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

Percentage Accurate: 99.9% → 100.0%

Time: 7.2s

Alternatives: 12

Speedup: 1.0×

• 27.0% 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

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

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 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. +-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-def 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. flip-+ 59.2%

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

   4. associate-*r/ 55.2%

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

   5. fma-neg 56.2%

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

   6. associate-+l+ 56.2%

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

   7. +-commutative 56.2%

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

   8. count-2 56.2%

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

   9. associate-+l+ 56.2%

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

   10. +-commutative 56.2%

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

   11. count-2 56.2%

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

   12. fma-neg 55.2%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

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 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. Final simplification 100.0%

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

Alternative 3: 77.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -235:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 0.0011:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0))))
        (t_2 (* y (+ 5.0 (* x 2.0))))
        (t_3 (+ (* y 5.0) (* x t))))
   (if (<= y -1.16e+129)
     t_2
     (if (<= y -6.6e+72)
       t_1
       (if (<= y -235.0)
         t_3
         (if (<= y -1.02e-50)
           t_1
           (if (<= y -2.1e-88)
             t_3
             (if (<= y 0.0011) t_1 (if (<= y 2.55e+91) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double t_3 = (y * 5.0) + (x * t);
	double tmp;
	if (y <= -1.16e+129) {
		tmp = t_2;
	} else if (y <= -6.6e+72) {
		tmp = t_1;
	} else if (y <= -235.0) {
		tmp = t_3;
	} else if (y <= -1.02e-50) {
		tmp = t_1;
	} else if (y <= -2.1e-88) {
		tmp = t_3;
	} else if (y <= 0.0011) {
		tmp = t_1;
	} else if (y <= 2.55e+91) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    t_3 = (y * 5.0d0) + (x * t)
    if (y <= (-1.16d+129)) then
        tmp = t_2
    else if (y <= (-6.6d+72)) then
        tmp = t_1
    else if (y <= (-235.0d0)) then
        tmp = t_3
    else if (y <= (-1.02d-50)) then
        tmp = t_1
    else if (y <= (-2.1d-88)) then
        tmp = t_3
    else if (y <= 0.0011d0) then
        tmp = t_1
    else if (y <= 2.55d+91) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double t_3 = (y * 5.0) + (x * t);
	double tmp;
	if (y <= -1.16e+129) {
		tmp = t_2;
	} else if (y <= -6.6e+72) {
		tmp = t_1;
	} else if (y <= -235.0) {
		tmp = t_3;
	} else if (y <= -1.02e-50) {
		tmp = t_1;
	} else if (y <= -2.1e-88) {
		tmp = t_3;
	} else if (y <= 0.0011) {
		tmp = t_1;
	} else if (y <= 2.55e+91) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	t_3 = (y * 5.0) + (x * t)
	tmp = 0
	if y <= -1.16e+129:
		tmp = t_2
	elif y <= -6.6e+72:
		tmp = t_1
	elif y <= -235.0:
		tmp = t_3
	elif y <= -1.02e-50:
		tmp = t_1
	elif y <= -2.1e-88:
		tmp = t_3
	elif y <= 0.0011:
		tmp = t_1
	elif y <= 2.55e+91:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	t_3 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (y <= -1.16e+129)
		tmp = t_2;
	elseif (y <= -6.6e+72)
		tmp = t_1;
	elseif (y <= -235.0)
		tmp = t_3;
	elseif (y <= -1.02e-50)
		tmp = t_1;
	elseif (y <= -2.1e-88)
		tmp = t_3;
	elseif (y <= 0.0011)
		tmp = t_1;
	elseif (y <= 2.55e+91)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	t_3 = (y * 5.0) + (x * t);
	tmp = 0.0;
	if (y <= -1.16e+129)
		tmp = t_2;
	elseif (y <= -6.6e+72)
		tmp = t_1;
	elseif (y <= -235.0)
		tmp = t_3;
	elseif (y <= -1.02e-50)
		tmp = t_1;
	elseif (y <= -2.1e-88)
		tmp = t_3;
	elseif (y <= 0.0011)
		tmp = t_1;
	elseif (y <= 2.55e+91)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.16e+129], t$95$2, If[LessEqual[y, -6.6e+72], t$95$1, If[LessEqual[y, -235.0], t$95$3, If[LessEqual[y, -1.02e-50], t$95$1, If[LessEqual[y, -2.1e-88], t$95$3, If[LessEqual[y, 0.0011], t$95$1, If[LessEqual[y, 2.55e+91], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.16e129 or 2.55000000000000007e91 < 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. Taylor expanded in y around inf 93.0%

