x <= 1.15e-76) {
		tmp = y * 5.0;
	} else if (x <= 1.65e+39) {
		tmp = x * t;
	} else if (x <= 8.5e+89) {
		tmp = t_2;
	} else if (x <= 3.1e+129) {
		tmp = t_1;
	} else if (x <= 2e+153) {
		tmp = x * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * 2.0)
	t_2 = x * (z * 2.0)
	tmp = 0
	if x <= -4.8e+219:
		tmp = t_1
	elif x <= -4.8e+178:
		tmp = t_2
	elif x <= -4.5e+22:
		tmp = t_1
	elif x <= 1.15e-76:
		tmp = y * 5.0
	elif x <= 1.65e+39:
		tmp = x * t
	elif x <= 8.5e+89:
		tmp = t_2
	elif x <= 3.1e+129:
		tmp = t_1
	elif x <= 2e+153:
		tmp = x * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * 2.0))
	t_2 = Float64(x * Float64(z * 2.0))
	tmp = 0.0
	if (x <= -4.8e+219)
		tmp = t_1;
	elseif (x <= -4.8e+178)
		tmp = t_2;
	elseif (x <= -4.5e+22)
		tmp = t_1;
	elseif (x <= 1.15e-76)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.65e+39)
		tmp = Float64(x * t);
	elseif (x <= 8.5e+89)
		tmp = t_2;
	elseif (x <= 3.1e+129)
		tmp = t_1;
	elseif (x <= 2e+153)
		tmp = Float64(x * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * 2.0);
	t_2 = x * (z * 2.0);
	tmp = 0.0;
	if (x <= -4.8e+219)
		tmp = t_1;
	elseif (x <= -4.8e+178)
		tmp = t_2;
	elseif (x <= -4.5e+22)
		tmp = t_1;
	elseif (x <= 1.15e-76)
		tmp = y * 5.0;
	elseif (x <= 1.65e+39)
		tmp = x * t;
	elseif (x <= 8.5e+89)
		tmp = t_2;
	elseif (x <= 3.1e+129)
		tmp = t_1;
	elseif (x <= 2e+153)
		tmp = x * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+219], t$95$1, If[LessEqual[x, -4.8e+178], t$95$2, If[LessEqual[x, -4.5e+22], t$95$1, If[LessEqual[x, 1.15e-76], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.65e+39], N[(x * t), $MachinePrecision], If[LessEqual[x, 8.5e+89], t$95$2, If[LessEqual[x, 3.1e+129], t$95$1, If[LessEqual[x, 2e+153], N[(x * t), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.8000000000000001e219 or -4.8e178 < x < -4.4999999999999998e22 or 8.50000000000000045e89 < x < 3.1e129

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto y \cdot \color{blue}{\left(2 \cdot x + 5\right)} \]

      2. *-commutative 45.4%

         \[\leadsto y \cdot \left(\color{blue}{x \cdot 2} + 5\right) \]

   7. Simplified 45.4%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot 2 + 5\right)} \]

   8. Taylor expanded in x around inf 43.6%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.6%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 2} \]

      2. *-commutative 43.6%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 2 \]

      3. associate-*r* 45.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]

   10. Simplified 45.4%

       \[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]

   if -4.8000000000000001e219 < x < -4.8e178 or 1.6500000000000001e39 < x < 8.50000000000000045e89 or 2e153 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 100.0%

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

      1. fma-define 100.0%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in z around inf 55.3%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 55.3%

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot x\right)} \]

      2. associate-*l* 55.3%

         \[\leadsto \color{blue}{\left(2 \cdot z\right) \cdot x} \]

      3. *-commutative 55.3%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot z\right)} \]

   10. Simplified 55.3%

       \[\leadsto \color{blue}{x \cdot \left(2 \cdot z\right)} \]

   if -4.4999999999999998e22 < x < 1.15000000000000003e-76

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 61.9%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 61.9%

      \[\leadsto \color{blue}{y \cdot 5} \]

   if 1.15000000000000003e-76 < x < 1.6500000000000001e39 or 3.1e129 < x < 2e153

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 97.1%

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

      1. fma-define 97.1%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 97.2%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 97.2%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 97.1%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 97.1%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in t around inf 50.1%

      \[\leadsto \color{blue}{t \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 50.1%

