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

Percentage Accurate: 99.8% → 99.9%

Time: 7.1s

Alternatives: 17

Speedup: 0.1×

• 26.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

   3. distribute-rgt-in 95.6%

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

   4. associate-+l+ 95.6%

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

   5. +-commutative 95.6%

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

   6. count-2 95.6%

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

   7. distribute-rgt-in 100.0%

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

   8. *-commutative 100.0%

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

   9. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x\right)\\ t_2 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.72 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-154}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 210000000000:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 x))) (t_2 (* 2.0 (* x z))))
   (if (<= y -1.72e-43)
     t_1
     (if (<= y -1.7e-131)
       t_2
       (if (<= y -1.4e-260)
         (* x t)
         (if (<= y 3.25e-205)
           t_2
           (if (<= y 9.2e-154)
             (* x t)
             (if (<= y 7e-51)
               t_2
               (if (<= y 210000000000.0) (* x t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + x);
	double t_2 = 2.0 * (x * z);
	double tmp;
	if (y <= -1.72e-43) {
		tmp = t_1;
	} else if (y <= -1.7e-131) {
		tmp = t_2;
	} else if (y <= -1.4e-260) {
		tmp = x * t;
	} else if (y <= 3.25e-205) {
		tmp = t_2;
	} else if (y <= 9.2e-154) {
		tmp = x * t;
	} else if (y <= 7e-51) {
		tmp = t_2;
	} else if (y <= 210000000000.0) {
		tmp = x * t;
	} 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 = y * (5.0d0 + x)
    t_2 = 2.0d0 * (x * z)
    if (y <= (-1.72d-43)) then
        tmp = t_1
    else if (y <= (-1.7d-131)) then
        tmp = t_2
    else if (y <= (-1.4d-260)) then
        tmp = x * t
    else if (y <= 3.25d-205) then
        tmp = t_2
    else if (y <= 9.2d-154) then
        tmp = x * t
    else if (y <= 7d-51) then
        tmp = t_2
    else if (y <= 210000000000.0d0) then
        tmp = x * t
    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);
	double t_2 = 2.0 * (x * z);
	double tmp;
	if (y <= -1.72e-43) {
		tmp = t_1;
	} else if (y <= -1.7e-131) {
		tmp = t_2;
	} else if (y <= -1.4e-260) {
		tmp = x * t;
	} else if (y <= 3.25e-205) {
		tmp = t_2;
	} else if (y <= 9.2e-154) {
		tmp = x * t;
	} else if (y <= 7e-51) {
		tmp = t_2;
	} else if (y <= 210000000000.0) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + x)
	t_2 = 2.0 * (x * z)
	tmp = 0
	if y <= -1.72e-43:
		tmp = t_1
	elif y <= -1.7e-131:
		tmp = t_2
	elif y <= -1.4e-260:
		tmp = x * t
	elif y <= 3.25e-205:
		tmp = t_2
	elif y <= 9.2e-154:
		tmp = x * t
	elif y <= 7e-51:
		tmp = t_2
	elif y <= 210000000000.0:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + x))
	t_2 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (y <= -1.72e-43)
		tmp = t_1;
	elseif (y <= -1.7e-131)
		tmp = t_2;
	elseif (y <= -1.4e-260)
		tmp = Float64(x * t);
	elseif (y <= 3.25e-205)
		tmp = t_2;
	elseif (y <= 9.2e-154)
		tmp = Float64(x * t);
	elseif (y <= 7e-51)
		tmp = t_2;
	elseif (y <= 210000000000.0)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + x);
	t_2 = 2.0 * (x * z);
	tmp = 0.0;
	if (y <= -1.72e-43)
		tmp = t_1;
	elseif (y <= -1.7e-131)
		tmp = t_2;
	elseif (y <= -1.4e-260)
		tmp = x * t;
	elseif (y <= 3.25e-205)
		tmp = t_2;
	elseif (y <= 9.2e-154)
		tmp = x * t;
	elseif (y <= 7e-51)
		tmp = t_2;
	elseif (y <= 210000000000.0)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.72e-43], t$95$1, If[LessEqual[y, -1.7e-131], t$95$2, If[LessEqual[y, -1.4e-260], N[(x * t), $MachinePrecision], If[LessEqual[y, 3.25e-205], t$95$2, If[LessEqual[y, 9.2e-154], N[(x * t), $MachinePrecision], If[LessEqual[y, 7e-51], t$95$2, If[LessEqual[y, 210000000000.0], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.72000000000000005e-43 or 2.1e11 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around inf 66.3%

