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

Percentage Accurate: 99.8% → 99.9%

Time: 6.7s

Alternatives: 16

Speedup: 1.0×

• 27.4% 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: 99.8% 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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. fma-def 99.6%

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

   3. distribute-rgt-in 95.7%

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

   4. associate-+l+ 95.7%

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

   5. +-commutative 95.7%

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

   6. count-2 95.7%

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

   7. distribute-rgt-in 99.6%

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

   8. *-commutative 99.6%

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

   9. fma-def 99.6%

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

3. Applied egg-rr 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. fma-def 99.6%

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

   2. associate-+l+ 99.6%

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

   3. +-commutative 99.6%

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

   4. count-2 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 3: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+95}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* z 2.0))) (t_2 (* y (+ 5.0 x))))
   (if (<= t -8.2e+95)
     (* x t)
     (if (<= t -6.8e-169)
       t_2
       (if (<= t -1.55e-229)
         t_1
         (if (<= t 2.6e-183)
           t_2
           (if (<= t 3e-41)
             t_1
             (if (<= t 6e-11) t_2 (if (<= t 4.6e+67) t_1 (* x t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z * 2.0);
	double t_2 = y * (5.0 + x);
	double tmp;
	if (t <= -8.2e+95) {
		tmp = x * t;
	} else if (t <= -6.8e-169) {
		tmp = t_2;
	} else if (t <= -1.55e-229) {
		tmp = t_1;
	} else if (t <= 2.6e-183) {
		tmp = t_2;
	} else if (t <= 3e-41) {
		tmp = t_1;
	} else if (t <= 6e-11) {
		tmp = t_2;
	} else if (t <= 4.6e+67) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z * 2.0d0)
    t_2 = y * (5.0d0 + x)
    if (t <= (-8.2d+95)) then
        tmp = x * t
    else if (t <= (-6.8d-169)) then
        tmp = t_2
    else if (t <= (-1.55d-229)) then
        tmp = t_1
    else if (t <= 2.6d-183) then
        tmp = t_2
    else if (t <= 3d-41) then
        tmp = t_1
    else if (t <= 6d-11) then
        tmp = t_2
    else if (t <= 4.6d+67) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z * 2.0);
	double t_2 = y * (5.0 + x);
	double tmp;
	if (t <= -8.2e+95) {
		tmp = x * t;
	} else if (t <= -6.8e-169) {
		tmp = t_2;
	} else if (t <= -1.55e-229) {
		tmp = t_1;
	} else if (t <= 2.6e-183) {
		tmp = t_2;
	} else if (t <= 3e-41) {
		tmp = t_1;
	} else if (t <= 6e-11) {
		tmp = t_2;
	} else if (t <= 4.6e+67) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z * 2.0)
	t_2 = y * (5.0 + x)
	tmp = 0
	if t <= -8.2e+95:
		tmp = x * t
	elif t <= -6.8e-169:
		tmp = t_2
	elif t <= -1.55e-229:
		tmp = t_1
	elif t <= 2.6e-183:
		tmp = t_2
	elif t <= 3e-41:
		tmp = t_1
	elif t <= 6e-11:
		tmp = t_2
	elif t <= 4.6e+67:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z * 2.0))
	t_2 = Float64(y * Float64(5.0 + x))
	tmp = 0.0
	if (t <= -8.2e+95)
		tmp = Float64(x * t);
	elseif (t <= -6.8e-169)
		tmp = t_2;
	elseif (t <= -1.55e-229)
		tmp = t_1;
	elseif (t <= 2.6e-183)
		tmp = t_2;
	elseif (t <= 3e-41)
		tmp = t_1;
	elseif (t <= 6e-11)
		tmp = t_2;
	elseif (t <= 4.6e+67)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z * 2.0);
	t_2 = y * (5.0 + x);
	tmp = 0.0;
	if (t <= -8.2e+95)
		tmp = x * t;
	elseif (t <= -6.8e-169)
		tmp = t_2;
	elseif (t <= -1.55e-229)
		tmp = t_1;
	elseif (t <= 2.6e-183)
		tmp = t_2;
	elseif (t <= 3e-41)
		tmp = t_1;
	elseif (t <= 6e-11)
		tmp = t_2;
	elseif (t <= 4.6e+67)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+95], N[(x * t), $MachinePrecision], If[LessEqual[t, -6.8e-169], t$95$2, If[LessEqual[t, -1.55e-229], t$95$1, If[LessEqual[t, 2.6e-183], t$95$2, If[LessEqual[t, 3e-41], t$95$1, If[LessEqual[t, 6e-11], t$95$2, If[LessEqual[t, 4.6e+67], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.19999999999999972e95 or 4.5999999999999997e67 < t

