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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 10

Speedup: 1.2×

• 26.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

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

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

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

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

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

   4. associate-+l+ N/A

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

   5. +-commutative N/A

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

   6. count-2 N/A

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

   7. *-commutative N/A

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

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

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

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

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

   10. *-lowering-*.f64 99.9%

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

3. Simplified 99.9%

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

   1. +-commutative N/A

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

   2. fma-define N/A

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

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

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

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

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

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

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

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

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

   7. +-lowering-+.f64 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(z \cdot 2 + \left(t + y \cdot \frac{5}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -7.4e+141)
     t_1
     (if (<= y 4.2e+127) (* x (+ (* z 2.0) (+ t (* y (/ 5.0 x))))) 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 <= -7.4e+141) {
		tmp = t_1;
	} else if (y <= 4.2e+127) {
		tmp = x * ((z * 2.0) + (t + (y * (5.0 / x))));
	} 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 <= (-7.4d+141)) then
        tmp = t_1
    else if (y <= 4.2d+127) then
        tmp = x * ((z * 2.0d0) + (t + (y * (5.0d0 / x))))
    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 <= -7.4e+141) {
		tmp = t_1;
	} else if (y <= 4.2e+127) {
		tmp = x * ((z * 2.0) + (t + (y * (5.0 / x))));
	} 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 <= -7.4e+141:
		tmp = t_1
	elif y <= 4.2e+127:
		tmp = x * ((z * 2.0) + (t + (y * (5.0 / x))))
	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 <= -7.4e+141)
		tmp = t_1;
	elseif (y <= 4.2e+127)
		tmp = Float64(x * Float64(Float64(z * 2.0) + Float64(t + Float64(y * Float64(5.0 / x)))));
	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 <= -7.4e+141)
		tmp = t_1;
	elseif (y <= 4.2e+127)
		tmp = x * ((z * 2.0) + (t + (y * (5.0 / x))));
	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, -7.4e+141], t$95$1, If[LessEqual[y, 4.2e+127], N[(x * N[(N[(z * 2.0), $MachinePrecision] + N[(t + N[(y * N[(5.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4000000000000006e141 or 4.19999999999999983e127 < y

   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 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 89.6%

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

   7. Simplified 89.6%

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

   if -7.4000000000000006e141 < y < 4.19999999999999983e127

   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

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

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

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. associate-+l+ N/A

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

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

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

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

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

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

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

      10. +-commutative N/A

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

      11. associate-*r/ N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. distribute-lft-out N/A

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

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

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

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

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

      18. /-lowering-/.f64 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 92.0%

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

   10. Simplified 92.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(z \cdot 2 + \left(t + y \cdot \frac{5}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.05e+130)
     t_1
     (if (<= y -2e-94)
       (+ (* x t) (* y 5.0))
       (if (<= y 2e+127) (* x (+ t (* z 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.05e+130) {
		tmp = t_1;
	} else if (y <= -2e-94) {
		tmp = (x * t) + (y * 5.0);
	} else if (y <= 2e+127) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.05d+130)) then
        tmp = t_1
    else if (y <= (-2d-94)) then
        tmp = (x * t) + (y * 5.0d0)
    else if (y <= 2d+127) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.05e+130) {
		tmp = t_1;
	} else if (y <= -2e-94) {
		tmp = (x * t) + (y * 5.0);
	} else if (y <= 2e+127) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.05e+130:
		tmp = t_1
	elif y <= -2e-94:
		tmp = (x * t) + (y * 5.0)
	elif y <= 2e+127:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.05e+130)
		tmp = t_1;
	elseif (y <= -2e-94)
		tmp = Float64(Float64(x * t) + Float64(y * 5.0));
	elseif (y <= 2e+127)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.05e+130)
		tmp = t_1;
	elseif (y <= -2e-94)
		tmp = (x * t) + (y * 5.0);
	elseif (y <= 2e+127)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+130], t$95$1, If[LessEqual[y, -2e-94], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+127], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999995e130 or 1.99999999999999991e127 < 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 87.2%

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

   7. Simplified 87.2%

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

   if -1.04999999999999995e130 < y < -1.9999999999999999e-94

   1. Initial program 99.9%

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

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

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

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

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

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

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. count-2 N/A

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

      7. *-commutative N/A

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

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

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

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

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

      10. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 71.7%

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

   7. Simplified 71.7%

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

   if -1.9999999999999999e-94 < y < 1.99999999999999991e127

   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 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 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-14}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -1.8) t_1 (if (<= x 9e-14) (+ (* 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 <= -1.8) {
		tmp = t_1;
	} else if (x <= 9e-14) {
		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 <= (-1.8d0)) then
        tmp = t_1
    else if (x <= 9d-14) 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 <= -1.8) {
		tmp = t_1;
	} else if (x <= 9e-14) {
		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 <= -1.8:
		tmp = t_1
	elif x <= 9e-14:
		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 <= -1.8)
		tmp = t_1;
	elseif (x <= 9e-14)
		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 <= -1.8)
		tmp = t_1;
	elseif (x <= 9e-14)
		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, -1.8], t$95$1, If[LessEqual[x, 9e-14], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000004 or 8.9999999999999995e-14 < 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 98.1%

