Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 94.4%

Time: 32.1s

Alternatives: 12

Speedup: 0.4×

• 32.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.4 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.4e+215)
   (+ (fma y z x) (* a (+ t (* b z))))
   (+ x (* b (* a (+ z (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.4e+215) {
		tmp = fma(y, z, x) + (a * (t + (b * z)));
	} else {
		tmp = x + (b * (a * (z + (t / b))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.4e+215)
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(b * z))));
	else
		tmp = Float64(x + Float64(b * Float64(a * Float64(z + Float64(t / b)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.4e+215], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(a * N[(z + N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.4e215

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. +-commutative 93.0%

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

      3. fma-define 93.0%

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

      4. associate-*l* 95.5%

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

      5. *-commutative 95.5%

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

      6. *-commutative 95.5%

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

      7. distribute-rgt-out 97.2%

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

      8. remove-double-neg 97.2%

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

      9. *-commutative 97.2%

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

      10. distribute-lft-neg-out 97.2%

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

      11. sub-neg 97.2%

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

      12. sub-neg 97.2%

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

      13. distribute-lft-neg-in 97.2%

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

      14. remove-double-neg 97.2%

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

   3. Simplified 97.2%

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

   if 5.4e215 < b

   1. Initial program 81.2%

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

      1. associate-+l+ 81.2%

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

      2. +-commutative 81.2%

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

      3. fma-define 81.2%

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

      4. associate-*l* 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. distribute-rgt-out 64.6%

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

      8. remove-double-neg 64.6%

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

      9. *-commutative 64.6%

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

      10. distribute-lft-neg-out 64.6%

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

      11. sub-neg 64.6%

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

      12. sub-neg 64.6%

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

      13. distribute-lft-neg-in 64.6%

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

      14. remove-double-neg 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in y around 0 77.1%

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

   6. Taylor expanded in b around inf 81.5%

      \[\leadsto x + \color{blue}{b \cdot \left(a \cdot z + \frac{a \cdot t}{b}\right)} \]
   7. Step-by-step derivation

      1. associate-/l* 94.0%

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

      2. distribute-lft-out 94.0%

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

   8. Simplified 94.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.4 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 39.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot z\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+56}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-211}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* b z))))
   (if (<= a -1.05e+168)
     t_1
     (if (<= a -1.7e+56)
       (* a t)
       (if (<= a -3.5e-59)
         (* z (* b a))
         (if (<= a -1.15e-211)
           (* y z)
           (if (<= a 3.4e-34) x (if (<= a 4.2e+248) t_1 (* a t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (b * z);
	double tmp;
	if (a <= -1.05e+168) {
		tmp = t_1;
	} else if (a <= -1.7e+56) {
		tmp = a * t;
	} else if (a <= -3.5e-59) {
		tmp = z * (b * a);
	} else if (a <= -1.15e-211) {
		tmp = y * z;
	} else if (a <= 3.4e-34) {
		tmp = x;
	} else if (a <= 4.2e+248) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * z)
    if (a <= (-1.05d+168)) then
        tmp = t_1
    else if (a <= (-1.7d+56)) then
        tmp = a * t
    else if (a <= (-3.5d-59)) then
        tmp = z * (b * a)
    else if (a <= (-1.15d-211)) then
        tmp = y * z
    else if (a <= 3.4d-34) then
        tmp = x
    else if (a <= 4.2d+248) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (b * z);
	double tmp;
	if (a <= -1.05e+168) {
		tmp = t_1;
	} else if (a <= -1.7e+56) {
		tmp = a * t;
	} else if (a <= -3.5e-59) {
		tmp = z * (b * a);
	} else if (a <= -1.15e-211) {
		tmp = y * z;
	} else if (a <= 3.4e-34) {
		tmp = x;
	} else if (a <= 4.2e+248) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (b * z)
	tmp = 0
	if a <= -1.05e+168:
		tmp = t_1
	elif a <= -1.7e+56:
		tmp = a * t
	elif a <= -3.5e-59:
		tmp = z * (b * a)
	elif a <= -1.15e-211:
		tmp = y * z
	elif a <= 3.4e-34:
		tmp = x
	elif a <= 4.2e+248:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(b * z))
	tmp = 0.0
	if (a <= -1.05e+168)
		tmp = t_1;
	elseif (a <= -1.7e+56)
		tmp = Float64(a * t);
	elseif (a <= -3.5e-59)
		tmp = Float64(z * Float64(b * a));
	elseif (a <= -1.15e-211)
		tmp = Float64(y * z);
	elseif (a <= 3.4e-34)
		tmp = x;
	elseif (a <= 4.2e+248)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (b * z);
	tmp = 0.0;
	if (a <= -1.05e+168)
		tmp = t_1;
	elseif (a <= -1.7e+56)
		tmp = a * t;
	elseif (a <= -3.5e-59)
		tmp = z * (b * a);
	elseif (a <= -1.15e-211)
		tmp = y * z;
	elseif (a <= 3.4e-34)
		tmp = x;
	elseif (a <= 4.2e+248)
		tmp = t_1;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+168], t$95$1, If[LessEqual[a, -1.7e+56], N[(a * t), $MachinePrecision], If[LessEqual[a, -3.5e-59], N[(z * N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e-211], N[(y * z), $MachinePrecision], If[LessEqual[a, 3.4e-34], x, If[LessEqual[a, 4.2e+248], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.05000000000000001e168 or 3.4000000000000001e-34 < a < 4.19999999999999977e248