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

   4. Simplified 93.0%

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

   if -1.16e129 < y < -6.6e72 or -235 < y < -1.0199999999999999e-50 or -2.1e-88 < y < 0.00110000000000000007

   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 88.6%

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

   if -6.6e72 < y < -235 or -1.0199999999999999e-50 < y < -2.1e-88 or 0.00110000000000000007 < y < 2.55000000000000007e91

   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. +-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-def 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. flip-+ 72.1%

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

      4. associate-*r/ 70.3%

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

      5. fma-neg 70.4%

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

      6. associate-+l+ 70.4%

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

      7. +-commutative 70.4%

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

      8. count-2 70.4%

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

      9. associate-+l+ 70.4%

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

      10. +-commutative 70.4%

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

      11. count-2 70.4%

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

      12. fma-neg 70.3%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 84.2%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{t \cdot x}\right) \]
   5. Step-by-step derivation

      1. *-commutative 84.2%

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

   6. Simplified 84.2%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot t}\right) \]
   7. Step-by-step derivation

      1. fma-udef 84.2%

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

   8. Applied egg-rr 84.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -235:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 0.0011:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+91}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 4: 87.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;t \leq -3 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))))
   (if (<= t -3e+124)
     t_1
     (if (<= t -1.3e+62)
       (* x (+ t (* (+ y z) 2.0)))
       (if (<= t 5e+129) (+ (* 2.0 (* x (+ y z))) (* y 5.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double tmp;
	if (t <= -3e+124) {
		tmp = t_1;
	} else if (t <= -1.3e+62) {
		tmp = x * (t + ((y + z) * 2.0));
	} else if (t <= 5e+129) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} 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 = (y * 5.0d0) + (x * t)
    if (t <= (-3d+124)) then
        tmp = t_1
    else if (t <= (-1.3d+62)) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else if (t <= 5d+129) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    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 = (y * 5.0) + (x * t);
	double tmp;
	if (t <= -3e+124) {
		tmp = t_1;
	} else if (t <= -1.3e+62) {
		tmp = x * (t + ((y + z) * 2.0));
	} else if (t <= 5e+129) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	tmp = 0
	if t <= -3e+124:
		tmp = t_1
	elif t <= -1.3e+62:
		tmp = x * (t + ((y + z) * 2.0))
	elif t <= 5e+129:
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (t <= -3e+124)
		tmp = t_1;
	elseif (t <= -1.3e+62)
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	elseif (t <= 5e+129)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	tmp = 0.0;
	if (t <= -3e+124)
		tmp = t_1;
	elseif (t <= -1.3e+62)
		tmp = x * (t + ((y + z) * 2.0));
	elseif (t <= 5e+129)
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = t_1;
	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]}, If[LessEqual[t, -3e+124], t$95$1, If[LessEqual[t, -1.3e+62], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+129], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e124 or 5.0000000000000003e129 < t

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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-def 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. flip-+ 40.7%

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

      4. associate-*r/ 37.1%

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

      5. fma-neg 40.4%

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

      6. associate-+l+ 40.4%

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

      7. +-commutative 40.4%

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

      8. count-2 40.4%

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

      9. associate-+l+ 40.4%

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

      10. +-commutative 40.4%

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

      11. count-2 40.4%

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

      12. fma-neg 37.1%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 89.8%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{t \cdot x}\right) \]
   5. Step-by-step derivation

