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

Percentage Accurate: 99.9% → 100.0%

Time: 7.7s

Alternatives: 15

Speedup: 1.2×

• 27.2% 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 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. 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: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + z\right) \cdot 2\\ t_2 := x \cdot \left(t + t\_1\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ y z) 2.0)) (t_2 (* x (+ t t_1))))
   (if (<= x -3.9e+31)
     t_2
     (if (<= x 1.04e-209)
       (+ (* y (+ 5.0 (* x 2.0))) (* x t))
       (if (<= x 1.9e-9) (+ (* y 5.0) (* x t_1)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y + z) * 2.0;
	double t_2 = x * (t + t_1);
	double tmp;
	if (x <= -3.9e+31) {
		tmp = t_2;
	} else if (x <= 1.04e-209) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else if (x <= 1.9e-9) {
		tmp = (y * 5.0) + (x * t_1);
	} 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 + z) * 2.0d0
    t_2 = x * (t + t_1)
    if (x <= (-3.9d+31)) then
        tmp = t_2
    else if (x <= 1.04d-209) then
        tmp = (y * (5.0d0 + (x * 2.0d0))) + (x * t)
    else if (x <= 1.9d-9) then
        tmp = (y * 5.0d0) + (x * t_1)
    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 + z) * 2.0;
	double t_2 = x * (t + t_1);
	double tmp;
	if (x <= -3.9e+31) {
		tmp = t_2;
	} else if (x <= 1.04e-209) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else if (x <= 1.9e-9) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y + z) * 2.0
	t_2 = x * (t + t_1)
	tmp = 0
	if x <= -3.9e+31:
		tmp = t_2
	elif x <= 1.04e-209:
		tmp = (y * (5.0 + (x * 2.0))) + (x * t)
	elif x <= 1.9e-9:
		tmp = (y * 5.0) + (x * t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y + z) * 2.0)
	t_2 = Float64(x * Float64(t + t_1))
	tmp = 0.0
	if (x <= -3.9e+31)
		tmp = t_2;
	elseif (x <= 1.04e-209)
		tmp = Float64(Float64(y * Float64(5.0 + Float64(x * 2.0))) + Float64(x * t));
	elseif (x <= 1.9e-9)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y + z) * 2.0;
	t_2 = x * (t + t_1);
	tmp = 0.0;
	if (x <= -3.9e+31)
		tmp = t_2;
	elseif (x <= 1.04e-209)
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	elseif (x <= 1.9e-9)
		tmp = (y * 5.0) + (x * t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+31], t$95$2, If[LessEqual[x, 1.04e-209], N[(N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-9], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999999e31 or 1.90000000000000006e-9 < 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 99.9%

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

   if -3.89999999999999999e31 < x < 1.0399999999999999e-209

   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 87.5%

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

   4. Taylor expanded in y around 0 87.5%

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

   if 1.0399999999999999e-209 < x < 1.90000000000000006e-9

   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 87.4%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -3.9e+31)
     t_1
     (if (<= x 3.25e-208)
       (+ (* y (+ 5.0 (* x 2.0))) (* x t))
       (if (<= x 2.1e-8) (+ (* y 5.0) (* 2.0 (* x z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -3.9e+31) {
		tmp = t_1;
	} else if (x <= 3.25e-208) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else if (x <= 2.1e-8) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} 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 * (t + ((y + z) * 2.0d0))
    if (x <= (-3.9d+31)) then
        tmp = t_1
    else if (x <= 3.25d-208) then
        tmp = (y * (5.0d0 + (x * 2.0d0))) + (x * t)
    else if (x <= 2.1d-8) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    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 * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -3.9e+31) {
		tmp = t_1;
	} else if (x <= 3.25e-208) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else if (x <= 2.1e-8) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -3.9e+31:
		tmp = t_1
	elif x <= 3.25e-208:
		tmp = (y * (5.0 + (x * 2.0))) + (x * t)
	elif x <= 2.1e-8:
		tmp = (y * 5.0) + (2.0 * (x * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -3.9e+31)
		tmp = t_1;
	elseif (x <= 3.25e-208)
		tmp = Float64(Float64(y * Float64(5.0 + Float64(x * 2.0))) + Float64(x * t));
	elseif (x <= 2.1e-8)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -3.9e+31)
		tmp = t_1;
	elseif (x <= 3.25e-208)
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	elseif (x <= 2.1e-8)
		tmp = (y * 5.0) + (2.0 * (x * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+31], t$95$1, If[LessEqual[x, 3.25e-208], N[(N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-8], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999999e31 or 2.09999999999999994e-8 < 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 99.9%