   1. Initial program 99.0%

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

      1. fma-def 99.0%

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

      2. associate-+l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. count-2 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 92.8%

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

   5. Taylor expanded in t around inf 73.9%

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

   if -8.19999999999999972e95 < t < -6.8e-169 or -1.55e-229 < t < 2.5999999999999999e-183 or 2.99999999999999989e-41 < t < 6e-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. Taylor expanded in y around 0 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in y around inf 57.5%

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

      1. +-commutative 57.5%

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

   7. Simplified 57.5%

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

   if -6.8e-169 < t < -1.55e-229 or 2.5999999999999999e-183 < t < 2.99999999999999989e-41 or 6e-11 < t < 4.5999999999999997e67

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 76.5%

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

   5. Taylor expanded in z around inf 58.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+95}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-183}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 4: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.1e+124)
     t_2
     (if (<= y -9.2e+23)
       t_1
       (if (<= y -7.8e-5)
         (* x (* (+ y z) 2.0))
         (if (<= y -6e-62)
           t_1
           (if (<= y 1.7e+108) (* x (+ t (* z 2.0))) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.1e+124) {
		tmp = t_2;
	} else if (y <= -9.2e+23) {
		tmp = t_1;
	} else if (y <= -7.8e-5) {
		tmp = x * ((y + z) * 2.0);
	} else if (y <= -6e-62) {
		tmp = t_1;
	} else if (y <= 1.7e+108) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * t)
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.1d+124)) then
        tmp = t_2
    else if (y <= (-9.2d+23)) then
        tmp = t_1
    else if (y <= (-7.8d-5)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (y <= (-6d-62)) then
        tmp = t_1
    else if (y <= 1.7d+108) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.1e+124) {
		tmp = t_2;
	} else if (y <= -9.2e+23) {
		tmp = t_1;
	} else if (y <= -7.8e-5) {
		tmp = x * ((y + z) * 2.0);
	} else if (y <= -6e-62) {
		tmp = t_1;
	} else if (y <= 1.7e+108) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.1e+124:
		tmp = t_2
	elif y <= -9.2e+23:
		tmp = t_1
	elif y <= -7.8e-5:
		tmp = x * ((y + z) * 2.0)
	elif y <= -6e-62:
		tmp = t_1
	elif y <= 1.7e+108:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.1e+124)
		tmp = t_2;
	elseif (y <= -9.2e+23)
		tmp = t_1;
	elseif (y <= -7.8e-5)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (y <= -6e-62)
		tmp = t_1;
	elseif (y <= 1.7e+108)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.1e+124)
		tmp = t_2;
	elseif (y <= -9.2e+23)
		tmp = t_1;
	elseif (y <= -7.8e-5)
		tmp = x * ((y + z) * 2.0);
	elseif (y <= -6e-62)
		tmp = t_1;
	elseif (y <= 1.7e+108)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+124], t$95$2, If[LessEqual[y, -9.2e+23], t$95$1, If[LessEqual[y, -7.8e-5], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-62], t$95$1, If[LessEqual[y, 1.7e+108], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1e124 or 1.69999999999999998e108 < y

   1. Initial program 98.5%

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

      1. fma-def 98.5%

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

      2. associate-+l+ 98.5%

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

      3. +-commutative 98.5%

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

      4. count-2 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around inf 87.1%

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

   if -1.1e124 < y < -9.2000000000000002e23 or -7.7999999999999999e-5 < y < -6.0000000000000002e-62

