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

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 13

Speedup: 1.2×

• 26.6% 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 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -1.46 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-163}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -1.46e+214)
     (* x (+ t (* y 2.0)))
     (if (<= x -6.5e+24)
       (* x (* (+ y z) 2.0))
       (if (<= x -4.2e-71) t_1 (if (<= x 1.55e-163) (* 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 <= -1.46e+214) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= -6.5e+24) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= -4.2e-71) {
		tmp = t_1;
	} else if (x <= 1.55e-163) {
		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 <= (-1.46d+214)) then
        tmp = x * (t + (y * 2.0d0))
    else if (x <= (-6.5d+24)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (x <= (-4.2d-71)) then
        tmp = t_1
    else if (x <= 1.55d-163) 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 <= -1.46e+214) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= -6.5e+24) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= -4.2e-71) {
		tmp = t_1;
	} else if (x <= 1.55e-163) {
		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 <= -1.46e+214:
		tmp = x * (t + (y * 2.0))
	elif x <= -6.5e+24:
		tmp = x * ((y + z) * 2.0)
	elif x <= -4.2e-71:
		tmp = t_1
	elif x <= 1.55e-163:
		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 <= -1.46e+214)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif (x <= -6.5e+24)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (x <= -4.2e-71)
		tmp = t_1;
	elseif (x <= 1.55e-163)
		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 <= -1.46e+214)
		tmp = x * (t + (y * 2.0));
	elseif (x <= -6.5e+24)
		tmp = x * ((y + z) * 2.0);
	elseif (x <= -4.2e-71)
		tmp = t_1;
	elseif (x <= 1.55e-163)
		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, -1.46e+214], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e+24], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-71], t$95$1, If[LessEqual[x, 1.55e-163], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.46e214

   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 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 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 94.7%

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

   10. Simplified 94.7%

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

   if -1.46e214 < x < -6.4999999999999996e24

   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 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 89.6%

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

   10. Simplified 89.6%

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

   if -6.4999999999999996e24 < x < -4.2000000000000002e-71 or 1.54999999999999987e-163 < 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 72.1%

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

   7. Simplified 72.1%

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

   if -4.2000000000000002e-71 < x < 1.54999999999999987e-163

   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 66.7%

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

   7. Simplified 66.7%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-163}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-265}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -1.9e-23)
     t_1
     (if (<= x -7.5e-265)
       (+ (* x t) (* y 5.0))
       (if (<= x 3.6e-57) (+ (* x (* z 2.0)) (* y 5.0)) 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 <= -1.9e-23) {
		tmp = t_1;
	} else if (x <= -7.5e-265) {
		tmp = (x * t) + (y * 5.0);
	} else if (x <= 3.6e-57) {
		tmp = (x * (z * 2.0)) + (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 + ((y + z) * 2.0d0))
    if (x <= (-1.9d-23)) then
        tmp = t_1
    else if (x <= (-7.5d-265)) then
        tmp = (x * t) + (y * 5.0d0)
    else if (x <= 3.6d-57) then
        tmp = (x * (z * 2.0d0)) + (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 + ((y + z) * 2.0));
	double tmp;
	if (x <= -1.9e-23) {
		tmp = t_1;
	} else if (x <= -7.5e-265) {
		tmp = (x * t) + (y * 5.0);
	} else if (x <= 3.6e-57) {
		tmp = (x * (z * 2.0)) + (y * 5.0);
	} 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 <= -1.9e-23:
		tmp = t_1
	elif x <= -7.5e-265:
		tmp = (x * t) + (y * 5.0)
	elif x <= 3.6e-57:
		tmp = (x * (z * 2.0)) + (y * 5.0)
	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 <= -1.9e-23)
		tmp = t_1;
	elseif (x <= -7.5e-265)
		tmp = Float64(Float64(x * t) + Float64(y * 5.0));
	elseif (x <= 3.6e-57)
		tmp = Float64(Float64(x * Float64(z * 2.0)) + 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 + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -1.9e-23)
		tmp = t_1;
	elseif (x <= -7.5e-265)
		tmp = (x * t) + (y * 5.0);
	elseif (x <= 3.6e-57)
		tmp = (x * (z * 2.0)) + (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[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e-23], t$95$1, If[LessEqual[x, -7.5e-265], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-57], N[(N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000006e-23 or 3.6000000000000002e-57 < 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 96.4%

