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

Percentage Accurate: 99.8% → 99.9%

Time: 11.3s

Alternatives: 11

Speedup: 1.2×

• 26.7% 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: 99.8% 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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(5.0 * y + N[(x * N[(2.0 * N[(y + z), $MachinePrecision] + t), $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. Add Preprocessing
3. Step-by-step derivation

   1. associate-+l+ N/A

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

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

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

   3. associate-+l+ N/A

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

   4. +-commutative N/A

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

   5. count-2 N/A

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

   6. accelerator-lowering-fma.f64 N/A

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

   7. +-lowering-+.f64 99.9

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in x around 0

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

   1. distribute-lft-in N/A

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

   2. *-commutative N/A

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

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

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

   4. *-commutative N/A

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

   5. distribute-lft-in N/A

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

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

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

   7. +-commutative N/A

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

   8. distribute-lft-in N/A

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

   9. accelerator-lowering-fma.f64 N/A

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

   10. +-lowering-+.f64 100.0

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

7. Simplified 100.0%

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

Alternative 2: 99.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \mathsf{fma}\left(2, y + z, t\right), 0\right)\\ \mathbf{if}\;x \leq -2.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.00045:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \mathsf{fma}\left(2, z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (fma 2.0 (+ y z) t) 0.0)))
   (if (<= x -2.5)
     t_1
     (if (<= x 0.00045) (fma y 5.0 (* x (fma 2.0 z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, fma(2.0, (y + z), t), 0.0);
	double tmp;
	if (x <= -2.5) {
		tmp = t_1;
	} else if (x <= 0.00045) {
		tmp = fma(y, 5.0, (x * fma(2.0, z, t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, fma(2.0, Float64(y + z), t), 0.0)
	tmp = 0.0
	if (x <= -2.5)
		tmp = t_1;
	elseif (x <= 0.00045)
		tmp = fma(y, 5.0, Float64(x * fma(2.0, z, 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] + 0.0), $MachinePrecision]}, If[LessEqual[x, -2.5], t$95$1, If[LessEqual[x, 0.00045], N[(y * 5.0 + N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 4.4999999999999999e-4 < 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

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

   5. Simplified 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(2, y + z, t\right), 0\right)} \]

   if -2.5 < x < 4.4999999999999999e-4

   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. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

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

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. flip-+ N/A

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

      7. +-inverses N/A

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right)\right) \]

      8. +-inverses N/A

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

      9. +-inverses N/A

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right)\right) \]

      10. +-inverses N/A

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

      11. flip-+ N/A

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

      12. count-2 N/A

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

      13. accelerator-lowering-fma.f64 99.3

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

   4. Applied egg-rr 99.3%

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

Alternative 3: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \mathsf{fma}\left(2, y + z, t\right), 0\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(5, y, x \cdot \mathsf{fma}\left(2, y, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (fma 2.0 (+ y z) t) 0.0)))
   (if (<= x -3.8e-23)
     t_1
     (if (<= x 8.2e-5) (fma 5.0 y (* x (fma 2.0 y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, fma(2.0, (y + z), t), 0.0);
	double tmp;
	if (x <= -3.8e-23) {
		tmp = t_1;
	} else if (x <= 8.2e-5) {
		tmp = fma(5.0, y, (x * fma(2.0, y, t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, fma(2.0, Float64(y + z), t), 0.0)
	tmp = 0.0
	if (x <= -3.8e-23)
		tmp = t_1;
	elseif (x <= 8.2e-5)
		tmp = fma(5.0, y, Float64(x * fma(2.0, y, 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] + 0.0), $MachinePrecision]}, If[LessEqual[x, -3.8e-23], t$95$1, If[LessEqual[x, 8.2e-5], N[(5.0 * y + N[(x * N[(2.0 * y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000011e-23 or 8.20000000000000009e-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

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

   5. Simplified 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(2, y + z, t\right), 0\right)} \]

   if -3.80000000000000011e-23 < x < 8.20000000000000009e-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. associate-+l+ N/A

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

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

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. count-2 N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. +-lowering-+.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. distribute-lft-in N/A

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

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

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

      7. +-commutative N/A

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

      8. distribute-lft-in N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. +-lowering-+.f64 100.0

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 85.9

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

   10. Simplified 85.9%

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

Alternative 4: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \mathsf{fma}\left(2, y + z, t\right), 0\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (fma 2.0 (+ y z) t) 0.0)))
   (if (<= x -1e-22) t_1 (if (<= x 1.7e-5) (fma y 5.0 (* x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, fma(2.0, (y + z), t), 0.0);
	double tmp;
	if (x <= -1e-22) {
		tmp = t_1;
	} else if (x <= 1.7e-5) {
		tmp = fma(y, 5.0, (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, fma(2.0, Float64(y + z), t), 0.0)
	tmp = 0.0
	if (x <= -1e-22)
		tmp = t_1;
	elseif (x <= 1.7e-5)
		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] + 0.0), $MachinePrecision]}, If[LessEqual[x, -1e-22], t$95$1, If[LessEqual[x, 1.7e-5], N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1e-22 or 1.7e-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