      1. *-commutative 89.8%

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

   6. Simplified 89.8%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot t}\right) \]
   7. Step-by-step derivation

      1. fma-udef 89.8%

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

   8. Applied egg-rr 89.8%

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

   if -3e124 < t < -1.29999999999999992e62

   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 85.6%

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

   if -1.29999999999999992e62 < t < 5.0000000000000003e129

   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 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 t around 0 91.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+124}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 5: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+129} \lor \neg \left(y \leq -1.4 \cdot 10^{+78}\right) \land \left(y \leq -2.4 \cdot 10^{+58} \lor \neg \left(y \leq 2.2 \cdot 10^{+55}\right)\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+129)
         (and (not (<= y -1.4e+78)) (or (<= y -2.4e+58) (not (<= y 2.2e+55)))))
   (* 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 <= -1.3e+129) || (!(y <= -1.4e+78) && ((y <= -2.4e+58) || !(y <= 2.2e+55)))) {
		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 <= (-1.3d+129)) .or. (.not. (y <= (-1.4d+78))) .and. (y <= (-2.4d+58)) .or. (.not. (y <= 2.2d+55))) 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 <= -1.3e+129) || (!(y <= -1.4e+78) && ((y <= -2.4e+58) || !(y <= 2.2e+55)))) {
		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 <= -1.3e+129) or (not (y <= -1.4e+78) and ((y <= -2.4e+58) or not (y <= 2.2e+55))):
		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 <= -1.3e+129) || (!(y <= -1.4e+78) && ((y <= -2.4e+58) || !(y <= 2.2e+55))))
		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 <= -1.3e+129) || (~((y <= -1.4e+78)) && ((y <= -2.4e+58) || ~((y <= 2.2e+55)))))
		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, -1.3e+129], And[N[Not[LessEqual[y, -1.4e+78]], $MachinePrecision], Or[LessEqual[y, -2.4e+58], N[Not[LessEqual[y, 2.2e+55]], $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 < -1.30000000000000006e129 or -1.4000000000000001e78 < y < -2.4e58 or 2.2000000000000001e55 < 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. Taylor expanded in y around inf 90.2%

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

   4. Simplified 90.2%

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

   if -1.30000000000000006e129 < y < -1.4000000000000001e78 or -2.4e58 < y < 2.2000000000000001e55

   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 80.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+129} \lor \neg \left(y \leq -1.4 \cdot 10^{+78}\right) \land \left(y \leq -2.4 \cdot 10^{+58} \lor \neg \left(y \leq 2.2 \cdot 10^{+55}\right)\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 6: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+47} \lor \neg \left(z \leq 1.3 \cdot 10^{+76}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+47) (not (<= z 1.3e+76)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))
   (+ (* y 5.0) (* x (+ t (+ y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+47) || !(z <= 1.3e+76)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	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 <= (-6.2d+47)) .or. (.not. (z <= 1.3d+76))) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+47) || !(z <= 1.3e+76)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+47) or not (z <= 1.3e+76):
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+47) || !(z <= 1.3e+76))
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+47) || ~((z <= 1.3e+76)))
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = (y * 5.0) + (x * (t + (y + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+47], N[Not[LessEqual[z, 1.3e+76]], $MachinePrecision]], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000001e47 or 1.3e76 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 t around 0 91.8%

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

   if -6.2000000000000001e47 < z < 1.3e76

   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 inf 95.7%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+47} \lor \neg \left(z \leq 1.3 \cdot 10^{+76}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * (t + (y + (z + (y + z))))) + (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 * (t + (y + (z + (y + z))))) + (y * 5.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 8: 46.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-60} \lor \neg \left(x \leq 2.9 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -1.45e+175)
     t_1
     (if (<= x -7.7e+146)
       (* x t)
       (if (<= x -5e+25)
         t_1
         (if (or (<= x -1.22e-60) (not (<= x 2.9e-31))) (* x t) (* y 5.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.45e+175) {
		tmp = t_1;
	} else if (x <= -7.7e+146) {
		tmp = x * t;
	} else if (x <= -5e+25) {
		tmp = t_1;
	} else if ((x <= -1.22e-60) || !(x <= 2.9e-31)) {
		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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-1.45d+175)) then
        tmp = t_1
    else if (x <= (-7.7d+146)) then
        tmp = x * t
    else if (x <= (-5d+25)) then
        tmp = t_1
    else if ((x <= (-1.22d-60)) .or. (.not. (x <= 2.9d-31))) 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 t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.45e+175) {
		tmp = t_1;
	} else if (x <= -7.7e+146) {
		tmp = x * t;
	} else if (x <= -5e+25) {
		tmp = t_1;
	} else if ((x <= -1.22e-60) || !(x <= 2.9e-31)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -1.45e+175:
		tmp = t_1
	elif x <= -7.7e+146:
		tmp = x * t
	elif x <= -5e+25:
		tmp = t_1
	elif (x <= -1.22e-60) or not (x <= 2.9e-31):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -1.45e+175)
		tmp = t_1;
	elseif (x <= -7.7e+146)
		tmp = Float64(x * t);
	elseif (x <= -5e+25)
		tmp = t_1;
	elseif ((x <= -1.22e-60) || !(x <= 2.9e-31))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -1.45e+175)
		tmp = t_1;
	elseif (x <= -7.7e+146)
		tmp = x * t;
	elseif (x <= -5e+25)
		tmp = t_1;
	elseif ((x <= -1.22e-60) || ~((x <= 2.9e-31)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+175], t$95$1, If[LessEqual[x, -7.7e+146], N[(x * t), $MachinePrecision], If[LessEqual[x, -5e+25], t$95$1, If[Or[LessEqual[x, -1.22e-60], N[Not[LessEqual[x, 2.9e-31]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e175 or -7.7000000000000002e146 < x < -5.00000000000000024e25