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

   7. Simplified 96.4%

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

   if -1.90000000000000006e-23 < x < -7.5000000000000001e-265

   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 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 83.9%

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

   7. Simplified 83.9%

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

   if -7.5000000000000001e-265 < x < 3.6000000000000002e-57

   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 83.1%

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

   7. Simplified 83.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-265}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+214}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e+214)
   (* x t)
   (if (<= x -1.7e+28)
     (* x (* y 2.0))
     (if (<= x -1.35e-69) (* x t) (if (<= x 4e-57) (* y 5.0) (* x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e+214) {
		tmp = x * t;
	} else if (x <= -1.7e+28) {
		tmp = x * (y * 2.0);
	} else if (x <= -1.35e-69) {
		tmp = x * t;
	} else if (x <= 4e-57) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.55d+214)) then
        tmp = x * t
    else if (x <= (-1.7d+28)) then
        tmp = x * (y * 2.0d0)
    else if (x <= (-1.35d-69)) then
        tmp = x * t
    else if (x <= 4d-57) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e+214) {
		tmp = x * t;
	} else if (x <= -1.7e+28) {
		tmp = x * (y * 2.0);
	} else if (x <= -1.35e-69) {
		tmp = x * t;
	} else if (x <= 4e-57) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e+214:
		tmp = x * t
	elif x <= -1.7e+28:
		tmp = x * (y * 2.0)
	elif x <= -1.35e-69:
		tmp = x * t
	elif x <= 4e-57:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e+214)
		tmp = Float64(x * t);
	elseif (x <= -1.7e+28)
		tmp = Float64(x * Float64(y * 2.0));
	elseif (x <= -1.35e-69)
		tmp = Float64(x * t);
	elseif (x <= 4e-57)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.55e+214)
		tmp = x * t;
	elseif (x <= -1.7e+28)
		tmp = x * (y * 2.0);
	elseif (x <= -1.35e-69)
		tmp = x * t;
	elseif (x <= 4e-57)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e+214], N[(x * t), $MachinePrecision], If[LessEqual[x, -1.7e+28], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-69], N[(x * t), $MachinePrecision], If[LessEqual[x, 4e-57], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.54999999999999989e214 or -1.7e28 < x < -1.3499999999999999e-69 or 3.99999999999999982e-57 < 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 46.2%

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

   7. Simplified 46.2%

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

   if -1.54999999999999989e214 < x < -1.7e28

   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 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 39.4%

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

   10. Simplified 39.4%

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

   if -1.3499999999999999e-69 < x < 3.99999999999999982e-57

   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 61.3%

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

   7. Simplified 61.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+214}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot \left(2 + \frac{z \cdot 2}{y}\right)\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x (+ 2.0 (/ (* z 2.0) y)))))))
   (if (<= y -9.8e+64)
     t_1
     (if (<= y 6.4e+23) (* x (+ t (* (+ y 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 + ((z * 2.0) / y))));
	double tmp;
	if (y <= -9.8e+64) {
		tmp = t_1;
	} else if (y <= 6.4e+23) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * (2.0d0 + ((z * 2.0d0) / y))))
    if (y <= (-9.8d+64)) then
        tmp = t_1
    else if (y <= 6.4d+23) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * (2.0 + ((z * 2.0) / y))));
	double tmp;
	if (y <= -9.8e+64) {
		tmp = t_1;
	} else if (y <= 6.4e+23) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * (2.0 + ((z * 2.0) / y))))
	tmp = 0
	if y <= -9.8e+64:
		tmp = t_1
	elif y <= 6.4e+23:
		tmp = x * (t + ((y + 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 * Float64(2.0 + Float64(Float64(z * 2.0) / y)))))
	tmp = 0.0
	if (y <= -9.8e+64)
		tmp = t_1;
	elseif (y <= 6.4e+23)
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * (2.0 + ((z * 2.0) / y))));
	tmp = 0.0;
	if (y <= -9.8e+64)
		tmp = t_1;
	elseif (y <= 6.4e+23)
		tmp = x * (t + ((y + 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 * N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+64], t$95$1, If[LessEqual[y, 6.4e+23], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.8000000000000005e64 or 6.4e23 < 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