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

      1. +-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -1.72000000000000005e-43 < y < -1.69999999999999998e-131 or -1.3999999999999999e-260 < y < 3.24999999999999978e-205 or 9.1999999999999999e-154 < y < 6.9999999999999995e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 65.9%

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

   if -1.69999999999999998e-131 < y < -1.3999999999999999e-260 or 3.24999999999999978e-205 < y < 9.1999999999999999e-154 or 6.9999999999999995e-51 < y < 2.1e11

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 59.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-205}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-154}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 210000000000:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 4: 53.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y + t\right)\\ t_2 := y \cdot \left(5 + x\right)\\ t_3 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.82 \cdot 10^{-131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-154}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ y t))) (t_2 (* y (+ 5.0 x))) (t_3 (* 2.0 (* x z))))
   (if (<= y -5.5e-42)
     t_2
     (if (<= y -1.82e-131)
       t_3
       (if (<= y -1.05e-260)
         t_1
         (if (<= y 1.45e-206)
           t_3
           (if (<= y 5.5e-154)
             (* x t)
             (if (<= y 2.6e-52) t_3 (if (<= y 5.3e+76) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double t_2 = y * (5.0 + x);
	double t_3 = 2.0 * (x * z);
	double tmp;
	if (y <= -5.5e-42) {
		tmp = t_2;
	} else if (y <= -1.82e-131) {
		tmp = t_3;
	} else if (y <= -1.05e-260) {
		tmp = t_1;
	} else if (y <= 1.45e-206) {
		tmp = t_3;
	} else if (y <= 5.5e-154) {
		tmp = x * t;
	} else if (y <= 2.6e-52) {
		tmp = t_3;
	} else if (y <= 5.3e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x * (y + t)
    t_2 = y * (5.0d0 + x)
    t_3 = 2.0d0 * (x * z)
    if (y <= (-5.5d-42)) then
        tmp = t_2
    else if (y <= (-1.82d-131)) then
        tmp = t_3
    else if (y <= (-1.05d-260)) then
        tmp = t_1
    else if (y <= 1.45d-206) then
        tmp = t_3
    else if (y <= 5.5d-154) then
        tmp = x * t
    else if (y <= 2.6d-52) then
        tmp = t_3
    else if (y <= 5.3d+76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y + t);
	double t_2 = y * (5.0 + x);
	double t_3 = 2.0 * (x * z);
	double tmp;
	if (y <= -5.5e-42) {
		tmp = t_2;
	} else if (y <= -1.82e-131) {
		tmp = t_3;
	} else if (y <= -1.05e-260) {
		tmp = t_1;
	} else if (y <= 1.45e-206) {
		tmp = t_3;
	} else if (y <= 5.5e-154) {
		tmp = x * t;
	} else if (y <= 2.6e-52) {
		tmp = t_3;
	} else if (y <= 5.3e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y + t)
	t_2 = y * (5.0 + x)
	t_3 = 2.0 * (x * z)
	tmp = 0
	if y <= -5.5e-42:
		tmp = t_2
	elif y <= -1.82e-131:
		tmp = t_3
	elif y <= -1.05e-260:
		tmp = t_1
	elif y <= 1.45e-206:
		tmp = t_3
	elif y <= 5.5e-154:
		tmp = x * t
	elif y <= 2.6e-52:
		tmp = t_3
	elif y <= 5.3e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y + t))
	t_2 = Float64(y * Float64(5.0 + x))
	t_3 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (y <= -5.5e-42)
		tmp = t_2;
	elseif (y <= -1.82e-131)
		tmp = t_3;
	elseif (y <= -1.05e-260)
		tmp = t_1;
	elseif (y <= 1.45e-206)
		tmp = t_3;
	elseif (y <= 5.5e-154)
		tmp = Float64(x * t);
	elseif (y <= 2.6e-52)
		tmp = t_3;
	elseif (y <= 5.3e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y + t);
	t_2 = y * (5.0 + x);
	t_3 = 2.0 * (x * z);
	tmp = 0.0;
	if (y <= -5.5e-42)
		tmp = t_2;
	elseif (y <= -1.82e-131)
		tmp = t_3;
	elseif (y <= -1.05e-260)
		tmp = t_1;
	elseif (y <= 1.45e-206)
		tmp = t_3;
	elseif (y <= 5.5e-154)
		tmp = x * t;
	elseif (y <= 2.6e-52)
		tmp = t_3;
	elseif (y <= 5.3e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e-42], t$95$2, If[LessEqual[y, -1.82e-131], t$95$3, If[LessEqual[y, -1.05e-260], t$95$1, If[LessEqual[y, 1.45e-206], t$95$3, If[LessEqual[y, 5.5e-154], N[(x * t), $MachinePrecision], If[LessEqual[y, 2.6e-52], t$95$3, If[LessEqual[y, 5.3e+76], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5e-42 or 5.30000000000000015e76 < 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. Taylor expanded in y around 0 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in y around inf 68.9%