   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 z around inf 51.3%

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

   if -1.45e175 < x < -7.7000000000000002e146 or -5.00000000000000024e25 < x < -1.22e-60 or 2.9000000000000001e-31 < 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 t around inf 48.4%

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

   if -1.22e-60 < x < 2.9000000000000001e-31

   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 x around 0 66.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+175}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7.7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+25}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-60} \lor \neg \left(x \leq 2.9 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 9: 87.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-50} \lor \neg \left(x \leq 2.25 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.8e-50) (not (<= x 2.25e-22)))
   (* 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 <= -9.8e-50) || !(x <= 2.25e-22)) {
		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 <= (-9.8d-50)) .or. (.not. (x <= 2.25d-22))) 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 <= -9.8e-50) || !(x <= 2.25e-22)) {
		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 <= -9.8e-50) or not (x <= 2.25e-22):
		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 <= -9.8e-50) || !(x <= 2.25e-22))
		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 <= -9.8e-50) || ~((x <= 2.25e-22)))
		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, -9.8e-50], N[Not[LessEqual[x, 2.25e-22]], $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 < -9.7999999999999997e-50 or 2.24999999999999993e-22 < 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 95.1%

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

   if -9.7999999999999997e-50 < x < 2.24999999999999993e-22

   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. +-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-def 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. flip-+ 38.6%

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

      4. associate-*r/ 38.6%

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

      5. fma-neg 38.9%

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

      6. associate-+l+ 38.9%

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

      7. +-commutative 38.9%

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

      8. count-2 38.9%

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

      9. associate-+l+ 38.9%

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

      10. +-commutative 38.9%

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

      11. count-2 38.9%

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

      12. fma-neg 38.6%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 82.9%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{t \cdot x}\right) \]
   5. Step-by-step derivation

      1. *-commutative 82.9%

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

   6. Simplified 82.9%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot t}\right) \]
   7. Step-by-step derivation

      1. fma-udef 82.8%

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

   8. Applied egg-rr 82.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-50} \lor \neg \left(x \leq 2.25 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 10: 64.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+143} \lor \neg \left(y \leq 3 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+143) (not (<= y 3e+55))) (* y 5.0) (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+143) || !(y <= 3e+55)) {
		tmp = y * 5.0;
	} 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 <= (-7.5d+143)) .or. (.not. (y <= 3d+55))) then
        tmp = y * 5.0d0
    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 <= -7.5e+143) || !(y <= 3e+55)) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+143) or not (y <= 3e+55):
		tmp = y * 5.0
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+143) || !(y <= 3e+55))
		tmp = Float64(y * 5.0);
	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 <= -7.5e+143) || ~((y <= 3e+55)))
		tmp = y * 5.0;
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+143], N[Not[LessEqual[y, 3e+55]], $MachinePrecision]], N[(y * 5.0), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999974e143 or 3.00000000000000017e55 < 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. Taylor expanded in x around 0 60.2%

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

   if -7.49999999999999974e143 < y < 3.00000000000000017e55

   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 77.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+143} \lor \neg \left(y \leq 3 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 11: 45.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-60} \lor \neg \left(x \leq 5.5 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.1e-60) (not (<= x 5.5e-29))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-60) || !(x <= 5.5e-29)) {
		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 <= (-2.1d-60)) .or. (.not. (x <= 5.5d-29))) 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 <= -2.1e-60) || !(x <= 5.5e-29)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.1e-60) or not (x <= 5.5e-29):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.1e-60) || !(x <= 5.5e-29))
		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 <= -2.1e-60) || ~((x <= 5.5e-29)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e-60], N[Not[LessEqual[x, 5.5e-29]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999991e-60 or 5.4999999999999999e-29 < 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 t around inf 42.8%

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

   if -2.09999999999999991e-60 < x < 5.4999999999999999e-29

   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 x around 0 66.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-60} \lor \neg \left(x \leq 5.5 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 12: 28.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 5 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = y * 5.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 33.0%

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

3. Final simplification 33.0%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023310 
(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)))