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

   10. Simplified 50.1%

       \[\leadsto \color{blue}{x \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;x \leq -1.56 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-156}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-260}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-118}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* 2.0 (* x z))))
        (t_2 (* x (+ t (* (+ y z) 2.0))))
        (t_3 (+ (* y 5.0) (* x t))))
   (if (<= x -1.56e-9)
     t_2
     (if (<= x -7.6e-83)
       t_1
       (if (<= x -3.4e-156)
         t_3
         (if (<= x -6.5e-247)
           t_1
           (if (<= x 9.6e-260)
             t_3
             (if (<= x 9.5e-173) t_1 (if (<= x 5e-118) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double t_3 = (y * 5.0) + (x * t);
	double tmp;
	if (x <= -1.56e-9) {
		tmp = t_2;
	} else if (x <= -7.6e-83) {
		tmp = t_1;
	} else if (x <= -3.4e-156) {
		tmp = t_3;
	} else if (x <= -6.5e-247) {
		tmp = t_1;
	} else if (x <= 9.6e-260) {
		tmp = t_3;
	} else if (x <= 9.5e-173) {
		tmp = t_1;
	} else if (x <= 5e-118) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (2.0d0 * (x * z))
    t_2 = x * (t + ((y + z) * 2.0d0))
    t_3 = (y * 5.0d0) + (x * t)
    if (x <= (-1.56d-9)) then
        tmp = t_2
    else if (x <= (-7.6d-83)) then
        tmp = t_1
    else if (x <= (-3.4d-156)) then
        tmp = t_3
    else if (x <= (-6.5d-247)) then
        tmp = t_1
    else if (x <= 9.6d-260) then
        tmp = t_3
    else if (x <= 9.5d-173) then
        tmp = t_1
    else if (x <= 5d-118) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double t_3 = (y * 5.0) + (x * t);
	double tmp;
	if (x <= -1.56e-9) {
		tmp = t_2;
	} else if (x <= -7.6e-83) {
		tmp = t_1;
	} else if (x <= -3.4e-156) {
		tmp = t_3;
	} else if (x <= -6.5e-247) {
		tmp = t_1;
	} else if (x <= 9.6e-260) {
		tmp = t_3;
	} else if (x <= 9.5e-173) {
		tmp = t_1;
	} else if (x <= 5e-118) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (2.0 * (x * z))
	t_2 = x * (t + ((y + z) * 2.0))
	t_3 = (y * 5.0) + (x * t)
	tmp = 0
	if x <= -1.56e-9:
		tmp = t_2
	elif x <= -7.6e-83:
		tmp = t_1
	elif x <= -3.4e-156:
		tmp = t_3
	elif x <= -6.5e-247:
		tmp = t_1
	elif x <= 9.6e-260:
		tmp = t_3
	elif x <= 9.5e-173:
		tmp = t_1
	elif x <= 5e-118:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)))
	t_2 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	t_3 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (x <= -1.56e-9)
		tmp = t_2;
	elseif (x <= -7.6e-83)
		tmp = t_1;
	elseif (x <= -3.4e-156)
		tmp = t_3;
	elseif (x <= -6.5e-247)
		tmp = t_1;
	elseif (x <= 9.6e-260)
		tmp = t_3;
	elseif (x <= 9.5e-173)
		tmp = t_1;
	elseif (x <= 5e-118)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (2.0 * (x * z));
	t_2 = x * (t + ((y + z) * 2.0));
	t_3 = (y * 5.0) + (x * t);
	tmp = 0.0;
	if (x <= -1.56e-9)
		tmp = t_2;
	elseif (x <= -7.6e-83)
		tmp = t_1;
	elseif (x <= -3.4e-156)
		tmp = t_3;
	elseif (x <= -6.5e-247)
		tmp = t_1;
	elseif (x <= 9.6e-260)
		tmp = t_3;
	elseif (x <= 9.5e-173)
		tmp = t_1;
	elseif (x <= 5e-118)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.56e-9], t$95$2, If[LessEqual[x, -7.6e-83], t$95$1, If[LessEqual[x, -3.4e-156], t$95$3, If[LessEqual[x, -6.5e-247], t$95$1, If[LessEqual[x, 9.6e-260], t$95$3, If[LessEqual[x, 9.5e-173], t$95$1, If[LessEqual[x, 5e-118], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.56e-9 or 5.00000000000000015e-118 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 98.7%