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

      1. +-commutative 68.9%

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

   7. Simplified 68.9%

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

   if -5.5e-42 < y < -1.8200000000000001e-131 or -1.05000000000000002e-260 < y < 1.4500000000000001e-206 or 5.50000000000000002e-154 < y < 2.5999999999999999e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 65.9%

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

   if -1.8200000000000001e-131 < y < -1.05000000000000002e-260 or 2.5999999999999999e-52 < y < 5.30000000000000015e76

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in z around 0 73.7%

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

      1. fma-def 73.7%

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

      2. +-commutative 73.7%

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

      3. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in x around inf 54.8%

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

   if 1.4500000000000001e-206 < y < 5.50000000000000002e-154

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;y \leq -1.82 \cdot 10^{-131}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-206}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-154}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-52}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 5: 99.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -66000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + \left(z + z\right)\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -66000.0) (not (<= x 5.0)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* x (+ t (+ y (+ z z)))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -66000.0) || !(x <= 5.0)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (x * (t + (y + (z + z)))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-66000.0d0)) .or. (.not. (x <= 5.0d0))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (x * (t + (y + (z + z)))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -66000.0) || !(x <= 5.0)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (x * (t + (y + (z + z)))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -66000.0) or not (x <= 5.0):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (x * (t + (y + (z + z)))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -66000.0) || !(x <= 5.0))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + Float64(z + z)))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -66000.0) || ~((x <= 5.0)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (x * (t + (y + (z + z)))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -66000.0], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -66000 or 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.5%

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

   if -66000 < x < 5

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 98.1%

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

   4. Simplified 98.1%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -66000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + \left(z + z\right)\right)\right) + y \cdot 5\\ \end{array} \]

Alternative 6: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+22} \lor \neg \left(y \leq 1.02 \cdot 10^{-14} \lor \neg \left(y \leq 0.0275\right) \land y \leq 2.9 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e+22)
         (not (or (<= y 1.02e-14) (and (not (<= y 0.0275)) (<= y 2.9e+55)))))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+22) || !((y <= 1.02e-14) || (!(y <= 0.0275) && (y <= 2.9e+55)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.2d+22)) .or. (.not. (y <= 1.02d-14) .or. (.not. (y <= 0.0275d0)) .and. (y <= 2.9d+55))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+22) || !((y <= 1.02e-14) || (!(y <= 0.0275) && (y <= 2.9e+55)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e+22) or not ((y <= 1.02e-14) or (not (y <= 0.0275) and (y <= 2.9e+55))):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e+22) || !((y <= 1.02e-14) || (!(y <= 0.0275) && (y <= 2.9e+55))))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.2e+22) || ~(((y <= 1.02e-14) || (~((y <= 0.0275)) && (y <= 2.9e+55)))))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e+22], N[Not[Or[LessEqual[y, 1.02e-14], And[N[Not[LessEqual[y, 0.0275]], $MachinePrecision], LessEqual[y, 2.9e+55]]]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e22 or 1.02e-14 < y < 0.0275000000000000001 or 2.8999999999999999e55 < y