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 77.0%

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

   if -9.2000000000000002e23 < y < -7.7999999999999999e-5

   1. Initial program 99.8%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 77.3%

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

   5. Taylor expanded in t around 0 77.3%

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

   if -6.0000000000000002e-62 < y < 1.69999999999999998e108

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.2%

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

   5. Taylor expanded in y around 0 82.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+23}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-62}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 5: 88.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* 2.0 (* x z)))) (t_2 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -3.5e-13)
     t_2
     (if (<= x -1.35e-264)
       t_1
       (if (<= x 1.7e-88) (+ (* y 5.0) (* x t)) (if (<= x 1.9e-9) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -3.5e-13) {
		tmp = t_2;
	} else if (x <= -1.35e-264) {
		tmp = t_1;
	} else if (x <= 1.7e-88) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.9e-9) {
		tmp = 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 * 5.0d0) + (2.0d0 * (x * z))
    t_2 = x * (t + ((y + z) * 2.0d0))
    if (x <= (-3.5d-13)) then
        tmp = t_2
    else if (x <= (-1.35d-264)) then
        tmp = t_1
    else if (x <= 1.7d-88) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 1.9d-9) then
        tmp = 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 * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -3.5e-13) {
		tmp = t_2;
	} else if (x <= -1.35e-264) {
		tmp = t_1;
	} else if (x <= 1.7e-88) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.9e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (2.0 * (x * z))
	t_2 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -3.5e-13:
		tmp = t_2
	elif x <= -1.35e-264:
		tmp = t_1
	elif x <= 1.7e-88:
		tmp = (y * 5.0) + (x * t)
	elif x <= 1.9e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)))
	t_2 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -3.5e-13)
		tmp = t_2;
	elseif (x <= -1.35e-264)
		tmp = t_1;
	elseif (x <= 1.7e-88)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 1.9e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (2.0 * (x * z));
	t_2 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -3.5e-13)
		tmp = t_2;
	elseif (x <= -1.35e-264)
		tmp = t_1;
	elseif (x <= 1.7e-88)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 1.9e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e-13], t$95$2, If[LessEqual[x, -1.35e-264], t$95$1, If[LessEqual[x, 1.7e-88], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-9], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5000000000000002e-13 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.8%

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

   if -3.5000000000000002e-13 < x < -1.34999999999999997e-264 or 1.69999999999999987e-88 < x < 1.90000000000000006e-9

   1. Initial program 98.7%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around inf 86.5%

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

   if -1.34999999999999997e-264 < x < 1.69999999999999987e-88

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 88.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-264}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+27} \lor \neg \left(x \leq 5.3 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + \left(z + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e+27) (not (<= x 5.3e-8)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x (+ t (+ y (+ z z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e+27) || !(x <= 5.3e-8)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (z + z))));
	}
	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 <= (-9.5d+27)) .or. (.not. (x <= 5.3d-8))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (z + z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e+27) || !(x <= 5.3e-8)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (z + z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.5e+27) or not (x <= 5.3e-8):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * (t + (y + (z + z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e+27) || !(x <= 5.3e-8))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(z + z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9.5e+27) || ~((x <= 5.3e-8)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * (t + (y + (z + z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e+27], N[Not[LessEqual[x, 5.3e-8]], $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[(y + N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999997e27 or 5.2999999999999998e-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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.8%

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

   if -9.4999999999999997e27 < x < 5.2999999999999998e-8

   1. Initial program 99.1%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+27} \lor \neg \left(x \leq 5.3 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + \left(z + z\right)\right)\right)\\ \end{array} \]

