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

Percentage Accurate: 99.9% → 100.0%

Time: 14.5s

Alternatives: 11

Speedup: 1.2×

• 25.9% 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: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-48}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+212}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= x -2.5e+43)
     t_2
     (if (<= x -1.65e-101)
       t_1
       (if (<= x 4.5e-48) (* 5.0 y) (if (<= x 1.05e+212) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -2.5e+43) {
		tmp = t_2;
	} else if (x <= -1.65e-101) {
		tmp = t_1;
	} else if (x <= 4.5e-48) {
		tmp = 5.0 * y;
	} else if (x <= 1.05e+212) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * z))
    t_2 = x * (t + (2.0d0 * y))
    if (x <= (-2.5d+43)) then
        tmp = t_2
    else if (x <= (-1.65d-101)) then
        tmp = t_1
    else if (x <= 4.5d-48) then
        tmp = 5.0d0 * y
    else if (x <= 1.05d+212) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -2.5e+43) {
		tmp = t_2;
	} else if (x <= -1.65e-101) {
		tmp = t_1;
	} else if (x <= 4.5e-48) {
		tmp = 5.0 * y;
	} else if (x <= 1.05e+212) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -2.5e+43:
		tmp = t_2
	elif x <= -1.65e-101:
		tmp = t_1
	elif x <= 4.5e-48:
		tmp = 5.0 * y
	elif x <= 1.05e+212:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -2.5e+43)
		tmp = t_2;
	elseif (x <= -1.65e-101)
		tmp = t_1;
	elseif (x <= 4.5e-48)
		tmp = Float64(5.0 * y);
	elseif (x <= 1.05e+212)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -2.5e+43)
		tmp = t_2;
	elseif (x <= -1.65e-101)
		tmp = t_1;
	elseif (x <= 4.5e-48)
		tmp = 5.0 * y;
	elseif (x <= 1.05e+212)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+43], t$95$2, If[LessEqual[x, -1.65e-101], t$95$1, If[LessEqual[x, 4.5e-48], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 1.05e+212], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5000000000000002e43 or 4.49999999999999988e-48 < x < 1.05e212

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -2.5000000000000002e43 < x < -1.64999999999999992e-101 or 1.05e212 < x

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.64999999999999992e-101 < x < 4.49999999999999988e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -6.1 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-48}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+235}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))))
   (if (<= x -6.1e-12)
     t_1
     (if (<= x 4.8e-48)
       (* 5.0 y)
       (if (<= x 1.4e+212) t_1 (if (<= x 1.5e+235) (* 2.0 (* x z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -6.1e-12) {
		tmp = t_1;
	} else if (x <= 4.8e-48) {
		tmp = 5.0 * y;
	} else if (x <= 1.4e+212) {
		tmp = t_1;
	} else if (x <= 1.5e+235) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * y))
    if (x <= (-6.1d-12)) then
        tmp = t_1
    else if (x <= 4.8d-48) then
        tmp = 5.0d0 * y
    else if (x <= 1.4d+212) then
        tmp = t_1
    else if (x <= 1.5d+235) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -6.1e-12) {
		tmp = t_1;
	} else if (x <= 4.8e-48) {
		tmp = 5.0 * y;
	} else if (x <= 1.4e+212) {
		tmp = t_1;
	} else if (x <= 1.5e+235) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -6.1e-12:
		tmp = t_1
	elif x <= 4.8e-48:
		tmp = 5.0 * y
	elif x <= 1.4e+212:
		tmp = t_1
	elif x <= 1.5e+235:
		tmp = 2.0 * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -6.1e-12)
		tmp = t_1;
	elseif (x <= 4.8e-48)
		tmp = Float64(5.0 * y);
	elseif (x <= 1.4e+212)
		tmp = t_1;
	elseif (x <= 1.5e+235)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -6.1e-12)
		tmp = t_1;
	elseif (x <= 4.8e-48)
		tmp = 5.0 * y;
	elseif (x <= 1.4e+212)
		tmp = t_1;
	elseif (x <= 1.5e+235)
		tmp = 2.0 * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.1e-12], t$95$1, If[LessEqual[x, 4.8e-48], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 1.4e+212], t$95$1, If[LessEqual[x, 1.5e+235], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1000000000000003e-12 or 4.8e-48 < x < 1.39999999999999999e212 or 1.50000000000000008e235 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -6.1000000000000003e-12 < x < 4.8e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1.39999999999999999e212 < x < 1.50000000000000008e235