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

      1. fma-define 98.7%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 98.8%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 98.8%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 98.7%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 98.7%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in x around inf 92.6%

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

   if -1.56e-9 < x < -7.59999999999999953e-83 or -3.3999999999999999e-156 < x < -6.4999999999999996e-247 or 9.6000000000000002e-260 < x < 9.49999999999999967e-173

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.1%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} + y \cdot 5 \]

   if -7.59999999999999953e-83 < x < -3.3999999999999999e-156 or -6.4999999999999996e-247 < x < 9.6000000000000002e-260 or 9.49999999999999967e-173 < x < 5.00000000000000015e-118

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.2%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-156}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-260}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-118}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -0.048:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+73} \lor \neg \left(x \leq 1.85 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* x (* (+ y z) 2.0))))
   (if (<= x -0.048)
     t_2
     (if (<= x -5e-34)
       t_1
       (if (<= x -1.8e-50)
         (* x (* z 2.0))
         (if (<= x 3e-8)
           t_1
           (if (or (<= x 2.2e+73) (not (<= x 1.85e+122)))
             (* x (+ t (* z 2.0)))
             t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -0.048) {
		tmp = t_2;
	} else if (x <= -5e-34) {
		tmp = t_1;
	} else if (x <= -1.8e-50) {
		tmp = x * (z * 2.0);
	} else if (x <= 3e-8) {
		tmp = t_1;
	} else if ((x <= 2.2e+73) || !(x <= 1.85e+122)) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * t)
    t_2 = x * ((y + z) * 2.0d0)
    if (x <= (-0.048d0)) then
        tmp = t_2
    else if (x <= (-5d-34)) then
        tmp = t_1
    else if (x <= (-1.8d-50)) then
        tmp = x * (z * 2.0d0)
    else if (x <= 3d-8) then
        tmp = t_1
    else if ((x <= 2.2d+73) .or. (.not. (x <= 1.85d+122))) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -0.048) {
		tmp = t_2;
	} else if (x <= -5e-34) {
		tmp = t_1;
	} else if (x <= -1.8e-50) {
		tmp = x * (z * 2.0);
	} else if (x <= 3e-8) {
		tmp = t_1;
	} else if ((x <= 2.2e+73) || !(x <= 1.85e+122)) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	t_2 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -0.048:
		tmp = t_2
	elif x <= -5e-34:
		tmp = t_1
	elif x <= -1.8e-50:
		tmp = x * (z * 2.0)
	elif x <= 3e-8:
		tmp = t_1
	elif (x <= 2.2e+73) or not (x <= 1.85e+122):
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	t_2 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -0.048)
		tmp = t_2;
	elseif (x <= -5e-34)
		tmp = t_1;
	elseif (x <= -1.8e-50)
		tmp = Float64(x * Float64(z * 2.0));
	elseif (x <= 3e-8)
		tmp = t_1;
	elseif ((x <= 2.2e+73) || !(x <= 1.85e+122))
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	t_2 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -0.048)
		tmp = t_2;
	elseif (x <= -5e-34)
		tmp = t_1;
	elseif (x <= -1.8e-50)
		tmp = x * (z * 2.0);
	elseif (x <= 3e-8)
		tmp = t_1;
	elseif ((x <= 2.2e+73) || ~((x <= 1.85e+122)))
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.048], t$95$2, If[LessEqual[x, -5e-34], t$95$1, If[LessEqual[x, -1.8e-50], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-8], t$95$1, If[Or[LessEqual[x, 2.2e+73], N[Not[LessEqual[x, 1.85e+122]], $MachinePrecision]], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.048000000000000001 or 2.2e73 < x < 1.8499999999999998e122

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 100.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. *-un-lft-identity 100.0%

         \[\leadsto x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right) + y \cdot 5 \]

      3. +-commutative 100.0%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      4. *-un-lft-identity 100.0%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      5. distribute-rgt-out 100.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right) + y \cdot 5 \]