Alternative 7: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-21} \lor \neg \left(y \leq 9.5 \cdot 10^{+106}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -9.8e+148)
     t_1
     (if (<= y -1.95e+54)
       (* x (+ t (* y 2.0)))
       (if (or (<= y -3.3e-21) (not (<= y 9.5e+106)))
         t_1
         (* x (+ t (* z 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -9.8e+148) {
		tmp = t_1;
	} else if (y <= -1.95e+54) {
		tmp = x * (t + (y * 2.0));
	} else if ((y <= -3.3e-21) || !(y <= 9.5e+106)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-9.8d+148)) then
        tmp = t_1
    else if (y <= (-1.95d+54)) then
        tmp = x * (t + (y * 2.0d0))
    else if ((y <= (-3.3d-21)) .or. (.not. (y <= 9.5d+106))) then
        tmp = t_1
    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 t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -9.8e+148) {
		tmp = t_1;
	} else if (y <= -1.95e+54) {
		tmp = x * (t + (y * 2.0));
	} else if ((y <= -3.3e-21) || !(y <= 9.5e+106)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -9.8e+148:
		tmp = t_1
	elif y <= -1.95e+54:
		tmp = x * (t + (y * 2.0))
	elif (y <= -3.3e-21) or not (y <= 9.5e+106):
		tmp = t_1
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -9.8e+148)
		tmp = t_1;
	elseif (y <= -1.95e+54)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif ((y <= -3.3e-21) || !(y <= 9.5e+106))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -9.8e+148)
		tmp = t_1;
	elseif (y <= -1.95e+54)
		tmp = x * (t + (y * 2.0));
	elseif ((y <= -3.3e-21) || ~((y <= 9.5e+106)))
		tmp = t_1;
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+148], t$95$1, If[LessEqual[y, -1.95e+54], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.3e-21], N[Not[LessEqual[y, 9.5e+106]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.8e148 or -1.9500000000000001e54 < y < -3.30000000000000009e-21 or 9.4999999999999995e106 < y

   1. Initial program 98.8%

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

      1. fma-def 98.8%

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

      2. associate-+l+ 98.8%

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

      3. +-commutative 98.8%

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

      4. count-2 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around inf 82.1%

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

   if -9.8e148 < y < -1.9500000000000001e54

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 79.1%

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

   5. Taylor expanded in z around 0 66.4%

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

   if -3.30000000000000009e-21 < y < 9.4999999999999995e106

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.3%

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

   5. Taylor expanded in y around 0 81.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-21} \lor \neg \left(y \leq 9.5 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 8: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ t_2 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))) (t_2 (* x (* (+ y z) 2.0))))
   (if (<= x -6.4e+94)
     t_2
     (if (<= x -3.65e-13)
       t_1
       (if (<= x 5.8e-9)
         (* y (+ 5.0 (* x 2.0)))
         (if (<= x 9.5e+260) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double t_2 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -6.4e+94) {
		tmp = t_2;
	} else if (x <= -3.65e-13) {
		tmp = t_1;
	} else if (x <= 5.8e-9) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (x <= 9.5e+260) {
		tmp = 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 = x * (t + (y * 2.0d0))
    t_2 = x * ((y + z) * 2.0d0)
    if (x <= (-6.4d+94)) then
        tmp = t_2
    else if (x <= (-3.65d-13)) then
        tmp = t_1
    else if (x <= 5.8d-9) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if (x <= 9.5d+260) then
        tmp = 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 = x * (t + (y * 2.0));
	double t_2 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -6.4e+94) {
		tmp = t_2;
	} else if (x <= -3.65e-13) {
		tmp = t_1;
	} else if (x <= 5.8e-9) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (x <= 9.5e+260) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	t_2 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -6.4e+94:
		tmp = t_2
	elif x <= -3.65e-13:
		tmp = t_1
	elif x <= 5.8e-9:
		tmp = y * (5.0 + (x * 2.0))
	elif x <= 9.5e+260:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	t_2 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -6.4e+94)
		tmp = t_2;
	elseif (x <= -3.65e-13)
		tmp = t_1;
	elseif (x <= 5.8e-9)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif (x <= 9.5e+260)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	t_2 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -6.4e+94)
		tmp = t_2;
	elseif (x <= -3.65e-13)
		tmp = t_1;
	elseif (x <= 5.8e-9)
		tmp = y * (5.0 + (x * 2.0));
	elseif (x <= 9.5e+260)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+94], t$95$2, If[LessEqual[x, -3.65e-13], t$95$1, If[LessEqual[x, 5.8e-9], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+260], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.40000000000000028e94 or 9.5000000000000004e260 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in t around 0 81.2%