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

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

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

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

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-out N/A

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

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

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

      8. +-commutative N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

      12. *-lowering-*.f64 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0

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

      1. *-lowering-*.f64 93.7%

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

   10. Simplified 93.7%

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

   if -9.8000000000000005e64 < y < 6.4e23

   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 87.2%

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

   7. Simplified 87.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(5 + x \cdot \left(2 + \frac{z \cdot 2}{y}\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot \left(2 + \frac{z \cdot 2}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -7e+214)
     t_1
     (if (<= x -2.4e-23)
       (* x (* (+ y z) 2.0))
       (if (<= x 4.7e-57) (* y 5.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -7e+214) {
		tmp = t_1;
	} else if (x <= -2.4e-23) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= 4.7e-57) {
		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 + (y * 2.0d0))
    if (x <= (-7d+214)) then
        tmp = t_1
    else if (x <= (-2.4d-23)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (x <= 4.7d-57) 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 + (y * 2.0));
	double tmp;
	if (x <= -7e+214) {
		tmp = t_1;
	} else if (x <= -2.4e-23) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= 4.7e-57) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -7e+214:
		tmp = t_1
	elif x <= -2.4e-23:
		tmp = x * ((y + z) * 2.0)
	elif x <= 4.7e-57:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -7e+214)
		tmp = t_1;
	elseif (x <= -2.4e-23)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (x <= 4.7e-57)
		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 + (y * 2.0));
	tmp = 0.0;
	if (x <= -7e+214)
		tmp = t_1;
	elseif (x <= -2.4e-23)
		tmp = x * ((y + z) * 2.0);
	elseif (x <= 4.7e-57)
		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[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+214], t$95$1, If[LessEqual[x, -2.4e-23], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e-57], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999999e214 or 4.6999999999999998e-57 < x

   1. Initial program 100.0%

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

      1. +-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 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 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 71.6%

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

   10. Simplified 71.6%

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

   if -6.9999999999999999e214 < x < -2.39999999999999996e-23

   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 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 83.2%

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

   10. Simplified 83.2%

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

   if -2.39999999999999996e-23 < x < 4.6999999999999998e-57

   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 56.9%

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

   7. Simplified 56.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -2.9e-23) t_1 (if (<= x 4e-57) (+ (* x t) (* y 5.0)) 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 <= -2.9e-23) {
		tmp = t_1;
	} else if (x <= 4e-57) {
		tmp = (x * t) + (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 + ((y + z) * 2.0d0))
    if (x <= (-2.9d-23)) then
        tmp = t_1
    else if (x <= 4d-57) then
        tmp = (x * t) + (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 + ((y + z) * 2.0));
	double tmp;
	if (x <= -2.9e-23) {
		tmp = t_1;
	} else if (x <= 4e-57) {
		tmp = (x * t) + (y * 5.0);
	} 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 <= -2.9e-23:
		tmp = t_1
	elif x <= 4e-57:
		tmp = (x * t) + (y * 5.0)
	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 <= -2.9e-23)
		tmp = t_1;
	elseif (x <= 4e-57)
		tmp = Float64(Float64(x * t) + 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 + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -2.9e-23)
		tmp = t_1;
	elseif (x <= 4e-57)
		tmp = (x * t) + (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[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e-23], t$95$1, If[LessEqual[x, 4e-57], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9000000000000002e-23 or 3.99999999999999982e-57 < 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 96.4%

