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

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

Alternatives: 11

Speedup: 1.0×

• 26.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.9%

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

Alternative 2: 47.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + z\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z z))))
   (if (<= x -2.8e+236)
     t_1
     (if (<= x -2.3e-10)
       (* x t)
       (if (<= x 2.05e-28)
         (* y 5.0)
         (if (<= x 1.5e+107) t_1 (* y (* x 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + z);
	double tmp;
	if (x <= -2.8e+236) {
		tmp = t_1;
	} else if (x <= -2.3e-10) {
		tmp = x * t;
	} else if (x <= 2.05e-28) {
		tmp = y * 5.0;
	} else if (x <= 1.5e+107) {
		tmp = t_1;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z + z)
    if (x <= (-2.8d+236)) then
        tmp = t_1
    else if (x <= (-2.3d-10)) then
        tmp = x * t
    else if (x <= 2.05d-28) then
        tmp = y * 5.0d0
    else if (x <= 1.5d+107) then
        tmp = t_1
    else
        tmp = y * (x * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + z);
	double tmp;
	if (x <= -2.8e+236) {
		tmp = t_1;
	} else if (x <= -2.3e-10) {
		tmp = x * t;
	} else if (x <= 2.05e-28) {
		tmp = y * 5.0;
	} else if (x <= 1.5e+107) {
		tmp = t_1;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + z)
	tmp = 0
	if x <= -2.8e+236:
		tmp = t_1
	elif x <= -2.3e-10:
		tmp = x * t
	elif x <= 2.05e-28:
		tmp = y * 5.0
	elif x <= 1.5e+107:
		tmp = t_1
	else:
		tmp = y * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + z))
	tmp = 0.0
	if (x <= -2.8e+236)
		tmp = t_1;
	elseif (x <= -2.3e-10)
		tmp = Float64(x * t);
	elseif (x <= 2.05e-28)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.5e+107)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + z);
	tmp = 0.0;
	if (x <= -2.8e+236)
		tmp = t_1;
	elseif (x <= -2.3e-10)
		tmp = x * t;
	elseif (x <= 2.05e-28)
		tmp = y * 5.0;
	elseif (x <= 1.5e+107)
		tmp = t_1;
	else
		tmp = y * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+236], t$95$1, If[LessEqual[x, -2.3e-10], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.05e-28], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.5e+107], t$95$1, N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.79999999999999992e236 or 2.0500000000000001e-28 < x < 1.50000000000000012e107

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.0

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

   5. Simplified 59.0%

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

      1. count-2 N/A

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

      2. lift-+.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 59.0

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

   7. Applied egg-rr 59.0%

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

   if -2.79999999999999992e236 < x < -2.30000000000000007e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 43.6

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

   5. Simplified 43.6%

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

   if -2.30000000000000007e-10 < x < 2.0500000000000001e-28

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 64.8

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

   5. Simplified 64.8%

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

   if 1.50000000000000012e107 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. neg-sub0 N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(0 - -2 \cdot x\right)} + 5\right) \]

      5. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      9. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - -2 \cdot x\right) + 5\right)} \]

      10. neg-sub0 N/A

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

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

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

      12. metadata-eval N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 57.0

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

   5. Simplified 57.0%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 57.0

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

   8. Simplified 57.0%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+236}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \mathbf{if}\;x \leq -1.28 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;x \leq -22:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 31000000000:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma y 2.0 t))))
   (if (<= x -1.28e+244)
     (* x (+ z z))
     (if (<= x -22.0) t_1 (if (<= x 31000000000.0) (fma y 5.0 (* x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(y, 2.0, t);
	double tmp;
	if (x <= -1.28e+244) {
		tmp = x * (z + z);
	} else if (x <= -22.0) {
		tmp = t_1;
	} else if (x <= 31000000000.0) {
		tmp = fma(y, 5.0, (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(y, 2.0, t))
	tmp = 0.0
	if (x <= -1.28e+244)
		tmp = Float64(x * Float64(z + z));
	elseif (x <= -22.0)
		tmp = t_1;
	elseif (x <= 31000000000.0)
		tmp = fma(y, 5.0, Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * 2.0 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.28e+244], N[(x * N[(z + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -22.0], t$95$1, If[LessEqual[x, 31000000000.0], N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.28000000000000007e244

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 80.1

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

   5. Simplified 80.1%

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

      1. count-2 N/A

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

      2. lift-+.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 80.1

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

   7. Applied egg-rr 80.1%

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

   if -1.28000000000000007e244 < x < -22 or 3.1e10 < 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 99.5