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

   if -6.40000000000000028e94 < x < -3.6500000000000001e-13 or 5.79999999999999982e-9 < x < 9.5000000000000004e260

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.7%

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

   5. Taylor expanded in z around 0 73.9%

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

   if -3.6500000000000001e-13 < x < 5.79999999999999982e-9

   1. Initial program 99.1%

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

      1. fma-def 99.1%

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

      2. associate-+l+ 99.1%

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

      3. +-commutative 99.1%

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

      4. count-2 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around inf 62.8%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+260}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Final simplification 99.6%

   \[\leadsto y \cdot 5 + x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) \]

Alternative 10: 56.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y + t\right)\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-15} \lor \neg \left(x \leq 2.05 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ y t))))
   (if (<= x -5.9e+171)
     t_1
     (if (<= x -1.45e+91)
       (* x (* z 2.0))
       (if (or (<= x -5e-15) (not (<= x 2.05e-9))) t_1 (* y (+ 5.0 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double tmp;
	if (x <= -5.9e+171) {
		tmp = t_1;
	} else if (x <= -1.45e+91) {
		tmp = x * (z * 2.0);
	} else if ((x <= -5e-15) || !(x <= 2.05e-9)) {
		tmp = t_1;
	} else {
		tmp = y * (5.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y + t)
    if (x <= (-5.9d+171)) then
        tmp = t_1
    else if (x <= (-1.45d+91)) then
        tmp = x * (z * 2.0d0)
    else if ((x <= (-5d-15)) .or. (.not. (x <= 2.05d-9))) then
        tmp = t_1
    else
        tmp = y * (5.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double tmp;
	if (x <= -5.9e+171) {
		tmp = t_1;
	} else if (x <= -1.45e+91) {
		tmp = x * (z * 2.0);
	} else if ((x <= -5e-15) || !(x <= 2.05e-9)) {
		tmp = t_1;
	} else {
		tmp = y * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y + t)
	tmp = 0
	if x <= -5.9e+171:
		tmp = t_1
	elif x <= -1.45e+91:
		tmp = x * (z * 2.0)
	elif (x <= -5e-15) or not (x <= 2.05e-9):
		tmp = t_1
	else:
		tmp = y * (5.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y + t))
	tmp = 0.0
	if (x <= -5.9e+171)
		tmp = t_1;
	elseif (x <= -1.45e+91)
		tmp = Float64(x * Float64(z * 2.0));
	elseif ((x <= -5e-15) || !(x <= 2.05e-9))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(5.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y + t);
	tmp = 0.0;
	if (x <= -5.9e+171)
		tmp = t_1;
	elseif (x <= -1.45e+91)
		tmp = x * (z * 2.0);
	elseif ((x <= -5e-15) || ~((x <= 2.05e-9)))
		tmp = t_1;
	else
		tmp = y * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.9e+171], t$95$1, If[LessEqual[x, -1.45e+91], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5e-15], N[Not[LessEqual[x, 2.05e-9]], $MachinePrecision]], t$95$1, N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.90000000000000035e171 or -1.45000000000000007e91 < x < -4.99999999999999999e-15 or 2.0500000000000002e-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. Taylor expanded in y around 0 90.7%