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 86.8%

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

   if -7.2e22 < y < 1.02e-14 or 0.0275000000000000001 < y < 2.8999999999999999e55

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+22} \lor \neg \left(y \leq 1.02 \cdot 10^{-14} \lor \neg \left(y \leq 0.0275\right) \land y \leq 2.9 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 7: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -24000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 0.027 \lor \neg \left(y \leq 5.7 \cdot 10^{+48}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -24000000000000.0)
     t_1
     (if (<= y 1.02e-14)
       (* x (+ t (* z 2.0)))
       (if (or (<= y 0.027) (not (<= y 5.7e+48)))
         t_1
         (+ (* y 5.0) (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -24000000000000.0) {
		tmp = t_1;
	} else if (y <= 1.02e-14) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 0.027) || !(y <= 5.7e+48)) {
		tmp = t_1;
	} else {
		tmp = (y * 5.0) + (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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-24000000000000.0d0)) then
        tmp = t_1
    else if (y <= 1.02d-14) then
        tmp = x * (t + (z * 2.0d0))
    else if ((y <= 0.027d0) .or. (.not. (y <= 5.7d+48))) then
        tmp = t_1
    else
        tmp = (y * 5.0d0) + (x * t)
    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 <= -24000000000000.0) {
		tmp = t_1;
	} else if (y <= 1.02e-14) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 0.027) || !(y <= 5.7e+48)) {
		tmp = t_1;
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -24000000000000.0:
		tmp = t_1
	elif y <= 1.02e-14:
		tmp = x * (t + (z * 2.0))
	elif (y <= 0.027) or not (y <= 5.7e+48):
		tmp = t_1
	else:
		tmp = (y * 5.0) + (x * t)
	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 <= -24000000000000.0)
		tmp = t_1;
	elseif (y <= 1.02e-14)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif ((y <= 0.027) || !(y <= 5.7e+48))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	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 <= -24000000000000.0)
		tmp = t_1;
	elseif (y <= 1.02e-14)
		tmp = x * (t + (z * 2.0));
	elseif ((y <= 0.027) || ~((y <= 5.7e+48)))
		tmp = t_1;
	else
		tmp = (y * 5.0) + (x * t);
	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, -24000000000000.0], t$95$1, If[LessEqual[y, 1.02e-14], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 0.027], N[Not[LessEqual[y, 5.7e+48]], $MachinePrecision]], t$95$1, N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e13 or 1.02e-14 < y < 0.0269999999999999997 or 5.69999999999999968e48 < y

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.0%

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

   if -2.4e13 < y < 1.02e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.5%

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

   if 0.0269999999999999997 < y < 5.69999999999999968e48

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in z around 0 79.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000000000000:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 0.027 \lor \neg \left(y \leq 5.7 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 8: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.003 \lor \neg \left(x \leq 7.2 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.003) (not (<= x 7.2e+14)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.003) || !(x <= 7.2e+14)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-0.003d0)) .or. (.not. (x <= 7.2d+14))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.003) || !(x <= 7.2e+14)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.003) or not (x <= 7.2e+14):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.003) || !(x <= 7.2e+14))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.003) || ~((x <= 7.2e+14)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.003], N[Not[LessEqual[x, 7.2e+14]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0030000000000000001 or 7.2e14 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.6%

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

   if -0.0030000000000000001 < x < 7.2e14

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 84.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.003 \lor \neg \left(x \leq 7.2 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \]

Alternative 9: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -66000 \lor \neg \left(x \leq 2.4\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -66000.0) (not (<= x 2.4)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -66000.0) || !(x <= 2.4)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-66000.0d0)) .or. (.not. (x <= 2.4d0))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * (t + (z * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -66000.0) || !(x <= 2.4)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -66000.0) or not (x <= 2.4):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -66000.0) || !(x <= 2.4))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(z * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -66000.0) || ~((x <= 2.4)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -66000.0], N[Not[LessEqual[x, 2.4]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -66000 or 2.39999999999999991 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.5%