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 77.8%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. *-commutative 77.8%

         \[\leadsto \color{blue}{\left(\left(y + z\right) \cdot x\right)} \cdot 2 + y \cdot 5 \]

      3. associate-*l* 77.8%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   8. Taylor expanded in x around inf 77.1%

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

      1. associate-*r* 77.1%

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

      2. *-commutative 77.1%

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

      3. +-commutative 77.1%

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

      4. associate-*r* 77.1%

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

   10. Simplified 77.1%

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

   if -0.048000000000000001 < x < -5.0000000000000003e-34 or -1.7999999999999999e-50 < x < 2.99999999999999973e-8

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 84.6%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]

   if -5.0000000000000003e-34 < x < -1.7999999999999999e-50

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 100.0%

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

      1. fma-define 100.0%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot x\right)} \]

      2. associate-*l* 100.0%

         \[\leadsto \color{blue}{\left(2 \cdot z\right) \cdot x} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot z\right)} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x \cdot \left(2 \cdot z\right)} \]

   if 2.99999999999999973e-8 < x < 2.2e73 or 1.8499999999999998e122 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 100.0%

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

      1. fma-define 100.0%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in y around 0 78.0%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.048:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-34}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+73} \lor \neg \left(x \leq 1.85 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-192}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= z -1e+17)
     (* x (+ t (* z 2.0)))
     (if (<= z -5.7e-11)
       (* y 5.0)
       (if (<= z -2.5e-176)
         t_1
         (if (<= z -1.55e-192)
           (* y 5.0)
           (if (<= z 6.8e-133)
             t_1
             (if (<= z 1.05e-104) (* y 5.0) (* x (* (+ y z) 2.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (z <= -1e+17) {
		tmp = x * (t + (z * 2.0));
	} else if (z <= -5.7e-11) {
		tmp = y * 5.0;
	} else if (z <= -2.5e-176) {
		tmp = t_1;
	} else if (z <= -1.55e-192) {
		tmp = y * 5.0;
	} else if (z <= 6.8e-133) {
		tmp = t_1;
	} else if (z <= 1.05e-104) {
		tmp = y * 5.0;
	} else {
		tmp = x * ((y + z) * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    if (z <= (-1d+17)) then
        tmp = x * (t + (z * 2.0d0))
    else if (z <= (-5.7d-11)) then
        tmp = y * 5.0d0
    else if (z <= (-2.5d-176)) then
        tmp = t_1
    else if (z <= (-1.55d-192)) then
        tmp = y * 5.0d0
    else if (z <= 6.8d-133) then
        tmp = t_1
    else if (z <= 1.05d-104) then
        tmp = y * 5.0d0
    else
        tmp = x * ((y + z) * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (z <= -1e+17) {
		tmp = x * (t + (z * 2.0));
	} else if (z <= -5.7e-11) {
		tmp = y * 5.0;
	} else if (z <= -2.5e-176) {
		tmp = t_1;
	} else if (z <= -1.55e-192) {
		tmp = y * 5.0;
	} else if (z <= 6.8e-133) {
		tmp = t_1;
	} else if (z <= 1.05e-104) {
		tmp = y * 5.0;
	} else {
		tmp = x * ((y + z) * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if z <= -1e+17:
		tmp = x * (t + (z * 2.0))
	elif z <= -5.7e-11:
		tmp = y * 5.0
	elif z <= -2.5e-176:
		tmp = t_1
	elif z <= -1.55e-192:
		tmp = y * 5.0
	elif z <= 6.8e-133:
		tmp = t_1
	elif z <= 1.05e-104:
		tmp = y * 5.0
	else:
		tmp = x * ((y + z) * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (z <= -1e+17)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (z <= -5.7e-11)
		tmp = Float64(y * 5.0);
	elseif (z <= -2.5e-176)
		tmp = t_1;
	elseif (z <= -1.55e-192)
		tmp = Float64(y * 5.0);
	elseif (z <= 6.8e-133)
		tmp = t_1;
	elseif (z <= 1.05e-104)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (z <= -1e+17)
		tmp = x * (t + (z * 2.0));
	elseif (z <= -5.7e-11)
		tmp = y * 5.0;
	elseif (z <= -2.5e-176)
		tmp = t_1;
	elseif (z <= -1.55e-192)
		tmp = y * 5.0;
	elseif (z <= 6.8e-133)
		tmp = t_1;
	elseif (z <= 1.05e-104)
		tmp = y * 5.0;
	else
		tmp = x * ((y + z) * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+17], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.7e-11], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, -2.5e-176], t$95$1, If[LessEqual[z, -1.55e-192], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 6.8e-133], t$95$1, If[LessEqual[z, 1.05e-104], N[(y * 5.0), $MachinePrecision], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1e17