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

   5. Simplified 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(2, y + z, t\right), 0\right)} \]

   if -1e-22 < x < 1.7e-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. Taylor expanded in t around inf

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

   5. Simplified 85.1%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 85.1

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

   7. Applied egg-rr 85.1%

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

Alternative 5: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + x\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (+ x x))))
   (if (<= x -2.8e-24)
     t_1
     (if (<= x 1.7e-5) (* 5.0 y) (if (<= x 3.6e+248) t_1 (* y (+ x x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x + x);
	double tmp;
	if (x <= -2.8e-24) {
		tmp = t_1;
	} else if (x <= 1.7e-5) {
		tmp = 5.0 * y;
	} else if (x <= 3.6e+248) {
		tmp = t_1;
	} else {
		tmp = y * (x + x);
	}
	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 = z * (x + x)
    if (x <= (-2.8d-24)) then
        tmp = t_1
    else if (x <= 1.7d-5) then
        tmp = 5.0d0 * y
    else if (x <= 3.6d+248) then
        tmp = t_1
    else
        tmp = y * (x + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x + x);
	double tmp;
	if (x <= -2.8e-24) {
		tmp = t_1;
	} else if (x <= 1.7e-5) {
		tmp = 5.0 * y;
	} else if (x <= 3.6e+248) {
		tmp = t_1;
	} else {
		tmp = y * (x + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x + x)
	tmp = 0
	if x <= -2.8e-24:
		tmp = t_1
	elif x <= 1.7e-5:
		tmp = 5.0 * y
	elif x <= 3.6e+248:
		tmp = t_1
	else:
		tmp = y * (x + x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x + x))
	tmp = 0.0
	if (x <= -2.8e-24)
		tmp = t_1;
	elseif (x <= 1.7e-5)
		tmp = Float64(5.0 * y);
	elseif (x <= 3.6e+248)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x + x);
	tmp = 0.0;
	if (x <= -2.8e-24)
		tmp = t_1;
	elseif (x <= 1.7e-5)
		tmp = 5.0 * y;
	elseif (x <= 3.6e+248)
		tmp = t_1;
	else
		tmp = y * (x + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e-24], t$95$1, If[LessEqual[x, 1.7e-5], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 3.6e+248], t$95$1, N[(y * N[(x + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8000000000000002e-24 or 1.7e-5 < x < 3.60000000000000001e248

   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. Step-by-step derivation

      1. associate-+l+ N/A

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

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

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. count-2 N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. +-lowering-+.f64 100.0

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

   4. Applied egg-rr 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

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

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

      8. *-lowering-*.f64 94.8

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 51.3

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

   9. Simplified 51.3%

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

   if -2.8000000000000002e-24 < x < 1.7e-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. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 66.9

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

   5. Simplified 66.9%

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

   if 3.60000000000000001e248 < 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. +-lft-identity N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. neg-sub0 N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate--r- N/A

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

      12. neg-sub0 N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. accelerator-lowering-fma.f64 73.6

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, 0\right) \]

   5. Simplified 73.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, 5\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. accelerator-lowering-fma.f64 73.6

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

   7. Applied egg-rr 73.6%

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

   8. Taylor expanded in x around inf

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

      1. count-2 N/A

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

      2. +-lowering-+.f64 73.6

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

   10. Simplified 73.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(x + x\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 5, y \cdot \left(x + x\right)\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma y 5.0 (* y (+ x x)))))
   (if (<= y -2.8e+38) t_1 (if (<= y 5e+84) (* x (fma 2.0 z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, 5.0, (y * (x + x)));
	double tmp;
	if (y <= -2.8e+38) {
		tmp = t_1;
	} else if (y <= 5e+84) {
		tmp = x * fma(2.0, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, 5.0, Float64(y * Float64(x + x)))
	tmp = 0.0
	if (y <= -2.8e+38)
		tmp = t_1;
	elseif (y <= 5e+84)
		tmp = Float64(x * fma(2.0, z, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * 5.0 + N[(y * N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+38], t$95$1, If[LessEqual[y, 5e+84], N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e38 or 5.0000000000000001e84 < 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. +-lft-identity N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. neg-sub0 N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate--r- N/A

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

      12. neg-sub0 N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. accelerator-lowering-fma.f64 90.6

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, 0\right) \]

   5. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, 5\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 90.6

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

   7. Applied egg-rr 90.6%

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

   8. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 90.6

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

   10. Simplified 90.6%

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

   if -2.8e38 < y < 5.0000000000000001e84

   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 0

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

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

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 77.7

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

   5. Simplified 77.7%

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

Alternative 7: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (fma x 2.0 5.0))))
   (if (<= y -3e+41) t_1 (if (<= y 1.3e+86) (* x (fma 2.0 z 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 <= -3e+41) {
		tmp = t_1;
	} else if (y <= 1.3e+86) {
		tmp = x * fma(2.0, z, 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 <= -3e+41)
		tmp = t_1;
	elseif (y <= 1.3e+86)
		tmp = Float64(x * fma(2.0, z, 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, -3e+41], t$95$1, If[LessEqual[y, 1.3e+86], N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999998e41 or 1.2999999999999999e86 < 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. +-lft-identity N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. neg-sub0 N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate--r- N/A