   1. Initial program 82.8%

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

      1. associate-+l+ 82.8%

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

      2. +-commutative 82.8%

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

      3. fma-define 82.8%

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

      4. associate-*l* 90.6%

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

      5. *-commutative 90.6%

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

      6. *-commutative 90.6%

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

      7. distribute-rgt-out 96.4%

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

      8. remove-double-neg 96.4%

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

      9. *-commutative 96.4%

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

      10. distribute-lft-neg-out 96.4%

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

      11. sub-neg 96.4%

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

      12. sub-neg 96.4%

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

      13. distribute-lft-neg-in 96.4%

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

      14. remove-double-neg 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 89.9%

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

   6. Taylor expanded in x around 0 79.3%

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

   7. Taylor expanded in t around 0 55.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot z\right)} \]

   if -1.05000000000000001e168 < a < -1.7e56 or 4.19999999999999977e248 < a

   1. Initial program 91.1%

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

      1. associate-+l+ 91.1%

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

      2. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 73.9%

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

   6. Taylor expanded in x around 0 58.2%

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

   if -1.7e56 < a < -3.5000000000000001e-59

   1. Initial program 96.6%

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

      1. add-cbrt-cube 69.5%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 69.5%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 69.5%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 69.5%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in z around inf 62.9%

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

      1. +-commutative 62.9%

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

   7. Simplified 62.9%

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

   8. Taylor expanded in a around inf 50.1%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -3.5000000000000001e-59 < a < -1.14999999999999994e-211

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 95.1%

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

      5. *-commutative 95.1%

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

      6. *-commutative 95.1%

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

      7. distribute-rgt-out 95.1%

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

      8. remove-double-neg 95.1%

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

      9. *-commutative 95.1%

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

      10. distribute-lft-neg-out 95.1%

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

      11. sub-neg 95.1%

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

      12. sub-neg 95.1%

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

      13. distribute-lft-neg-in 95.1%

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

      14. remove-double-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 79.2%

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

      1. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in t around inf 79.3%

      \[\leadsto z \cdot y + a \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf 56.3%

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

       1. *-commutative 56.3%

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

   11. Simplified 56.3%

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

   if -1.14999999999999994e-211 < a < 3.4000000000000001e-34

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 53.7%

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

   6. Taylor expanded in x around inf 46.8%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+168}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+56}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-211}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+248}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;\left(t\_1 + a \cdot t\right) + b \cdot \left(z \cdot a\right) \leq \infty:\\ \;\;\;\;t\_1 + \left(a \cdot t + a \cdot \left(b \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= (+ (+ t_1 (* a t)) (* b (* z a))) INFINITY)
     (+ t_1 (+ (* a t) (* a (* b z))))
     (+ x (* a (+ t (* b z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (((t_1 + (a * t)) + (b * (z * a))) <= ((double) INFINITY)) {
		tmp = t_1 + ((a * t) + (a * (b * z)));
	} else {
		tmp = x + (a * (t + (b * z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (((t_1 + (a * t)) + (b * (z * a))) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + ((a * t) + (a * (b * z)));
	} else {
		tmp = x + (a * (t + (b * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if ((t_1 + (a * t)) + (b * (z * a))) <= math.inf:
		tmp = t_1 + ((a * t) + (a * (b * z)))
	else:
		tmp = x + (a * (t + (b * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (Float64(Float64(t_1 + Float64(a * t)) + Float64(b * Float64(z * a))) <= Inf)
		tmp = Float64(t_1 + Float64(Float64(a * t) + Float64(a * Float64(b * z))));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(b * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (((t_1 + (a * t)) + (b * (z * a))) <= Inf)
		tmp = t_1 + ((a * t) + (a * (b * z)));
	else
		tmp = x + (a * (t + (b * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(N[(a * t), $MachinePrecision] + N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < +inf.0

   1. Initial program 96.8%

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

      1. associate-+l+ 96.8%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. fma-define 0.0%