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 84.3%

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

      1. fma-define 84.3%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 84.3%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 84.3%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 84.3%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 84.3%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in y around 0 70.3%

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

   if -1e17 < z < -5.6999999999999997e-11 or -2.5e-176 < z < -1.55e-192 or 6.80000000000000012e-133 < z < 1.04999999999999999e-104

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.3%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 94.3%

      \[\leadsto \color{blue}{y \cdot 5} \]

   if -5.6999999999999997e-11 < z < -2.5e-176 or -1.55e-192 < z < 6.80000000000000012e-133

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 95.8%

      \[\leadsto x \cdot \left(\left(\color{blue}{y} + y\right) + t\right) + y \cdot 5 \]

   4. Taylor expanded in x around inf 68.4%

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

   if 1.04999999999999999e-104 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. *-un-lft-identity 99.9%

         \[\leadsto x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right) + y \cdot 5 \]

      3. +-commutative 99.9%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      4. *-un-lft-identity 99.9%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      5. distribute-rgt-out 99.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right) + y \cdot 5 \]

      6. metadata-eval 99.9%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.9%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 87.5%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. *-commutative 87.5%

         \[\leadsto \color{blue}{\left(\left(y + z\right) \cdot x\right)} \cdot 2 + y \cdot 5 \]

      3. associate-*l* 87.5%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   7. Simplified 87.5%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   8. Taylor expanded in x around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

      3. +-commutative 64.4%

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

      4. associate-*r* 64.4%

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

   10. Simplified 64.4%

       \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(z + y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-192}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+89} \lor \neg \left(t \leq -3.3 \cdot 10^{-14} \lor \neg \left(t \leq -1.9 \cdot 10^{-17}\right) \land t \leq 6.2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e+89)
         (not (or (<= t -3.3e-14) (and (not (<= t -1.9e-17)) (<= t 6.2e-52)))))
   (* x t)
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e+89) || !((t <= -3.3e-14) || (!(t <= -1.9e-17) && (t <= 6.2e-52)))) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	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 <= (-3.5d+89)) .or. (.not. (t <= (-3.3d-14)) .or. (.not. (t <= (-1.9d-17))) .and. (t <= 6.2d-52))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e+89) || !((t <= -3.3e-14) || (!(t <= -1.9e-17) && (t <= 6.2e-52)))) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e+89) or not ((t <= -3.3e-14) or (not (t <= -1.9e-17) and (t <= 6.2e-52))):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e+89) || !((t <= -3.3e-14) || (!(t <= -1.9e-17) && (t <= 6.2e-52))))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e+89) || ~(((t <= -3.3e-14) || (~((t <= -1.9e-17)) && (t <= 6.2e-52)))))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e+89], N[Not[Or[LessEqual[t, -3.3e-14], And[N[Not[LessEqual[t, -1.9e-17]], $MachinePrecision], LessEqual[t, 6.2e-52]]]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000001e89 or -3.2999999999999998e-14 < t < -1.9000000000000001e-17 or 6.1999999999999998e-52 < t

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 85.8%

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

      1. fma-define 85.8%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 85.8%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 85.8%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 85.8%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 85.8%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in t around inf 55.8%

      \[\leadsto \color{blue}{t \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if -3.5000000000000001e89 < t < -3.2999999999999998e-14 or -1.9000000000000001e-17 < t < 6.1999999999999998e-52