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

   5. Simplified 99.5%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 69.9

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

   8. Simplified 69.9%

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

   if -22 < x < 3.1e10

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 81.3

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

   5. Simplified 81.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 81.4

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

   7. Applied egg-rr 81.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;x \leq -22:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \mathbf{elif}\;x \leq 31000000000:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (fma x 2.0 5.0))))
   (if (<= y -1.55e+29)
     t_1
     (if (<= y 1.5e-176)
       (* x (+ z z))
       (if (<= y 6e+34) (* x (fma y 2.0 t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * fma(x, 2.0, 5.0);
	double tmp;
	if (y <= -1.55e+29) {
		tmp = t_1;
	} else if (y <= 1.5e-176) {
		tmp = x * (z + z);
	} else if (y <= 6e+34) {
		tmp = x * fma(y, 2.0, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * fma(x, 2.0, 5.0))
	tmp = 0.0
	if (y <= -1.55e+29)
		tmp = t_1;
	elseif (y <= 1.5e-176)
		tmp = Float64(x * Float64(z + z));
	elseif (y <= 6e+34)
		tmp = Float64(x * fma(y, 2.0, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0 + 5.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+29], t$95$1, If[LessEqual[y, 1.5e-176], N[(x * N[(z + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+34], N[(x * N[(y * 2.0 + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5499999999999999e29 or 6.00000000000000037e34 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. neg-sub0 N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(0 - -2 \cdot x\right)} + 5\right) \]

      5. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      9. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - -2 \cdot x\right) + 5\right)} \]

      10. neg-sub0 N/A

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

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

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

      12. metadata-eval N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 84.2

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

   5. Simplified 84.2%

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

   if -1.5499999999999999e29 < y < 1.5e-176

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 53.2

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

   5. Simplified 53.2%

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

      1. count-2 N/A

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

      2. lift-+.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 53.2

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

   7. Applied egg-rr 53.2%

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

   if 1.5e-176 < y < 6.00000000000000037e34

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 82.3

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

   5. Simplified 82.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 63.0

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

   8. Simplified 63.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma y 2.0 t))))
   (if (<= x -6.4e+243)
     (* x (+ z z))
     (if (<= x -3.65e-10) t_1 (if (<= x 1.02e-28) (* y 5.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(y, 2.0, t);
	double tmp;
	if (x <= -6.4e+243) {
		tmp = x * (z + z);
	} else if (x <= -3.65e-10) {
		tmp = t_1;
	} else if (x <= 1.02e-28) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(y, 2.0, t))
	tmp = 0.0
	if (x <= -6.4e+243)
		tmp = Float64(x * Float64(z + z));
	elseif (x <= -3.65e-10)
		tmp = t_1;
	elseif (x <= 1.02e-28)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * 2.0 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+243], N[(x * N[(z + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.65e-10], t$95$1, If[LessEqual[x, 1.02e-28], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.40000000000000033e243

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 80.1

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

   5. Simplified 80.1%

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

      1. count-2 N/A

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

      2. lift-+.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 80.1

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

   7. Applied egg-rr 80.1%

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

   if -6.40000000000000033e243 < x < -3.6499999999999998e-10 or 1.01999999999999997e-28 < 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 97.8

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

   5. Simplified 97.8%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 68.2

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

   8. Simplified 68.2%

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

   if -3.6499999999999998e-10 < x < 1.01999999999999997e-28

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 64.8

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

   5. Simplified 64.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y, 2, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{if}\;x \leq -22:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(z + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma 2.0 (+ y z) t))))
   (if (<= x -22.0) t_1 (if (<= x 2.5) (fma y 5.0 (* x (+ t (+ z z)))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(2.0, (y + z), t);
	double tmp;
	if (x <= -22.0) {
		tmp = t_1;
	} else if (x <= 2.5) {
		tmp = fma(y, 5.0, (x * (t + (z + z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(2.0, Float64(y + z), t))
	tmp = 0.0
	if (x <= -22.0)
		tmp = t_1;
	elseif (x <= 2.5)
		tmp = fma(y, 5.0, Float64(x * Float64(t + Float64(z + z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -22.0], t$95$1, If[LessEqual[x, 2.5], N[(y * 5.0 + N[(x * N[(t + N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -22 or 2.5 < 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 99.5