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

   if -3.89999999999999999e31 < x < 3.2499999999999999e-208

   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 87.5%

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

   4. Taylor expanded in y around 0 87.5%

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

   if 3.2499999999999999e-208 < x < 2.09999999999999994e-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 z around inf 86.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -0.0145:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -0.0145)
     t_1
     (if (<= x 1.8e-209)
       (+ (* y 5.0) (* x t))
       (if (<= x 2.7e-9) (+ (* y 5.0) (* 2.0 (* x z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -0.0145) {
		tmp = t_1;
	} else if (x <= 1.8e-209) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 2.7e-9) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} 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 * (t + ((y + z) * 2.0d0))
    if (x <= (-0.0145d0)) then
        tmp = t_1
    else if (x <= 1.8d-209) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 2.7d-9) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    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 * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -0.0145) {
		tmp = t_1;
	} else if (x <= 1.8e-209) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 2.7e-9) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -0.0145:
		tmp = t_1
	elif x <= 1.8e-209:
		tmp = (y * 5.0) + (x * t)
	elif x <= 2.7e-9:
		tmp = (y * 5.0) + (2.0 * (x * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -0.0145)
		tmp = t_1;
	elseif (x <= 1.8e-209)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 2.7e-9)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -0.0145)
		tmp = t_1;
	elseif (x <= 1.8e-209)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 2.7e-9)
		tmp = (y * 5.0) + (2.0 * (x * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0145], t$95$1, If[LessEqual[x, 1.8e-209], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-9], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0145000000000000007 or 2.7000000000000002e-9 < 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 98.8%

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

   if -0.0145000000000000007 < x < 1.80000000000000008e-209

   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 87.2%

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

   if 1.80000000000000008e-209 < x < 2.7000000000000002e-9

   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 86.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0145:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -3.25 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-69}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -3.25e-109)
     t_1
     (if (<= x 8.6e-69)
       (* y 5.0)
       (if (<= x 6e+45) t_1 (* x (+ t (* y 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -3.25e-109) {
		tmp = t_1;
	} else if (x <= 8.6e-69) {
		tmp = y * 5.0;
	} else if (x <= 6e+45) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 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 + (z * 2.0d0))
    if (x <= (-3.25d-109)) then
        tmp = t_1
    else if (x <= 8.6d-69) then
        tmp = y * 5.0d0
    else if (x <= 6d+45) then
        tmp = t_1
    else
        tmp = x * (t + (y * 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 + (z * 2.0));
	double tmp;
	if (x <= -3.25e-109) {
		tmp = t_1;
	} else if (x <= 8.6e-69) {
		tmp = y * 5.0;
	} else if (x <= 6e+45) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -3.25e-109:
		tmp = t_1
	elif x <= 8.6e-69:
		tmp = y * 5.0
	elif x <= 6e+45:
		tmp = t_1
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -3.25e-109)
		tmp = t_1;
	elseif (x <= 8.6e-69)
		tmp = Float64(y * 5.0);
	elseif (x <= 6e+45)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -3.25e-109)
		tmp = t_1;
	elseif (x <= 8.6e-69)
		tmp = y * 5.0;
	elseif (x <= 6e+45)
		tmp = t_1;
	else
		tmp = x * (t + (y * 2.0));
	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]}, If[LessEqual[x, -3.25e-109], t$95$1, If[LessEqual[x, 8.6e-69], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6e+45], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2499999999999998e-109 or 8.59999999999999999e-69 < x < 6.00000000000000021e45

   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 y around 0 69.8%

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

      1. +-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -3.2499999999999998e-109 < x < 8.59999999999999999e-69

   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 0 69.3%

      \[\leadsto \color{blue}{5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 69.3%

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

   7. Simplified 69.3%

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

   if 6.00000000000000021e45 < 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%

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

   6. Taylor expanded in z around 0 75.2%

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

      1. +-commutative 75.2%

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

   8. Simplified 75.2%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-69}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 4.4e-7)))
   (* 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 <= -2.5) || !(x <= 4.4e-7)) {
		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 <= (-2.5d0)) .or. (.not. (x <= 4.4d-7))) 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 <= -2.5) || !(x <= 4.4e-7)) {
		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 <= -2.5) or not (x <= 4.4e-7):
		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 <= -2.5) || !(x <= 4.4e-7))
		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 <= -2.5) || ~((x <= 4.4e-7)))
		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, -2.5], N[Not[LessEqual[x, 4.4e-7]], $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 < -2.5 or 4.4000000000000002e-7 < 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 98.8%