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-48}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+211}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+238}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e-8)
   (* x (* 2.0 y))
   (if (<= x 9e-48)
     (* 5.0 y)
     (if (<= x 9.2e+211)
       (* x t)
       (if (<= x 4.4e+238) (* 2.0 (* x z)) (* x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-8) {
		tmp = x * (2.0 * y);
	} else if (x <= 9e-48) {
		tmp = 5.0 * y;
	} else if (x <= 9.2e+211) {
		tmp = x * t;
	} else if (x <= 4.4e+238) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.02d-8)) then
        tmp = x * (2.0d0 * y)
    else if (x <= 9d-48) then
        tmp = 5.0d0 * y
    else if (x <= 9.2d+211) then
        tmp = x * t
    else if (x <= 4.4d+238) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-8) {
		tmp = x * (2.0 * y);
	} else if (x <= 9e-48) {
		tmp = 5.0 * y;
	} else if (x <= 9.2e+211) {
		tmp = x * t;
	} else if (x <= 4.4e+238) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.02e-8:
		tmp = x * (2.0 * y)
	elif x <= 9e-48:
		tmp = 5.0 * y
	elif x <= 9.2e+211:
		tmp = x * t
	elif x <= 4.4e+238:
		tmp = 2.0 * (x * z)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e-8)
		tmp = Float64(x * Float64(2.0 * y));
	elseif (x <= 9e-48)
		tmp = Float64(5.0 * y);
	elseif (x <= 9.2e+211)
		tmp = Float64(x * t);
	elseif (x <= 4.4e+238)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.02e-8)
		tmp = x * (2.0 * y);
	elseif (x <= 9e-48)
		tmp = 5.0 * y;
	elseif (x <= 9.2e+211)
		tmp = x * t;
	elseif (x <= 4.4e+238)
		tmp = 2.0 * (x * z);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e-8], N[(x * N[(2.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-48], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 9.2e+211], N[(x * t), $MachinePrecision], If[LessEqual[x, 4.4e+238], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.02000000000000003e-8

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.02000000000000003e-8 < x < 8.99999999999999977e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 8.99999999999999977e-48 < x < 9.20000000000000044e211 or 4.4000000000000001e238 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 9.20000000000000044e211 < x < 4.4000000000000001e238

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+211}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+236}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -3.4e-51)
     t_1
     (if (<= x 8.5e-48)
       (* 5.0 y)
       (if (<= x 4.6e+211) (* x t) (if (<= x 2.5e+236) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.4e-51) {
		tmp = t_1;
	} else if (x <= 8.5e-48) {
		tmp = 5.0 * y;
	} else if (x <= 4.6e+211) {
		tmp = x * t;
	} else if (x <= 2.5e+236) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-3.4d-51)) then
        tmp = t_1
    else if (x <= 8.5d-48) then
        tmp = 5.0d0 * y
    else if (x <= 4.6d+211) then
        tmp = x * t
    else if (x <= 2.5d+236) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.4e-51) {
		tmp = t_1;
	} else if (x <= 8.5e-48) {
		tmp = 5.0 * y;
	} else if (x <= 4.6e+211) {
		tmp = x * t;
	} else if (x <= 2.5e+236) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -3.4e-51:
		tmp = t_1
	elif x <= 8.5e-48:
		tmp = 5.0 * y
	elif x <= 4.6e+211:
		tmp = x * t
	elif x <= 2.5e+236:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -3.4e-51)
		tmp = t_1;
	elseif (x <= 8.5e-48)
		tmp = Float64(5.0 * y);
	elseif (x <= 4.6e+211)
		tmp = Float64(x * t);
	elseif (x <= 2.5e+236)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -3.4e-51)
		tmp = t_1;
	elseif (x <= 8.5e-48)
		tmp = 5.0 * y;
	elseif (x <= 4.6e+211)
		tmp = x * t;
	elseif (x <= 2.5e+236)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-51], t$95$1, If[LessEqual[x, 8.5e-48], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 4.6e+211], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.5e+236], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000003e-51 or 4.60000000000000022e211 < x < 2.49999999999999985e236

