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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 11

Speedup: 1.2×

• 27.8% 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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   4. associate-+l+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   6. count-2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   10. *-lowering-*.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

3. Simplified 99.9%

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

   1. +-commutative N/A

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

   2. fma-define N/A

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

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

      \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{5}, \left(x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(y, 5, \mathsf{*.f64}\left(x, \left(\left(y + z\right) \cdot 2 + t\right)\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(y, 5, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(y, 5, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right)\right) \]

   7. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{fma.f64}\left(y, 5, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right)\right) \]

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;x \cdot t - y \cdot \left(-5 + x \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -8.5e-72)
     t_1
     (if (<= x 3.2e-263)
       (+ (* y 5.0) (* x (* z 2.0)))
       (if (<= x 4.6e-63) (- (* x t) (* y (+ -5.0 (* x -2.0)))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -8.5e-72) {
		tmp = t_1;
	} else if (x <= 3.2e-263) {
		tmp = (y * 5.0) + (x * (z * 2.0));
	} else if (x <= 4.6e-63) {
		tmp = (x * t) - (y * (-5.0 + (x * -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 * (t + ((y + z) * 2.0d0))
    if (x <= (-8.5d-72)) then
        tmp = t_1
    else if (x <= 3.2d-263) then
        tmp = (y * 5.0d0) + (x * (z * 2.0d0))
    else if (x <= 4.6d-63) then
        tmp = (x * t) - (y * ((-5.0d0) + (x * (-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 * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -8.5e-72) {
		tmp = t_1;
	} else if (x <= 3.2e-263) {
		tmp = (y * 5.0) + (x * (z * 2.0));
	} else if (x <= 4.6e-63) {
		tmp = (x * t) - (y * (-5.0 + (x * -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -8.5e-72:
		tmp = t_1
	elif x <= 3.2e-263:
		tmp = (y * 5.0) + (x * (z * 2.0))
	elif x <= 4.6e-63:
		tmp = (x * t) - (y * (-5.0 + (x * -2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -8.5e-72)
		tmp = t_1;
	elseif (x <= 3.2e-263)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(z * 2.0)));
	elseif (x <= 4.6e-63)
		tmp = Float64(Float64(x * t) - Float64(y * Float64(-5.0 + Float64(x * -2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -8.5e-72)
		tmp = t_1;
	elseif (x <= 3.2e-263)
		tmp = (y * 5.0) + (x * (z * 2.0));
	elseif (x <= 4.6e-63)
		tmp = (x * t) - (y * (-5.0 + (x * -2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-72], t$95$1, If[LessEqual[x, 3.2e-263], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-63], N[(N[(x * t), $MachinePrecision] - N[(y * N[(-5.0 + N[(x * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.50000000000000008e-72 or 4.6e-63 < x

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. +-lowering-+.f64 93.0%

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

   7. Simplified 93.0%

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

   if -8.50000000000000008e-72 < x < 3.2e-263

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot \left(x \cdot z\right)\right)}, \mathsf{*.f64}\left(y, 5\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(2 \cdot x\right) \cdot z\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x \cdot 2\right) \cdot z\right), \mathsf{*.f64}\left(y, 5\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(2 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(2 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      5. *-lowering-*.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(2, z\right)\right), \mathsf{*.f64}\left(y, 5\right)\right) \]

   7. Simplified 93.3%

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

   if 3.2e-263 < x < 4.6e-63

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(t \cdot x + x \cdot \left(2 \cdot y\right)\right) + 5 \cdot y \]

      4. associate-+l+ N/A

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

      5. *-commutative N/A

         \[\leadsto t \cdot x + \left(x \cdot \left(y \cdot 2\right) + 5 \cdot y\right) \]

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

         \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(-2\right)\right) \cdot \left(x \cdot y\right) + 5 \cdot y\right) \]

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

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

      10. associate-*l* N/A

          \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(\left(-2 \cdot x\right) \cdot y\right)\right) + 5 \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x\right)\right)\right) + 5 \cdot y\right) \]

      12. metadata-eval N/A

          \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x\right)\right)\right) + \left(-5 \cdot -1\right) \cdot y\right) \]

      13. associate-*r* N/A

          \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x\right)\right)\right) + -5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      14. mul-1-neg N/A