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

   if -2.5 < x < 4.4000000000000002e-7

   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 99.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+78} \lor \neg \left(z \leq 7 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e+78) (not (<= z 7e-11)))
   (+ (* y 5.0) (* x (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x (+ t (* y 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e+78) || !(z <= 7e-11)) {
		tmp = (y * 5.0) + (x * ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (y * 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 ((z <= (-2.3d+78)) .or. (.not. (z <= 7d-11))) then
        tmp = (y * 5.0d0) + (x * ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * (t + (y * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e+78) || !(z <= 7e-11)) {
		tmp = (y * 5.0) + (x * ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.3e+78) or not (z <= 7e-11):
		tmp = (y * 5.0) + (x * ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * (t + (y * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e+78) || !(z <= 7e-11))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e+78) || ~((z <= 7e-11)))
		tmp = (y * 5.0) + (x * ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.3e+78], N[Not[LessEqual[z, 7e-11]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000002e78 or 7.00000000000000038e-11 < z

   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 90.7%

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

   if -2.3000000000000002e78 < z < 7.00000000000000038e-11

   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 94.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+78} \lor \neg \left(z \leq 7 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-45}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e-67)
   (* x t)
   (if (<= x 3.8e-45)
     (* y 5.0)
     (if (<= x 8e+46) (* x (* z 2.0)) (* y (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e-67) {
		tmp = x * t;
	} else if (x <= 3.8e-45) {
		tmp = y * 5.0;
	} else if (x <= 8e+46) {
		tmp = x * (z * 2.0);
	} else {
		tmp = y * (x * 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 <= (-2.1d-67)) then
        tmp = x * t
    else if (x <= 3.8d-45) then
        tmp = y * 5.0d0
    else if (x <= 8d+46) then
        tmp = x * (z * 2.0d0)
    else
        tmp = y * (x * 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 <= -2.1e-67) {
		tmp = x * t;
	} else if (x <= 3.8e-45) {
		tmp = y * 5.0;
	} else if (x <= 8e+46) {
		tmp = x * (z * 2.0);
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e-67:
		tmp = x * t
	elif x <= 3.8e-45:
		tmp = y * 5.0
	elif x <= 8e+46:
		tmp = x * (z * 2.0)
	else:
		tmp = y * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e-67)
		tmp = Float64(x * t);
	elseif (x <= 3.8e-45)
		tmp = Float64(y * 5.0);
	elseif (x <= 8e+46)
		tmp = Float64(x * Float64(z * 2.0));
	else
		tmp = Float64(y * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.1e-67)
		tmp = x * t;
	elseif (x <= 3.8e-45)
		tmp = y * 5.0;
	elseif (x <= 8e+46)
		tmp = x * (z * 2.0);
	else
		tmp = y * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e-67], N[(x * t), $MachinePrecision], If[LessEqual[x, 3.8e-45], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 8e+46], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1000000000000002e-67

   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 t around inf 42.8%

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

      1. *-commutative 42.8%

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

   7. Simplified 42.8%

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

   if -2.1000000000000002e-67 < x < 3.79999999999999997e-45

   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 0 66.2%

      \[\leadsto \color{blue}{5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if 3.79999999999999997e-45 < x < 7.9999999999999999e46

   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 z around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*r* 48.8%

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

   7. Simplified 48.8%

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

   if 7.9999999999999999e46 < 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. Taylor expanded in y around inf 45.1%

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

   4. Taylor expanded in x around inf 45.1%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-45}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0145 \lor \neg \left(x \leq 3.8 \cdot 10^{-45}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.0145) (not (<= x 3.8e-45)))
   (* 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 <= -0.0145) || !(x <= 3.8e-45)) {
		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 <= (-0.0145d0)) .or. (.not. (x <= 3.8d-45))) 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 <= -0.0145) || !(x <= 3.8e-45)) {
		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 <= -0.0145) or not (x <= 3.8e-45):
		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 <= -0.0145) || !(x <= 3.8e-45))
		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 <= -0.0145) || ~((x <= 3.8e-45)))
		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, -0.0145], N[Not[LessEqual[x, 3.8e-45]], $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 < -0.0145000000000000007 or 3.79999999999999997e-45 < 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 97.6%