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

   if -66000 < x < 2.39999999999999991

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

   3. Taylor expanded in z around inf 98.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -66000 \lor \neg \left(x \leq 2.4\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 99.9%

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

3. Final simplification 99.9%

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

Alternative 11: 62.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-13} \lor \neg \left(x \leq 7.8 \cdot 10^{-57}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e+158)
   (* x (+ y t))
   (if (or (<= x -5.2e-13) (not (<= x 7.8e-57)))
     (* 2.0 (* x (+ y z)))
     (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e+158) {
		tmp = x * (y + t);
	} else if ((x <= -5.2e-13) || !(x <= 7.8e-57)) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.6d+158)) then
        tmp = x * (y + t)
    else if ((x <= (-5.2d-13)) .or. (.not. (x <= 7.8d-57))) then
        tmp = 2.0d0 * (x * (y + z))
    else
        tmp = y * 5.0d0
    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+158) {
		tmp = x * (y + t);
	} else if ((x <= -5.2e-13) || !(x <= 7.8e-57)) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e+158:
		tmp = x * (y + t)
	elif (x <= -5.2e-13) or not (x <= 7.8e-57):
		tmp = 2.0 * (x * (y + z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e+158)
		tmp = Float64(x * Float64(y + t));
	elseif ((x <= -5.2e-13) || !(x <= 7.8e-57))
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.6e+158)
		tmp = x * (y + t);
	elseif ((x <= -5.2e-13) || ~((x <= 7.8e-57)))
		tmp = 2.0 * (x * (y + z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e+158], N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.2e-13], N[Not[LessEqual[x, 7.8e-57]], $MachinePrecision]], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.59999999999999988e158

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 74.8%

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

      1. fma-def 74.8%

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

      2. +-commutative 74.8%

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

      3. *-commutative 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x around inf 74.8%

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

   if -3.59999999999999988e158 < x < -5.2000000000000001e-13 or 7.80000000000000013e-57 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 76.0%

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

   5. Taylor expanded in x around inf 71.4%

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

   if -5.2000000000000001e-13 < x < 7.80000000000000013e-57

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 65.7%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-13} \lor \neg \left(x \leq 7.8 \cdot 10^{-57}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 12: 62.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-7} \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.5e+157)
   (* x (+ y t))
   (if (or (<= x -9.5e-7) (not (<= x 1.45)))
     (* 2.0 (* x (+ y z)))
     (* y (+ 5.0 (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+157) {
		tmp = x * (y + t);
	} else if ((x <= -9.5e-7) || !(x <= 1.45)) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.5d+157)) then
        tmp = x * (y + t)
    else if ((x <= (-9.5d-7)) .or. (.not. (x <= 1.45d0))) then
        tmp = 2.0d0 * (x * (y + z))
    else
        tmp = y * (5.0d0 + (x * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+157) {
		tmp = x * (y + t);
	} else if ((x <= -9.5e-7) || !(x <= 1.45)) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.5e+157:
		tmp = x * (y + t)
	elif (x <= -9.5e-7) or not (x <= 1.45):
		tmp = 2.0 * (x * (y + z))
	else:
		tmp = y * (5.0 + (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.5e+157)
		tmp = Float64(x * Float64(y + t));
	elseif ((x <= -9.5e-7) || !(x <= 1.45))
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	else
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.5e+157)
		tmp = x * (y + t);
	elseif ((x <= -9.5e-7) || ~((x <= 1.45)))
		tmp = 2.0 * (x * (y + z));
	else
		tmp = y * (5.0 + (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.5e+157], N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -9.5e-7], N[Not[LessEqual[x, 1.45]], $MachinePrecision]], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000005e157

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 74.8%

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

      1. fma-def 74.8%

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

      2. +-commutative 74.8%

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

      3. *-commutative 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x around inf 74.8%

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

   if -1.50000000000000005e157 < x < -9.5000000000000001e-7 or 1.44999999999999996 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 74.7%