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

   4. Simplified 90.7%

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

   5. Taylor expanded in z around 0 64.4%

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

   6. Taylor expanded in x around inf 64.4%

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

   if -5.90000000000000035e171 < x < -1.45000000000000007e91

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around inf 65.8%

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

   if -4.99999999999999999e-15 < x < 2.0500000000000002e-9

   1. Initial program 99.1%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in y around inf 62.0%

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

      1. +-commutative 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-15} \lor \neg \left(x \leq 2.05 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 11: 60.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y + t\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ y t))))
   (if (<= t -9.2e+95)
     t_1
     (if (<= t -3e+60)
       (* y (+ 5.0 x))
       (if (<= t 1.75e+77) (* x (* (+ y z) 2.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double tmp;
	if (t <= -9.2e+95) {
		tmp = t_1;
	} else if (t <= -3e+60) {
		tmp = y * (5.0 + x);
	} else if (t <= 1.75e+77) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y + t)
    if (t <= (-9.2d+95)) then
        tmp = t_1
    else if (t <= (-3d+60)) then
        tmp = y * (5.0d0 + x)
    else if (t <= 1.75d+77) then
        tmp = x * ((y + z) * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double tmp;
	if (t <= -9.2e+95) {
		tmp = t_1;
	} else if (t <= -3e+60) {
		tmp = y * (5.0 + x);
	} else if (t <= 1.75e+77) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y + t)
	tmp = 0
	if t <= -9.2e+95:
		tmp = t_1
	elif t <= -3e+60:
		tmp = y * (5.0 + x)
	elif t <= 1.75e+77:
		tmp = x * ((y + z) * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y + t))
	tmp = 0.0
	if (t <= -9.2e+95)
		tmp = t_1;
	elseif (t <= -3e+60)
		tmp = Float64(y * Float64(5.0 + x));
	elseif (t <= 1.75e+77)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y + t);
	tmp = 0.0;
	if (t <= -9.2e+95)
		tmp = t_1;
	elseif (t <= -3e+60)
		tmp = y * (5.0 + x);
	elseif (t <= 1.75e+77)
		tmp = x * ((y + z) * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+95], t$95$1, If[LessEqual[t, -3e+60], N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+77], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.19999999999999989e95 or 1.7500000000000001e77 < t

   1. Initial program 99.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in z around 0 93.9%

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

   6. Taylor expanded in x around inf 78.1%

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

   if -9.19999999999999989e95 < t < -2.9999999999999998e60

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 92.5%

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

   4. Simplified 92.5%

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

   5. Taylor expanded in y around inf 81.3%

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

      1. +-commutative 81.3%

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

   7. Simplified 81.3%

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

   if -2.9999999999999998e60 < t < 1.7500000000000001e77

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 66.2%

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

   5. Taylor expanded in t around 0 59.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \end{array} \]

Alternative 12: 60.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y + t\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ y t))))
   (if (<= t -1.3e+96)
     t_1
     (if (<= t -1.65e-103)
       (* y (+ 5.0 (* x 2.0)))
       (if (<= t 4.6e+73) (* x (* (+ y z) 2.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double tmp;
	if (t <= -1.3e+96) {
		tmp = t_1;
	} else if (t <= -1.65e-103) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (t <= 4.6e+73) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y + t)
    if (t <= (-1.3d+96)) then
        tmp = t_1
    else if (t <= (-1.65d-103)) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if (t <= 4.6d+73) then
        tmp = x * ((y + z) * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double tmp;
	if (t <= -1.3e+96) {
		tmp = t_1;
	} else if (t <= -1.65e-103) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (t <= 4.6e+73) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y + t)
	tmp = 0
	if t <= -1.3e+96:
		tmp = t_1
	elif t <= -1.65e-103:
		tmp = y * (5.0 + (x * 2.0))
	elif t <= 4.6e+73:
		tmp = x * ((y + z) * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y + t))
	tmp = 0.0
	if (t <= -1.3e+96)
		tmp = t_1;
	elseif (t <= -1.65e-103)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif (t <= 4.6e+73)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y + t);
	tmp = 0.0;
	if (t <= -1.3e+96)
		tmp = t_1;
	elseif (t <= -1.65e-103)
		tmp = y * (5.0 + (x * 2.0));
	elseif (t <= 4.6e+73)
		tmp = x * ((y + z) * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+96], t$95$1, If[LessEqual[t, -1.65e-103], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+73], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e96 or 4.6e73 < t