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

   if -0.0145000000000000007 < x < 3.79999999999999997e-45

   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 83.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0145 \lor \neg \left(x \leq 3.8 \cdot 10^{-45}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+65} \lor \neg \left(y \leq 3.1 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e+65) (not (<= y 3.1e+57)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+65) || !(y <= 3.1e+57)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = 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 ((y <= (-1.15d+65)) .or. (.not. (y <= 3.1d+57))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = 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 ((y <= -1.15e+65) || !(y <= 3.1e+57)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e+65) or not (y <= 3.1e+57):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e+65) || !(y <= 3.1e+57))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = 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 ((y <= -1.15e+65) || ~((y <= 3.1e+57)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e+65], N[Not[LessEqual[y, 3.1e+57]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e65 or 3.10000000000000013e57 < y

   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 82.7%

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

   if -1.15e65 < y < 3.10000000000000013e57

   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 y around 0 80.0%

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

      1. +-commutative 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+65} \lor \neg \left(y \leq 3.1 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-67} \lor \neg \left(x \leq 1100\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.1e-67) (not (<= x 1100.0))) (* x (+ t (* y 2.0))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-67) || !(x <= 1100.0)) {
		tmp = x * (t + (y * 2.0));
	} 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 ((x <= (-2.1d-67)) .or. (.not. (x <= 1100.0d0))) then
        tmp = x * (t + (y * 2.0d0))
    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 ((x <= -2.1e-67) || !(x <= 1100.0)) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.1e-67) or not (x <= 1100.0):
		tmp = x * (t + (y * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.1e-67) || !(x <= 1100.0))
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.1e-67) || ~((x <= 1100.0)))
		tmp = x * (t + (y * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e-67], N[Not[LessEqual[x, 1100.0]], $MachinePrecision]], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000002e-67 or 1100 < 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 96.3%

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

   6. Taylor expanded in z around 0 70.4%

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

      1. +-commutative 70.4%

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

   8. Simplified 70.4%

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

   if -2.1000000000000002e-67 < x < 1100

   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 0 63.5%

      \[\leadsto \color{blue}{5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-67} \lor \neg \left(x \leq 1100\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e-67) (* x t) (if (<= x 4.4e-7) (* y 5.0) (* y (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e-67) {
		tmp = x * t;
	} else if (x <= 4.4e-7) {
		tmp = y * 5.0;
	} else {
		tmp = y * (x * 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 <= (-2.1d-67)) then
        tmp = x * t
    else if (x <= 4.4d-7) then
        tmp = y * 5.0d0
    else
        tmp = y * (x * 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 <= -2.1e-67) {
		tmp = x * t;
	} else if (x <= 4.4e-7) {
		tmp = y * 5.0;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e-67:
		tmp = x * t
	elif x <= 4.4e-7:
		tmp = y * 5.0
	else:
		tmp = y * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e-67)
		tmp = Float64(x * t);
	elseif (x <= 4.4e-7)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(y * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.1e-67)
		tmp = x * t;
	elseif (x <= 4.4e-7)
		tmp = y * 5.0;
	else
		tmp = y * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e-67], N[(x * t), $MachinePrecision], If[LessEqual[x, 4.4e-7], N[(y * 5.0), $MachinePrecision], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1000000000000002e-67

   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 t around inf 42.8%

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

      1. *-commutative 42.8%

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

   7. Simplified 42.8%

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

   if -2.1000000000000002e-67 < x < 4.4000000000000002e-7

   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 0 64.7%

      \[\leadsto \color{blue}{5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 64.7%

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

   7. Simplified 64.7%

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

   if 4.4000000000000002e-7 < 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. Taylor expanded in y around inf 39.8%

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

   4. Taylor expanded in x around inf 39.6%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-67} \lor \neg \left(x \leq 1100\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.05e-67) (not (<= x 1100.0))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.05e-67) || !(x <= 1100.0)) {
		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 ((x <= (-2.05d-67)) .or. (.not. (x <= 1100.0d0))) 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 ((x <= -2.05e-67) || !(x <= 1100.0)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.05e-67) or not (x <= 1100.0):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.05e-67) || !(x <= 1100.0))
		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 ((x <= -2.05e-67) || ~((x <= 1100.0)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.05e-67], N[Not[LessEqual[x, 1100.0]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0499999999999999e-67 or 1100 < 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 t around inf 39.5%

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

      1. *-commutative 39.5%

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

   7. Simplified 39.5%

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

   if -2.0499999999999999e-67 < x < 1100

   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 0 63.5%

      \[\leadsto \color{blue}{5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-67} \lor \neg \left(x \leq 1100\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 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. Final simplification 99.9%

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

Alternative 15: 31.1% 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 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 t around inf 31.4%

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

   1. *-commutative 31.4%

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

7. Simplified 31.4%

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

Reproduce

herbie shell --seed 2024144 
(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)))