          \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x\right)\right)\right) + -5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right) \]

      15. distribute-rgt-neg-out N/A

          \[\leadsto t \cdot x + \left(\left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x\right)\right)\right) + \left(\mathsf{neg}\left(-5 \cdot y\right)\right)\right) \]

      16. distribute-neg-in N/A

          \[\leadsto t \cdot x + \left(\mathsf{neg}\left(\left(y \cdot \left(-2 \cdot x\right) + -5 \cdot y\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto t \cdot x + \left(\mathsf{neg}\left(\left(y \cdot \left(-2 \cdot x\right) + y \cdot -5\right)\right)\right) \]

      18. distribute-lft-in N/A

          \[\leadsto t \cdot x + \left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x + -5\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto t \cdot x + \left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x + \left(\mathsf{neg}\left(5\right)\right)\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto t \cdot x + \left(\mathsf{neg}\left(y \cdot \left(-2 \cdot x - 5\right)\right)\right) \]

   7. Simplified 89.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;x \cdot t - y \cdot \left(-5 + x \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -7.5e-72)
     t_1
     (if (<= x 1.95e-268)
       (+ (* y 5.0) (* x (* z 2.0)))
       (if (<= x 5.5e-63) (+ (* y 5.0) (* x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -7.5e-72) {
		tmp = t_1;
	} else if (x <= 1.95e-268) {
		tmp = (y * 5.0) + (x * (z * 2.0));
	} else if (x <= 5.5e-63) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + ((y + z) * 2.0d0))
    if (x <= (-7.5d-72)) then
        tmp = t_1
    else if (x <= 1.95d-268) then
        tmp = (y * 5.0d0) + (x * (z * 2.0d0))
    else if (x <= 5.5d-63) then
        tmp = (y * 5.0d0) + (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -7.5e-72) {
		tmp = t_1;
	} else if (x <= 1.95e-268) {
		tmp = (y * 5.0) + (x * (z * 2.0));
	} else if (x <= 5.5e-63) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -7.5e-72:
		tmp = t_1
	elif x <= 1.95e-268:
		tmp = (y * 5.0) + (x * (z * 2.0))
	elif x <= 5.5e-63:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -7.5e-72)
		tmp = t_1;
	elseif (x <= 1.95e-268)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(z * 2.0)));
	elseif (x <= 5.5e-63)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -7.5e-72)
		tmp = t_1;
	elseif (x <= 1.95e-268)
		tmp = (y * 5.0) + (x * (z * 2.0));
	elseif (x <= 5.5e-63)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e-72], t$95$1, If[LessEqual[x, 1.95e-268], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-63], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000004e-72 or 5.50000000000000043e-63 < x

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. +-lowering-+.f64 93.0%

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

   7. Simplified 93.0%

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

   if -7.5000000000000004e-72 < x < 1.9499999999999999e-268

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot \left(x \cdot z\right)\right)}, \mathsf{*.f64}\left(y, 5\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(2 \cdot x\right) \cdot z\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x \cdot 2\right) \cdot z\right), \mathsf{*.f64}\left(y, 5\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(2 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(2 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      5. *-lowering-*.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(2, z\right)\right), \mathsf{*.f64}\left(y, 5\right)\right) \]

   7. Simplified 93.3%

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

   if 1.9499999999999999e-268 < x < 5.50000000000000043e-63

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot x\right)}, \mathsf{*.f64}\left(y, 5\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot t\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      2. *-lowering-*.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, t\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

   7. Simplified 89.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 10^{+53}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.8e+109)
     t_1
     (if (<= y -8.2e-63)
       (+ (* y 5.0) (* x t))
       (if (<= y 1e+53) (* x (+ t (* z 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.8e+109) {
		tmp = t_1;
	} else if (y <= -8.2e-63) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1e+53) {
		tmp = x * (t + (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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.8d+109)) then
        tmp = t_1
    else if (y <= (-8.2d-63)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1d+53) then
        tmp = x * (t + (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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.8e+109) {
		tmp = t_1;
	} else if (y <= -8.2e-63) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1e+53) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.8e+109:
		tmp = t_1
	elif y <= -8.2e-63:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1e+53:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_1
	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 <= -1.8e+109)
		tmp = t_1;
	elseif (y <= -8.2e-63)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1e+53)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_1;
	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 <= -1.8e+109)
		tmp = t_1;
	elseif (y <= -8.2e-63)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1e+53)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_1;
	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, -1.8e+109], t$95$1, If[LessEqual[y, -8.2e-63], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+53], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e109 or 9.9999999999999999e52 < 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. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(5 + 2 \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(5, \color{blue}{\left(2 \cdot x\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(5, \left(x \cdot \color{blue}{2}\right)\right)\right) \]