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

   5. Simplified 99.5%

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

   if -22 < x < 2.5

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 100.0

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

   4. Applied egg-rr 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(z + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + z\right)\\ \mathbf{if}\;x \leq -3.35 \cdot 10^{+236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z z))))
   (if (<= x -3.35e+236)
     t_1
     (if (<= x -1.25e-9) (* x t) (if (<= x 8.5e-29) (* y 5.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + z);
	double tmp;
	if (x <= -3.35e+236) {
		tmp = t_1;
	} else if (x <= -1.25e-9) {
		tmp = x * t;
	} else if (x <= 8.5e-29) {
		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 * (z + z)
    if (x <= (-3.35d+236)) then
        tmp = t_1
    else if (x <= (-1.25d-9)) then
        tmp = x * t
    else if (x <= 8.5d-29) 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 * (z + z);
	double tmp;
	if (x <= -3.35e+236) {
		tmp = t_1;
	} else if (x <= -1.25e-9) {
		tmp = x * t;
	} else if (x <= 8.5e-29) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + z)
	tmp = 0
	if x <= -3.35e+236:
		tmp = t_1
	elif x <= -1.25e-9:
		tmp = x * t
	elif x <= 8.5e-29:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + z))
	tmp = 0.0
	if (x <= -3.35e+236)
		tmp = t_1;
	elseif (x <= -1.25e-9)
		tmp = Float64(x * t);
	elseif (x <= 8.5e-29)
		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 * (z + z);
	tmp = 0.0;
	if (x <= -3.35e+236)
		tmp = t_1;
	elseif (x <= -1.25e-9)
		tmp = x * t;
	elseif (x <= 8.5e-29)
		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[(z + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.35e+236], t$95$1, If[LessEqual[x, -1.25e-9], N[(x * t), $MachinePrecision], If[LessEqual[x, 8.5e-29], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3500000000000002e236 or 8.5000000000000001e-29 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 47.6

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

   5. Simplified 47.6%

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

      1. count-2 N/A

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

      2. lift-+.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 47.6

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

   7. Applied egg-rr 47.6%

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

   if -3.3500000000000002e236 < x < -1.25e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 43.6

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

   5. Simplified 43.6%

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

   if -1.25e-9 < x < 8.5000000000000001e-29

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 64.8

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

   5. Simplified 64.8%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+236}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{if}\;x \leq -22:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma 2.0 (+ y z) t))))
   (if (<= x -22.0) t_1 (if (<= x 1.55e-28) (fma y 5.0 (* x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(2.0, (y + z), t);
	double tmp;
	if (x <= -22.0) {
		tmp = t_1;
	} else if (x <= 1.55e-28) {
		tmp = fma(y, 5.0, (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(2.0, Float64(y + z), t))
	tmp = 0.0
	if (x <= -22.0)
		tmp = t_1;
	elseif (x <= 1.55e-28)
		tmp = fma(y, 5.0, Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -22.0], t$95$1, If[LessEqual[x, 1.55e-28], N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -22 or 1.54999999999999996e-28 < 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 98.2

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

   5. Simplified 98.2%

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

   if -22 < x < 1.54999999999999996e-28

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 84.0

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

   5. Simplified 84.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 84.0

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

   7. Applied egg-rr 84.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -9500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1040000000:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -9500.0) t_1 (if (<= x 1040000000.0) (fma y 5.0 (* x t)) 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 <= -9500.0) {
		tmp = t_1;
	} else if (x <= 1040000000.0) {
		tmp = fma(y, 5.0, (x * t));
	} 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 <= -9500.0)
		tmp = t_1;
	elseif (x <= 1040000000.0)
		tmp = fma(y, 5.0, Float64(x * t));
	else
		tmp = t_1;
	end
	return 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, -9500.0], t$95$1, If[LessEqual[x, 1040000000.0], N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9500 or 1.04e9 < 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 99.5

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

   5. Simplified 99.5%

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

   6. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 76.2

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

   8. Simplified 76.2%

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

   if -9500 < x < 1.04e9

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 82.5

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

   5. Simplified 82.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 82.6

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

   7. Applied egg-rr 82.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9500:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1040000000:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e-11) (* x t) (if (<= x 6.9e-28) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e-11) {
		tmp = x * t;
	} else if (x <= 6.9e-28) {
		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 <= (-2.35d-11)) then
        tmp = x * t
    else if (x <= 6.9d-28) 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 <= -2.35e-11) {
		tmp = x * t;
	} else if (x <= 6.9e-28) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e-11:
		tmp = x * t
	elif x <= 6.9e-28:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e-11)
		tmp = Float64(x * t);
	elseif (x <= 6.9e-28)
		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 <= -2.35e-11)
		tmp = x * t;
	elseif (x <= 6.9e-28)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e-11], N[(x * t), $MachinePrecision], If[LessEqual[x, 6.9e-28], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.34999999999999996e-11 or 6.90000000000000001e-28 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.7

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

   5. Simplified 35.7%

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

   if -2.34999999999999996e-11 < x < 6.90000000000000001e-28

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 64.8

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

   5. Simplified 64.8%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.8% accurate, 4.3× 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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. lower-*.f64 32.9

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

5. Simplified 32.9%

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

6. Final simplification 32.9%

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

Reproduce

herbie shell --seed 2024207 
(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)))