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

   5. Taylor expanded in x around inf 73.8%

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

   if -9.5000000000000001e-7 < x < 1.44999999999999996

   1. Initial program 99.8%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-7} \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 13: 88.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-17} \lor \neg \left(x \leq 5.4 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.7e-17) (not (<= x 5.4e-58)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e-17) || !(x <= 5.4e-58)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (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 <= (-3.7d-17)) .or. (.not. (x <= 5.4d-58))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (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 <= -3.7e-17) || !(x <= 5.4e-58)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.7e-17) or not (x <= 5.4e-58):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.7e-17) || !(x <= 5.4e-58))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.7e-17) || ~((x <= 5.4e-58)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.7e-17], N[Not[LessEqual[x, 5.4e-58]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999997e-17 or 5.3999999999999998e-58 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 95.9%

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

   if -3.6999999999999997e-17 < x < 5.3999999999999998e-58

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

   3. Taylor expanded in z around inf 99.8%

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

   4. Taylor expanded in z around 0 81.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-17} \lor \neg \left(x \leq 5.4 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 14: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.002 \lor \neg \left(x \leq 3 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.002) (not (<= x 3e-5)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.002) || !(x <= 3e-5)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	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 <= (-0.002d0)) .or. (.not. (x <= 3d-5))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.002) || !(x <= 3e-5)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.002) or not (x <= 3e-5):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.002) || !(x <= 3e-5))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.002) || ~((x <= 3e-5)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.002], N[Not[LessEqual[x, 3e-5]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2e-3 or 3.00000000000000008e-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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.5%

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

   if -2e-3 < x < 3.00000000000000008e-5

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 84.3%

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

   5. Taylor expanded in y around 0 82.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.002 \lor \neg \left(x \leq 3 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 15: 45.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+56}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= z -9e+111)
     t_1
     (if (<= z 7e-133) (* y 5.0) (if (<= z 1.4e+56) (* x t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -9e+111) {
		tmp = t_1;
	} else if (z <= 7e-133) {
		tmp = y * 5.0;
	} else if (z <= 1.4e+56) {
		tmp = x * t;
	} 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 = 2.0d0 * (x * z)
    if (z <= (-9d+111)) then
        tmp = t_1
    else if (z <= 7d-133) then
        tmp = y * 5.0d0
    else if (z <= 1.4d+56) then
        tmp = x * t
    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 = 2.0 * (x * z);
	double tmp;
	if (z <= -9e+111) {
		tmp = t_1;
	} else if (z <= 7e-133) {
		tmp = y * 5.0;
	} else if (z <= 1.4e+56) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if z <= -9e+111:
		tmp = t_1
	elif z <= 7e-133:
		tmp = y * 5.0
	elif z <= 1.4e+56:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -9e+111)
		tmp = t_1;
	elseif (z <= 7e-133)
		tmp = Float64(y * 5.0);
	elseif (z <= 1.4e+56)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (z <= -9e+111)
		tmp = t_1;
	elseif (z <= 7e-133)
		tmp = y * 5.0;
	elseif (z <= 1.4e+56)
		tmp = x * t;
	else
		tmp = t_1;
	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[z, -9e+111], t$95$1, If[LessEqual[z, 7e-133], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 1.4e+56], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000001e111 or 1.40000000000000004e56 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 63.3%

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

   if -9.00000000000000001e111 < z < 7.00000000000000006e-133

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 39.5%

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

   if 7.00000000000000006e-133 < z < 1.40000000000000004e56

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 44.9%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+56}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 16: 47.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-13}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.06e-13) (* x t) (if (<= x 1.8e+15) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.06e-13) {
		tmp = x * t;
	} else if (x <= 1.8e+15) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.06d-13)) then
        tmp = x * t
    else if (x <= 1.8d+15) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.06e-13) {
		tmp = x * t;
	} else if (x <= 1.8e+15) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.06e-13:
		tmp = x * t
	elif x <= 1.8e+15:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.06e-13)
		tmp = Float64(x * t);
	elseif (x <= 1.8e+15)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.06e-13)
		tmp = x * t;
	elseif (x <= 1.8e+15)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.06e-13], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.8e+15], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e-13 or 1.8e15 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 36.7%

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

   if -1.06e-13 < x < 1.8e15

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 61.4%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-13}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 17: 30.3% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 31.0%

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

3. Final simplification 31.0%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023192 
(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)))