      4. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(5, \mathsf{*.f64}\left(x, \color{blue}{2}\right)\right)\right) \]

   7. Simplified 84.4%

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

   if -1.8e109 < y < -8.1999999999999995e-63

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot x\right)}, \mathsf{*.f64}\left(y, 5\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot t\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      2. *-lowering-*.f64 75.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, t\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

   7. Simplified 75.1%

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

   if -8.1999999999999995e-63 < y < 9.9999999999999999e52

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

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

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

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

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

      3. *-lowering-*.f64 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 10^{+53}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-72}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9e-72)
   (* x t)
   (if (<= x 3.3e-63) (* y 5.0) (if (<= x 1.4e+68) (* x (* z 2.0)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9e-72) {
		tmp = x * t;
	} else if (x <= 3.3e-63) {
		tmp = y * 5.0;
	} else if (x <= 1.4e+68) {
		tmp = x * (z * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9d-72)) then
        tmp = x * t
    else if (x <= 3.3d-63) then
        tmp = y * 5.0d0
    else if (x <= 1.4d+68) then
        tmp = x * (z * 2.0d0)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9e-72) {
		tmp = x * t;
	} else if (x <= 3.3e-63) {
		tmp = y * 5.0;
	} else if (x <= 1.4e+68) {
		tmp = x * (z * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9e-72:
		tmp = x * t
	elif x <= 3.3e-63:
		tmp = y * 5.0
	elif x <= 1.4e+68:
		tmp = x * (z * 2.0)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9e-72)
		tmp = Float64(x * t);
	elseif (x <= 3.3e-63)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.4e+68)
		tmp = Float64(x * Float64(z * 2.0));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9e-72)
		tmp = x * t;
	elseif (x <= 3.3e-63)
		tmp = y * 5.0;
	elseif (x <= 1.4e+68)
		tmp = x * (z * 2.0);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9e-72], N[(x * t), $MachinePrecision], If[LessEqual[x, 3.3e-63], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.4e+68], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e-72 or 1.4e68 < x

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 54.2%

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

   7. Simplified 54.2%

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

   if -9e-72 < x < 3.29999999999999994e-63

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{y}\right) \]

   7. Simplified 70.6%

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

   if 3.29999999999999994e-63 < x < 1.4e68

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(x \cdot 2\right) \cdot z \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(2, \color{blue}{z}\right)\right) \]

   7. Simplified 56.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-72}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-69}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -8.5e-57) t_1 (if (<= x 2.25e-69) (+ (* y 5.0) (* x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -8.5e-57) {
		tmp = t_1;
	} else if (x <= 2.25e-69) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + ((y + z) * 2.0d0))
    if (x <= (-8.5d-57)) then
        tmp = t_1
    else if (x <= 2.25d-69) then
        tmp = (y * 5.0d0) + (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -8.5e-57) {
		tmp = t_1;
	} else if (x <= 2.25e-69) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -8.5e-57:
		tmp = t_1
	elif x <= 2.25e-69:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -8.5e-57)
		tmp = t_1;
	elseif (x <= 2.25e-69)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -8.5e-57)
		tmp = t_1;
	elseif (x <= 2.25e-69)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-57], t$95$1, If[LessEqual[x, 2.25e-69], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999955e-57 or 2.25000000000000005e-69 < x

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. +-lowering-+.f64 93.5%

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

   7. Simplified 93.5%

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

   if -8.49999999999999955e-57 < x < 2.25000000000000005e-69

   1. Initial program 99.9%

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot x\right)}, \mathsf{*.f64}\left(y, 5\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot t\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

      2. *-lowering-*.f64 85.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, t\right), \mathsf{*.f64}\left(\color{blue}{y}, 5\right)\right) \]