   1. Initial program 99.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in z around 0 93.9%

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

   6. Taylor expanded in x around inf 78.1%

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

   if -1.3e96 < t < -1.64999999999999995e-103

   1. Initial program 99.8%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.0%

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

   if -1.64999999999999995e-103 < t < 4.6e73

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 68.4%

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

   5. Taylor expanded in t around 0 61.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \end{array} \]

Alternative 13: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-37} \lor \neg \left(x \leq 5.5 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e-37) (not (<= x 5.5e-26)))
   (* 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 <= -4.5e-37) || !(x <= 5.5e-26)) {
		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 <= (-4.5d-37)) .or. (.not. (x <= 5.5d-26))) 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 <= -4.5e-37) || !(x <= 5.5e-26)) {
		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 <= -4.5e-37) or not (x <= 5.5e-26):
		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 <= -4.5e-37) || !(x <= 5.5e-26))
		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 <= -4.5e-37) || ~((x <= 5.5e-26)))
		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, -4.5e-37], N[Not[LessEqual[x, 5.5e-26]], $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 < -4.5000000000000004e-37 or 5.5000000000000005e-26 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 95.6%

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

   if -4.5000000000000004e-37 < x < 5.5000000000000005e-26

   1. Initial program 98.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 81.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-37} \lor \neg \left(x \leq 5.5 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 14: 53.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+96} \lor \neg \left(t \leq 4.6 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.9e+96) (not (<= t 4.6e+68))) (* x t) (* y (+ 5.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e+96) || !(t <= 4.6e+68)) {
		tmp = x * t;
	} else {
		tmp = y * (5.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.9d+96)) .or. (.not. (t <= 4.6d+68))) then
        tmp = x * t
    else
        tmp = y * (5.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e+96) || !(t <= 4.6e+68)) {
		tmp = x * t;
	} else {
		tmp = y * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.9e+96) or not (t <= 4.6e+68):
		tmp = x * t
	else:
		tmp = y * (5.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.9e+96) || !(t <= 4.6e+68))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * Float64(5.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.9e+96) || ~((t <= 4.6e+68)))
		tmp = x * t;
	else
		tmp = y * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.9e+96], N[Not[LessEqual[t, 4.6e+68]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999978e96 or 4.6e68 < t

   1. Initial program 99.0%

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

      1. fma-def 99.0%

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

      2. associate-+l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. count-2 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 92.8%

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

   5. Taylor expanded in t around inf 73.9%

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

   if -2.89999999999999978e96 < t < 4.6e68

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in y around inf 45.8%

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

      1. +-commutative 45.8%

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

   7. Simplified 45.8%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+96} \lor \neg \left(t \leq 4.6 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 15: 48.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-12}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.12e-12) (* x t) (if (<= x 2.95e-8) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.12e-12) {
		tmp = x * t;
	} else if (x <= 2.95e-8) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.12d-12)) then
        tmp = x * t
    else if (x <= 2.95d-8) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.12e-12) {
		tmp = x * t;
	} else if (x <= 2.95e-8) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.12e-12:
		tmp = x * t
	elif x <= 2.95e-8:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.12e-12)
		tmp = Float64(x * t);
	elseif (x <= 2.95e-8)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.12e-12)
		tmp = x * t;
	elseif (x <= 2.95e-8)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.12e-12], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.95e-8], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1200000000000001e-12 or 2.9499999999999999e-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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 92.0%

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

   5. Taylor expanded in t around inf 47.2%

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

   if -1.1200000000000001e-12 < x < 2.9499999999999999e-8

   1. Initial program 99.1%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 61.9%

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

   4. Simplified 61.9%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-12}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 16: 30.6% 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 99.6%

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

   1. fma-def 99.6%

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

   2. associate-+l+ 99.6%

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

   3. +-commutative 99.6%

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

   4. count-2 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in y around 0 95.6%

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

5. Taylor expanded in t around inf 34.3%

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

6. Final simplification 34.3%

   \[\leadsto x \cdot t \]

Reproduce

herbie shell --seed 2023257 
(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)))