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.40000000000000003e-51 < x < 8.5000000000000004e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 8.5000000000000004e-48 < x < 4.60000000000000022e211 or 2.49999999999999985e236 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 (+ y z))))))
   (if (<= x -1.05e-14)
     t_1
     (if (<= x -1.15e-193)
       (+ (* x (* 2.0 z)) (* y 5.0))
       (if (<= x 8.5e-48) (+ (* x t) (* y 5.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -1.05e-14) {
		tmp = t_1;
	} else if (x <= -1.15e-193) {
		tmp = (x * (2.0 * z)) + (y * 5.0);
	} else if (x <= 8.5e-48) {
		tmp = (x * t) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * (y + z)))
    if (x <= (-1.05d-14)) then
        tmp = t_1
    else if (x <= (-1.15d-193)) then
        tmp = (x * (2.0d0 * z)) + (y * 5.0d0)
    else if (x <= 8.5d-48) then
        tmp = (x * t) + (y * 5.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -1.05e-14) {
		tmp = t_1;
	} else if (x <= -1.15e-193) {
		tmp = (x * (2.0 * z)) + (y * 5.0);
	} else if (x <= 8.5e-48) {
		tmp = (x * t) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * (y + z)))
	tmp = 0
	if x <= -1.05e-14:
		tmp = t_1
	elif x <= -1.15e-193:
		tmp = (x * (2.0 * z)) + (y * 5.0)
	elif x <= 8.5e-48:
		tmp = (x * t) + (y * 5.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))))
	tmp = 0.0
	if (x <= -1.05e-14)
		tmp = t_1;
	elseif (x <= -1.15e-193)
		tmp = Float64(Float64(x * Float64(2.0 * z)) + Float64(y * 5.0));
	elseif (x <= 8.5e-48)
		tmp = Float64(Float64(x * t) + Float64(y * 5.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * (y + z)));
	tmp = 0.0;
	if (x <= -1.05e-14)
		tmp = t_1;
	elseif (x <= -1.15e-193)
		tmp = (x * (2.0 * z)) + (y * 5.0);
	elseif (x <= 8.5e-48)
		tmp = (x * t) + (y * 5.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-14], t$95$1, If[LessEqual[x, -1.15e-193], N[(N[(x * N[(2.0 * z), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-48], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0499999999999999e-14 or 8.5000000000000004e-48 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.0499999999999999e-14 < x < -1.15000000000000004e-193

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.15000000000000004e-193 < x < 8.5000000000000004e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-48}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 (+ y z))))))
   (if (<= x -4.5e-52) t_1 (if (<= x 7.2e-48) (+ (* x t) (* y 5.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -4.5e-52) {
		tmp = t_1;
	} else if (x <= 7.2e-48) {
		tmp = (x * t) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * (y + z)))
    if (x <= (-4.5d-52)) then
        tmp = t_1
    else if (x <= 7.2d-48) then
        tmp = (x * t) + (y * 5.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -4.5e-52) {
		tmp = t_1;
	} else if (x <= 7.2e-48) {
		tmp = (x * t) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * (y + z)))
	tmp = 0
	if x <= -4.5e-52:
		tmp = t_1
	elif x <= 7.2e-48:
		tmp = (x * t) + (y * 5.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))))
	tmp = 0.0
	if (x <= -4.5e-52)
		tmp = t_1;
	elseif (x <= 7.2e-48)
		tmp = Float64(Float64(x * t) + Float64(y * 5.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * (y + z)));
	tmp = 0.0;
	if (x <= -4.5e-52)
		tmp = t_1;
	elseif (x <= 7.2e-48)
		tmp = (x * t) + (y * 5.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e-52], t$95$1, If[LessEqual[x, 7.2e-48], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e-52 or 7.2000000000000003e-48 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.5e-52 < x < 7.2000000000000003e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.15e+23) t_1 (if (<= y 7.4e+77) (* x (+ t (* 2.0 z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.15e+23) {
		tmp = t_1;
	} else if (y <= 7.4e+77) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.15d+23)) then
        tmp = t_1
    else if (y <= 7.4d+77) then
        tmp = x * (t + (2.0d0 * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.15e+23) {
		tmp = t_1;
	} else if (y <= 7.4e+77) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -2.15e+23:
		tmp = t_1
	elif y <= 7.4e+77:
		tmp = x * (t + (2.0 * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -2.15e+23)
		tmp = t_1;
	elseif (y <= 7.4e+77)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -2.15e+23)
		tmp = t_1;
	elseif (y <= 7.4e+77)
		tmp = x * (t + (2.0 * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+23], t$95$1, If[LessEqual[y, 7.4e+77], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e23 or 7.3999999999999999e77 < y

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.1499999999999999e23 < y < 7.3999999999999999e77

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 47.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-48}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e-13) (* x t) (if (<= x 7.8e-48) (* 5.0 y) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e-13) {
		tmp = x * t;
	} else if (x <= 7.8e-48) {
		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 <= (-3.6d-13)) then
        tmp = x * t
    else if (x <= 7.8d-48) 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 <= -3.6e-13) {
		tmp = x * t;
	} else if (x <= 7.8e-48) {
		tmp = 5.0 * y;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e-13:
		tmp = x * t
	elif x <= 7.8e-48:
		tmp = 5.0 * y
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e-13)
		tmp = Float64(x * t);
	elseif (x <= 7.8e-48)
		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 <= -3.6e-13)
		tmp = x * t;
	elseif (x <= 7.8e-48)
		tmp = 5.0 * y;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e-13], N[(x * t), $MachinePrecision], If[LessEqual[x, 7.8e-48], N[(5.0 * y), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999998e-13 or 7.800000000000001e-48 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.5999999999999998e-13 < x < 7.800000000000001e-48

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * (((y + z) * 2.0) + 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) * 2.0d0) + t)) + (y * 5.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 11: 29.5% accurate, 5.0× 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%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))