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 39.4%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 39.4%

      \[\leadsto \color{blue}{y \cdot 5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+89} \lor \neg \left(t \leq -3.3 \cdot 10^{-14} \lor \neg \left(t \leq -1.9 \cdot 10^{-17}\right) \land t \leq 6.2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -0.22:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -0.22)
     t_1
     (if (<= x 2.3e-77)
       (* y 5.0)
       (if (<= x 6e+63) (* x (+ t (* y 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -0.22) {
		tmp = t_1;
	} else if (x <= 2.3e-77) {
		tmp = y * 5.0;
	} else if (x <= 6e+63) {
		tmp = x * (t + (y * 2.0));
	} 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 = x * ((y + z) * 2.0d0)
    if (x <= (-0.22d0)) then
        tmp = t_1
    else if (x <= 2.3d-77) then
        tmp = y * 5.0d0
    else if (x <= 6d+63) then
        tmp = x * (t + (y * 2.0d0))
    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 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -0.22) {
		tmp = t_1;
	} else if (x <= 2.3e-77) {
		tmp = y * 5.0;
	} else if (x <= 6e+63) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -0.22:
		tmp = t_1
	elif x <= 2.3e-77:
		tmp = y * 5.0
	elif x <= 6e+63:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -0.22)
		tmp = t_1;
	elseif (x <= 2.3e-77)
		tmp = Float64(y * 5.0);
	elseif (x <= 6e+63)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -0.22)
		tmp = t_1;
	elseif (x <= 2.3e-77)
		tmp = y * 5.0;
	elseif (x <= 6e+63)
		tmp = x * (t + (y * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.22], t$95$1, If[LessEqual[x, 2.3e-77], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6e+63], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.220000000000000001 or 5.99999999999999998e63 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 100.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. *-un-lft-identity 100.0%

         \[\leadsto x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right) + y \cdot 5 \]

      3. +-commutative 100.0%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      4. *-un-lft-identity 100.0%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      5. distribute-rgt-out 100.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right) + y \cdot 5 \]

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 73.4%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. *-commutative 73.4%

         \[\leadsto \color{blue}{\left(\left(y + z\right) \cdot x\right)} \cdot 2 + y \cdot 5 \]

      3. associate-*l* 73.4%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   7. Simplified 73.4%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   8. Taylor expanded in x around inf 73.0%

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

      1. associate-*r* 73.0%

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

      2. *-commutative 73.0%

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

      3. +-commutative 73.0%

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

      4. associate-*r* 73.0%

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

   10. Simplified 73.0%

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

   if -0.220000000000000001 < x < 2.29999999999999999e-77

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{y \cdot 5} \]

   if 2.29999999999999999e-77 < x < 5.99999999999999998e63

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.6%

      \[\leadsto x \cdot \left(\left(\color{blue}{y} + y\right) + t\right) + y \cdot 5 \]

   4. Taylor expanded in x around inf 54.3%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.22:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.6e+88)
   (* x t)
   (if (<= t -3.1e-14)
     (* y 5.0)
     (if (<= t 1.25e+94) (* x (* (+ y z) 2.0)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e+88) {
		tmp = x * t;
	} else if (t <= -3.1e-14) {
		tmp = y * 5.0;
	} else if (t <= 1.25e+94) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = 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 (t <= (-5.6d+88)) then
        tmp = x * t
    else if (t <= (-3.1d-14)) then
        tmp = y * 5.0d0
    else if (t <= 1.25d+94) then
        tmp = x * ((y + z) * 2.0d0)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e+88) {
		tmp = x * t;
	} else if (t <= -3.1e-14) {
		tmp = y * 5.0;
	} else if (t <= 1.25e+94) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.6e+88:
		tmp = x * t
	elif t <= -3.1e-14:
		tmp = y * 5.0
	elif t <= 1.25e+94:
		tmp = x * ((y + z) * 2.0)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.6e+88)
		tmp = Float64(x * t);
	elseif (t <= -3.1e-14)
		tmp = Float64(y * 5.0);
	elseif (t <= 1.25e+94)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.6e+88)
		tmp = x * t;
	elseif (t <= -3.1e-14)
		tmp = y * 5.0;
	elseif (t <= 1.25e+94)
		tmp = x * ((y + z) * 2.0);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.6e+88], N[(x * t), $MachinePrecision], If[LessEqual[t, -3.1e-14], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 1.25e+94], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.59999999999999977e88 or 1.25000000000000003e94 < t