   7. Simplified 85.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-69}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -8.5e+90) t_1 (if (<= y 5.2e+51) (* x (+ t (* z 2.0))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.5e+90) {
		tmp = t_1;
	} else if (y <= 5.2e+51) {
		tmp = x * (t + (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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-8.5d+90)) then
        tmp = t_1
    else if (y <= 5.2d+51) then
        tmp = x * (t + (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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.5e+90) {
		tmp = t_1;
	} else if (y <= 5.2e+51) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -8.5e+90:
		tmp = t_1
	elif y <= 5.2e+51:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_1
	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 <= -8.5e+90)
		tmp = t_1;
	elseif (y <= 5.2e+51)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_1;
	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 <= -8.5e+90)
		tmp = t_1;
	elseif (y <= 5.2e+51)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_1;
	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, -8.5e+90], t$95$1, If[LessEqual[y, 5.2e+51], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000002e90 or 5.2000000000000002e51 < 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. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(5 + 2 \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(5, \color{blue}{\left(2 \cdot x\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(5, \left(x \cdot \color{blue}{2}\right)\right)\right) \]

      4. *-lowering-*.f64 82.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(5, \mathsf{*.f64}\left(x, \color{blue}{2}\right)\right)\right) \]

   7. Simplified 82.9%

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

   if -8.5000000000000002e90 < y < 5.2000000000000002e51

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

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

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

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

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

      3. *-lowering-*.f64 79.9%

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

   7. Simplified 79.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -1.65e-77) t_1 (if (<= x 3.1e-125) (* y 5.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -1.65e-77) {
		tmp = t_1;
	} else if (x <= 3.1e-125) {
		tmp = 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 = x * (t + (z * 2.0d0))
    if (x <= (-1.65d-77)) then
        tmp = t_1
    else if (x <= 3.1d-125) then
        tmp = 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 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -1.65e-77) {
		tmp = t_1;
	} else if (x <= 3.1e-125) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -1.65e-77:
		tmp = t_1
	elif x <= 3.1e-125:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -1.65e-77)
		tmp = t_1;
	elseif (x <= 3.1e-125)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -1.65e-77)
		tmp = t_1;
	elseif (x <= 3.1e-125)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e-77], t$95$1, If[LessEqual[x, 3.1e-125], N[(y * 5.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.64999999999999996e-77 or 3.10000000000000013e-125 < x

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

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

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

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

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

      3. *-lowering-*.f64 75.1%

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

   7. Simplified 75.1%

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

   if -1.64999999999999996e-77 < x < 3.10000000000000013e-125

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 76.0%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{y}\right) \]

   7. Simplified 76.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.145:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.2e-72) (* x t) (if (<= x 0.145) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.2e-72) {
		tmp = x * t;
	} else if (x <= 0.145) {
		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 <= (-8.2d-72)) then
        tmp = x * t
    else if (x <= 0.145d0) 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 <= -8.2e-72) {
		tmp = x * t;
	} else if (x <= 0.145) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.2e-72:
		tmp = x * t
	elif x <= 0.145:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.2e-72)
		tmp = Float64(x * t);
	elseif (x <= 0.145)
		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 <= -8.2e-72)
		tmp = x * t;
	elseif (x <= 0.145)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.2e-72], N[(x * t), $MachinePrecision], If[LessEqual[x, 0.145], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000007e-72 or 0.14499999999999999 < x

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 50.5%

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

   7. Simplified 50.5%

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

   if -8.20000000000000007e-72 < x < 0.14499999999999999

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      6. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 65.7%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{y}\right) \]

   7. Simplified 65.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.145:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   4. associate-+l+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   6. count-2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   10. *-lowering-*.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 11: 29.1% 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 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. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \color{blue}{\left(y \cdot 5\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right), \left(\color{blue}{y} \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\left(y + z\right) + z\right) + y\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   4. associate-+l+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(z + y\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) + \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   6. count-2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(2 \cdot \left(y + z\right)\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(y + z\right) \cdot 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \left(y \cdot 5\right)\right) \]

   10. *-lowering-*.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, z\right), 2\right), t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{5}\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 33.0%

      \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{y}\right) \]

7. Simplified 33.0%

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

8. Final simplification 33.0%

   \[\leadsto y \cdot 5 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(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)))