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

   7. Simplified 98.1%

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

   if -1.80000000000000004 < x < 8.9999999999999995e-14

   1. Initial program 99.9%

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

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

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

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

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

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

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. count-2 N/A

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

      7. *-commutative N/A

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

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

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

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

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

      10. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-14}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.9e+61) t_1 (if (<= y 3.6e+127) (* x (+ t (* z 2.0))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.9e+61) {
		tmp = t_1;
	} else if (y <= 3.6e+127) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.9d+61)) then
        tmp = t_1
    else if (y <= 3.6d+127) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.9e+61) {
		tmp = t_1;
	} else if (y <= 3.6e+127) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.9e+61:
		tmp = t_1
	elif y <= 3.6e+127:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.9e+61)
		tmp = t_1;
	elseif (y <= 3.6e+127)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.9e+61)
		tmp = t_1;
	elseif (y <= 3.6e+127)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+61], t$95$1, If[LessEqual[y, 3.6e+127], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999998e61 or 3.59999999999999979e127 < 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 83.5%

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

   7. Simplified 83.5%

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

   if -1.89999999999999998e61 < y < 3.59999999999999979e127

   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 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 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 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8)
   (* x (* (+ y z) 2.0))
   (if (<= x 3.15e-27) (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= 3.15e-27) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.8d0)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (x <= 3.15d-27) then
        tmp = y * 5.0d0
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= 3.15e-27) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8:
		tmp = x * ((y + z) * 2.0)
	elif x <= 3.15e-27:
		tmp = y * 5.0
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (x <= 3.15e-27)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8)
		tmp = x * ((y + z) * 2.0);
	elseif (x <= 3.15e-27)
		tmp = y * 5.0;
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.15e-27], N[(y * 5.0), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000004

   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 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in t around 0

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 72.5%

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

   10. Simplified 72.5%

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

   if -1.80000000000000004 < x < 3.15000000000000005e-27

   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 59.9%

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

   7. Simplified 59.9%

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

   if 3.15000000000000005e-27 < 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 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 73.7%

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

   7. Simplified 73.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -1.8) t_1 (if (<= x 2.2e-14) (* y 5.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -1.8) {
		tmp = t_1;
	} else if (x <= 2.2e-14) {
		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 * ((y + z) * 2.0d0)
    if (x <= (-1.8d0)) then
        tmp = t_1
    else if (x <= 2.2d-14) 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 * ((y + z) * 2.0);
	double tmp;
	if (x <= -1.8) {
		tmp = t_1;
	} else if (x <= 2.2e-14) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -1.8:
		tmp = t_1
	elif x <= 2.2e-14:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -1.8)
		tmp = t_1;
	elseif (x <= 2.2e-14)
		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 * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -1.8)
		tmp = t_1;
	elseif (x <= 2.2e-14)
		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[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8], t$95$1, If[LessEqual[x, 2.2e-14], N[(y * 5.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000004 or 2.2000000000000001e-14 < 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 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in t around 0

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 72.0%

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

   10. Simplified 72.0%

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

   if -1.80000000000000004 < x < 2.2000000000000001e-14

   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 58.9%

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

   7. Simplified 58.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9e+73) (* x t) (if (<= t 4.3e+136) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e+73) {
		tmp = x * t;
	} else if (t <= 4.3e+136) {
		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 (t <= (-9d+73)) then
        tmp = x * t
    else if (t <= 4.3d+136) 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 (t <= -9e+73) {
		tmp = x * t;
	} else if (t <= 4.3e+136) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9e+73:
		tmp = x * t
	elif t <= 4.3e+136:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9e+73)
		tmp = Float64(x * t);
	elseif (t <= 4.3e+136)
		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 (t <= -9e+73)
		tmp = x * t;
	elseif (t <= 4.3e+136)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9e+73], N[(x * t), $MachinePrecision], If[LessEqual[t, 4.3e+136], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999969e73 or 4.2999999999999999e136 < t

   1. Initial program 100.0%

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

      1. +-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 69.5%

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

   7. Simplified 69.5%

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

   if -8.99999999999999969e73 < t < 4.2999999999999999e136

   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 41.5%

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

   7. Simplified 41.5%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 10: 30.1% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

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

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

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

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

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

   4. associate-+l+ N/A

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

   5. +-commutative N/A

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

   6. count-2 N/A

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

   7. *-commutative N/A

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

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

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

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

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

   10. *-lowering-*.f64 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 31.9%

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

7. Simplified 31.9%

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

8. Final simplification 31.9%

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

Reproduce

herbie shell --seed 2024138 
(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)))