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 81.6%

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

      1. fma-define 81.6%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 81.6%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 81.6%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 81.6%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 81.6%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in t around inf 66.1%

      \[\leadsto \color{blue}{t \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 66.1%

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

   10. Simplified 66.1%

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

   if -5.59999999999999977e88 < t < -3.10000000000000004e-14

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 55.7%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{y \cdot 5} \]

   if -3.10000000000000004e-14 < t < 1.25000000000000003e94

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. *-un-lft-identity 99.9%

         \[\leadsto x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right) + y \cdot 5 \]

      3. +-commutative 99.9%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      4. *-un-lft-identity 99.9%

         \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      5. distribute-rgt-out 99.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right) + y \cdot 5 \]

      6. metadata-eval 99.9%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.9%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 94.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 94.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{\left(\left(y + z\right) \cdot x\right)} \cdot 2 + y \cdot 5 \]

      3. associate-*l* 94.7%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   7. Simplified 94.7%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \left(x \cdot 2\right)} + y \cdot 5 \]

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. *-commutative 64.6%

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

      3. +-commutative 64.6%

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

      4. associate-*r* 64.6%

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

   10. Simplified 64.6%

       \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(z + y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -31000000 \lor \neg \left(x \leq 6 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -31000000.0) (not (<= x 6e-34)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -31000000.0) || !(x <= 6e-34)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-31000000.0d0)) .or. (.not. (x <= 6d-34))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * (t + (z * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -31000000.0) || !(x <= 6e-34)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -31000000.0) or not (x <= 6e-34):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -31000000.0) || !(x <= 6e-34))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(z * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -31000000.0) || ~((x <= 6e-34)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -31000000.0], N[Not[LessEqual[x, 6e-34]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e7 or 6e-34 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 100.0%

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

      1. fma-define 100.0%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 100.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in x around inf 97.6%

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

   if -3.1e7 < x < 6e-34

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.9%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -31000000 \lor \neg \left(x \leq 6 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 160000000000:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.2e+87)
   (* x t)
   (if (<= t -6.3e-15)
     (* y 5.0)
     (if (<= t 160000000000.0) (* x (* z 2.0)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.2e+87) {
		tmp = x * t;
	} else if (t <= -6.3e-15) {
		tmp = y * 5.0;
	} else if (t <= 160000000000.0) {
		tmp = x * (z * 2.0);
	} else {
		tmp = 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 (t <= (-7.2d+87)) then
        tmp = x * t
    else if (t <= (-6.3d-15)) then
        tmp = y * 5.0d0
    else if (t <= 160000000000.0d0) then
        tmp = x * (z * 2.0d0)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.2e+87) {
		tmp = x * t;
	} else if (t <= -6.3e-15) {
		tmp = y * 5.0;
	} else if (t <= 160000000000.0) {
		tmp = x * (z * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.2e+87:
		tmp = x * t
	elif t <= -6.3e-15:
		tmp = y * 5.0
	elif t <= 160000000000.0:
		tmp = x * (z * 2.0)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.2e+87)
		tmp = Float64(x * t);
	elseif (t <= -6.3e-15)
		tmp = Float64(y * 5.0);
	elseif (t <= 160000000000.0)
		tmp = Float64(x * Float64(z * 2.0));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.2e+87)
		tmp = x * t;
	elseif (t <= -6.3e-15)
		tmp = y * 5.0;
	elseif (t <= 160000000000.0)
		tmp = x * (z * 2.0);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.2e+87], N[(x * t), $MachinePrecision], If[LessEqual[t, -6.3e-15], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 160000000000.0], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999988e87 or 1.6e11 < t

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 83.7%

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

      1. fma-define 83.7%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 83.7%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 83.7%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 83.7%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 83.7%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in t around inf 61.6%

      \[\leadsto \color{blue}{t \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 61.6%

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

   10. Simplified 61.6%

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

   if -7.19999999999999988e87 < t < -6.29999999999999982e-15

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 55.7%

      \[\leadsto \color{blue}{5 \cdot y} \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{y \cdot 5} \]

   if -6.29999999999999982e-15 < t < 1.6e11

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 94.0%

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

      1. fma-define 94.0%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 94.1%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 94.1%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 94.0%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 94.0%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in z around inf 40.6%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot x\right)} \]