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

      12. neg-sub0 N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. accelerator-lowering-fma.f64 90.6

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, 2, 5\right)}, 0\right) \]

   5. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, 2, 5\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. accelerator-lowering-fma.f64 90.6

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

   7. Applied egg-rr 90.6%

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

   if -2.9999999999999998e41 < y < 1.2999999999999999e86

   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 0

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

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

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 77.7

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

   5. Simplified 77.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-71}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma 2.0 z t))))
   (if (<= x -1.22e-116) t_1 (if (<= x 7e-71) (* 5.0 y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(2.0, z, t);
	double tmp;
	if (x <= -1.22e-116) {
		tmp = t_1;
	} else if (x <= 7e-71) {
		tmp = 5.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(2.0, z, t))
	tmp = 0.0
	if (x <= -1.22e-116)
		tmp = t_1;
	elseif (x <= 7e-71)
		tmp = Float64(5.0 * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e-116], t$95$1, If[LessEqual[x, 7e-71], N[(5.0 * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.22e-116 or 6.9999999999999998e-71 < 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 0

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

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

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 71.9

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

   5. Simplified 71.9%

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

   if -1.22e-116 < x < 6.9999999999999998e-71

   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. *-lowering-*.f64 74.5

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

   5. Simplified 74.5%

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

Alternative 9: 48.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + x\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (+ x x))))
   (if (<= x -1.75e-25) t_1 (if (<= x 1.7e-5) (* 5.0 y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x + x);
	double tmp;
	if (x <= -1.75e-25) {
		tmp = t_1;
	} else if (x <= 1.7e-5) {
		tmp = 5.0 * y;
	} 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 = z * (x + x)
    if (x <= (-1.75d-25)) then
        tmp = t_1
    else if (x <= 1.7d-5) then
        tmp = 5.0d0 * y
    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 = z * (x + x);
	double tmp;
	if (x <= -1.75e-25) {
		tmp = t_1;
	} else if (x <= 1.7e-5) {
		tmp = 5.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x + x)
	tmp = 0
	if x <= -1.75e-25:
		tmp = t_1
	elif x <= 1.7e-5:
		tmp = 5.0 * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x + x))
	tmp = 0.0
	if (x <= -1.75e-25)
		tmp = t_1;
	elseif (x <= 1.7e-5)
		tmp = Float64(5.0 * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x + x);
	tmp = 0.0;
	if (x <= -1.75e-25)
		tmp = t_1;
	elseif (x <= 1.7e-5)
		tmp = 5.0 * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e-25], t$95$1, If[LessEqual[x, 1.7e-5], N[(5.0 * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-25 or 1.7e-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. Step-by-step derivation

      1. associate-+l+ N/A

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

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

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. count-2 N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. +-lowering-+.f64 100.0

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

   4. Applied egg-rr 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

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

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

      8. *-lowering-*.f64 95.2

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 49.3

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

   9. Simplified 49.3%

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

   if -1.7500000000000001e-25 < x < 1.7e-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. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 66.9

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

   5. Simplified 66.9%

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

Alternative 10: 47.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-15}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.6e-25) (* x t) (if (<= x 9.5e-15) (* 5.0 y) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.6e-25) {
		tmp = x * t;
	} else if (x <= 9.5e-15) {
		tmp = 5.0 * y;
	} 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 <= (-5.6d-25)) then
        tmp = x * t
    else if (x <= 9.5d-15) then
        tmp = 5.0d0 * y
    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 <= -5.6e-25) {
		tmp = x * t;
	} else if (x <= 9.5e-15) {
		tmp = 5.0 * y;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.6e-25:
		tmp = x * t
	elif x <= 9.5e-15:
		tmp = 5.0 * y
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.6e-25)
		tmp = Float64(x * t);
	elseif (x <= 9.5e-15)
		tmp = Float64(5.0 * y);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.6e-25)
		tmp = x * t;
	elseif (x <= 9.5e-15)
		tmp = 5.0 * y;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.6e-25], N[(x * t), $MachinePrecision], If[LessEqual[x, 9.5e-15], N[(5.0 * y), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.59999999999999976e-25 or 9.5000000000000005e-15 < 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. *-lowering-*.f64 36.1

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

   5. Simplified 36.1%

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

   if -5.59999999999999976e-25 < x < 9.5000000000000005e-15

   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. *-lowering-*.f64 68.3

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

   5. Simplified 68.3%

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

Alternative 11: 29.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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 = 5.0d0 * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(5.0 * y), $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. *-lowering-*.f64 35.2

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

5. Simplified 35.2%

   \[\leadsto \color{blue}{5 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024195 
(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)))