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

   7. Simplified 96.4%

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

   if -2.9000000000000002e-23 < x < 3.99999999999999982e-57

   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 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 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.9e+214)
   (* x t)
   (if (<= x -2e-23) (* x (* z 2.0)) (if (<= x 2.6e-57) (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e+214) {
		tmp = x * t;
	} else if (x <= -2e-23) {
		tmp = x * (z * 2.0);
	} else if (x <= 2.6e-57) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.9d+214)) then
        tmp = x * t
    else if (x <= (-2d-23)) then
        tmp = x * (z * 2.0d0)
    else if (x <= 2.6d-57) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e+214) {
		tmp = x * t;
	} else if (x <= -2e-23) {
		tmp = x * (z * 2.0);
	} else if (x <= 2.6e-57) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e+214:
		tmp = x * t
	elif x <= -2e-23:
		tmp = x * (z * 2.0)
	elif x <= 2.6e-57:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e+214)
		tmp = Float64(x * t);
	elseif (x <= -2e-23)
		tmp = Float64(x * Float64(z * 2.0));
	elseif (x <= 2.6e-57)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.9e+214)
		tmp = x * t;
	elseif (x <= -2e-23)
		tmp = x * (z * 2.0);
	elseif (x <= 2.6e-57)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.9e+214], N[(x * t), $MachinePrecision], If[LessEqual[x, -2e-23], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-57], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.89999999999999999e214 or 2.59999999999999985e-57 < x

   1. Initial program 100.0%

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

      1. +-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

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.2%

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

   7. Simplified 49.2%

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

   if -1.89999999999999999e214 < x < -1.99999999999999992e-23

   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 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 53.9%

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

   7. Simplified 53.9%

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

   if -1.99999999999999992e-23 < x < 2.59999999999999985e-57

   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 56.9%

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

   7. Simplified 56.9%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -6.8e+127) t_1 (if (<= y 6.5e+86) (* 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 <= -6.8e+127) {
		tmp = t_1;
	} else if (y <= 6.5e+86) {
		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 <= (-6.8d+127)) then
        tmp = t_1
    else if (y <= 6.5d+86) 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 <= -6.8e+127) {
		tmp = t_1;
	} else if (y <= 6.5e+86) {
		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 <= -6.8e+127:
		tmp = t_1
	elif y <= 6.5e+86:
		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 <= -6.8e+127)
		tmp = t_1;
	elseif (y <= 6.5e+86)
		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 <= -6.8e+127)
		tmp = t_1;
	elseif (y <= 6.5e+86)
		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, -6.8e+127], t$95$1, If[LessEqual[y, 6.5e+86], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.79999999999999955e127 or 6.49999999999999996e86 < 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 84.8%

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

   7. Simplified 84.8%

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

   if -6.79999999999999955e127 < y < 6.49999999999999996e86

   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 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e+22)
   (* x t)
   (if (<= t 2.55e+132) (* x (* (+ y z) 2.0)) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+22) {
		tmp = x * t;
	} else if (t <= 2.55e+132) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d+22)) then
        tmp = x * t
    else if (t <= 2.55d+132) then
        tmp = x * ((y + z) * 2.0d0)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+22) {
		tmp = x * t;
	} else if (t <= 2.55e+132) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e+22:
		tmp = x * t
	elif t <= 2.55e+132:
		tmp = x * ((y + z) * 2.0)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e+22)
		tmp = Float64(x * t);
	elseif (t <= 2.55e+132)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e+22)
		tmp = x * t;
	elseif (t <= 2.55e+132)
		tmp = x * ((y + z) * 2.0);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e+22], N[(x * t), $MachinePrecision], If[LessEqual[t, 2.55e+132], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e22 or 2.55e132 < t

   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 62.2%

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

   7. Simplified 62.2%

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

   if -1.5e22 < t < 2.55e132

   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 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 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-69) (* x t) (if (<= x 2.5e-57) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-69) {
		tmp = x * t;
	} else if (x <= 2.5e-57) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.35d-69)) then
        tmp = x * t
    else if (x <= 2.5d-57) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-69) {
		tmp = x * t;
	} else if (x <= 2.5e-57) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-69:
		tmp = x * t
	elif x <= 2.5e-57:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-69)
		tmp = Float64(x * t);
	elseif (x <= 2.5e-57)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.35e-69)
		tmp = x * t;
	elseif (x <= 2.5e-57)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-69], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.5e-57], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3499999999999999e-69 or 2.5000000000000001e-57 < 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 37.0%

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

   7. Simplified 37.0%

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

   if -1.3499999999999999e-69 < x < 2.5000000000000001e-57

   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 61.3%

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

   7. Simplified 61.3%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 13: 30.5% 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 24.7%

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

7. Simplified 24.7%

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

8. Final simplification 24.7%

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

Reproduce

herbie shell --seed 2024161 
(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)))