      2. associate-*l* 40.6%

         \[\leadsto \color{blue}{\left(2 \cdot z\right) \cdot x} \]

      3. *-commutative 40.6%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot z\right)} \]

   10. Simplified 40.6%

       \[\leadsto \color{blue}{x \cdot \left(2 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 160000000000:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-7} \lor \neg \left(x \leq 1.4 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.1e-7) (not (<= x 1.4e-76)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-7) || !(x <= 1.4e-76)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-2.1d-7)) .or. (.not. (x <= 1.4d-76))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-7) || !(x <= 1.4e-76)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.1e-7) or not (x <= 1.4e-76):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.1e-7) || !(x <= 1.4e-76))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.1e-7) || ~((x <= 1.4e-76)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e-7], N[Not[LessEqual[x, 1.4e-76]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e-7 or 1.40000000000000005e-76 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      2. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      3. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      5. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      8. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      9. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   5. Taylor expanded in x around inf 99.3%

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

      1. fma-define 99.3%

         \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

      2. associate-*r/ 99.3%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

      3. *-commutative 99.3%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

      4. associate-/l* 99.3%

         \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

   7. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

   8. Taylor expanded in x around inf 95.4%

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

   if -2.1e-7 < x < 1.40000000000000005e-76

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.7%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-7} \lor \neg \left(x \leq 1.4 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ y \cdot 5 + x \cdot \left(t + \left(y + z\right) \cdot 2\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* y 5.0) (* x (+ t (* (+ y z) 2.0)))))

C

double code(double x, double y, double z, double t) {
	return (y * 5.0) + (x * (t + ((y + z) * 2.0)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * 5.0d0) + (x * (t + ((y + z) * 2.0d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (y * 5.0) + (x * (t + ((y + z) * 2.0)));
}

Python

def code(x, y, z, t):
	return (y * 5.0) + (x * (t + ((y + z) * 2.0)))

Julia

function code(x, y, z, t)
	return Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(Float64(y + z) * 2.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y * 5.0) + (x * (t + ((y + z) * 2.0)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-+l+ 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

   2. *-un-lft-identity 100.0%

      \[\leadsto x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right) + y \cdot 5 \]

   3. +-commutative 100.0%

      \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

   4. *-un-lft-identity 100.0%

      \[\leadsto x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right) + y \cdot 5 \]

   5. distribute-rgt-out 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right) + y \cdot 5 \]

   6. metadata-eval 100.0%

      \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

4. Applied egg-rr 100.0%

   \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

5. Final simplification 100.0%

   \[\leadsto y \cdot 5 + x \cdot \left(t + \left(y + z\right) \cdot 2\right) \]
6. Add Preprocessing

Alternative 14: 30.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * 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 = x * t
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(x * t)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

   3. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

   4. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

   5. associate-+l+ 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]

   6. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

   7. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

   8. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

   9. distribute-rgt-out 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

   10. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

5. Taylor expanded in x around inf 90.4%

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

   1. fma-define 90.4%

      \[\leadsto x \cdot \left(t + \color{blue}{\mathsf{fma}\left(2, y + z, 5 \cdot \frac{y}{x}\right)}\right) \]

   2. associate-*r/ 90.5%

      \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{\frac{5 \cdot y}{x}}\right)\right) \]

   3. *-commutative 90.5%

      \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \frac{\color{blue}{y \cdot 5}}{x}\right)\right) \]

   4. associate-/l* 90.4%

      \[\leadsto x \cdot \left(t + \mathsf{fma}\left(2, y + z, \color{blue}{y \cdot \frac{5}{x}}\right)\right) \]

7. Simplified 90.4%

   \[\leadsto \color{blue}{x \cdot \left(t + \mathsf{fma}\left(2, y + z, y \cdot \frac{5}{x}\right)\right)} \]

8. Taylor expanded in t around inf 29.9%

   \[\leadsto \color{blue}{t \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 29.9%

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

10. Simplified 29.9%

    \[\leadsto \color{blue}{x \cdot t} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024105 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))