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

      4. associate-*l* 8.3%

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

      5. *-commutative 8.3%

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

      6. *-commutative 8.3%

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

      7. distribute-rgt-out 50.0%

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

      8. remove-double-neg 50.0%

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

      9. *-commutative 50.0%

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

      10. distribute-lft-neg-out 50.0%

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

      11. sub-neg 50.0%

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

      12. sub-neg 50.0%

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

      13. distribute-lft-neg-in 50.0%

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

      14. remove-double-neg 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y around 0 83.3%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + b \cdot \left(z \cdot a\right) \leq \infty:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot t + a \cdot \left(b \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot z\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-210}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+247}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* b z))))
   (if (<= a -7.2e-59)
     t_1
     (if (<= a -2.05e-210)
       (* y z)
       (if (<= a 5.1e-28) x (if (<= a 2.3e+247) t_1 (* a t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (b * z);
	double tmp;
	if (a <= -7.2e-59) {
		tmp = t_1;
	} else if (a <= -2.05e-210) {
		tmp = y * z;
	} else if (a <= 5.1e-28) {
		tmp = x;
	} else if (a <= 2.3e+247) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * z)
    if (a <= (-7.2d-59)) then
        tmp = t_1
    else if (a <= (-2.05d-210)) then
        tmp = y * z
    else if (a <= 5.1d-28) then
        tmp = x
    else if (a <= 2.3d+247) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (b * z);
	double tmp;
	if (a <= -7.2e-59) {
		tmp = t_1;
	} else if (a <= -2.05e-210) {
		tmp = y * z;
	} else if (a <= 5.1e-28) {
		tmp = x;
	} else if (a <= 2.3e+247) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (b * z)
	tmp = 0
	if a <= -7.2e-59:
		tmp = t_1
	elif a <= -2.05e-210:
		tmp = y * z
	elif a <= 5.1e-28:
		tmp = x
	elif a <= 2.3e+247:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(b * z))
	tmp = 0.0
	if (a <= -7.2e-59)
		tmp = t_1;
	elseif (a <= -2.05e-210)
		tmp = Float64(y * z);
	elseif (a <= 5.1e-28)
		tmp = x;
	elseif (a <= 2.3e+247)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (b * z);
	tmp = 0.0;
	if (a <= -7.2e-59)
		tmp = t_1;
	elseif (a <= -2.05e-210)
		tmp = y * z;
	elseif (a <= 5.1e-28)
		tmp = x;
	elseif (a <= 2.3e+247)
		tmp = t_1;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e-59], t$95$1, If[LessEqual[a, -2.05e-210], N[(y * z), $MachinePrecision], If[LessEqual[a, 5.1e-28], x, If[LessEqual[a, 2.3e+247], t$95$1, N[(a * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.20000000000000001e-59 or 5.10000000000000009e-28 < a < 2.29999999999999991e247

   1. Initial program 86.9%

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

      1. associate-+l+ 86.9%

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

      2. +-commutative 86.9%

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

      3. fma-define 86.9%

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

      4. associate-*l* 91.7%

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

      5. *-commutative 91.7%

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

      6. *-commutative 91.7%

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

      7. distribute-rgt-out 95.1%

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

      8. remove-double-neg 95.1%

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

      9. *-commutative 95.1%

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

      10. distribute-lft-neg-out 95.1%

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

      11. sub-neg 95.1%

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

      12. sub-neg 95.1%

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

      13. distribute-lft-neg-in 95.1%

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

      14. remove-double-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around 0 89.2%

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

   6. Taylor expanded in x around 0 75.0%

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

   7. Taylor expanded in t around 0 47.7%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot z\right)} \]

   if -7.20000000000000001e-59 < a < -2.04999999999999995e-210

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 95.1%

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

      5. *-commutative 95.1%

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

      6. *-commutative 95.1%

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

      7. distribute-rgt-out 95.1%

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

      8. remove-double-neg 95.1%

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

      9. *-commutative 95.1%

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

      10. distribute-lft-neg-out 95.1%

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

      11. sub-neg 95.1%

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

      12. sub-neg 95.1%

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

      13. distribute-lft-neg-in 95.1%

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

      14. remove-double-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 79.2%

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

      1. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in t around inf 79.3%

      \[\leadsto z \cdot y + a \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf 56.3%

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

       1. *-commutative 56.3%

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

   11. Simplified 56.3%

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

   if -2.04999999999999995e-210 < a < 5.10000000000000009e-28

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 53.7%

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

   6. Taylor expanded in x around inf 46.8%

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

   if 2.29999999999999991e247 < a

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 93.7%

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

   6. Taylor expanded in x around 0 79.9%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-210}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+247}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{if}\;a \leq -1.72 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (+ t (* b z))))))
   (if (<= a -1.72e-59)
     t_1
     (if (<= a -1.25e-135)
       (+ (* a t) (* y z))
       (if (<= a 1.35e-35) (+ x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (t + (b * z)));
	double tmp;
	if (a <= -1.72e-59) {
		tmp = t_1;
	} else if (a <= -1.25e-135) {
		tmp = (a * t) + (y * z);
	} else if (a <= 1.35e-35) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * (t + (b * z)))
    if (a <= (-1.72d-59)) then
        tmp = t_1
    else if (a <= (-1.25d-135)) then
        tmp = (a * t) + (y * z)
    else if (a <= 1.35d-35) then
        tmp = x + (y * 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 a, double b) {
	double t_1 = x + (a * (t + (b * z)));
	double tmp;
	if (a <= -1.72e-59) {
		tmp = t_1;
	} else if (a <= -1.25e-135) {
		tmp = (a * t) + (y * z);
	} else if (a <= 1.35e-35) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (t + (b * z)))
	tmp = 0
	if a <= -1.72e-59:
		tmp = t_1
	elif a <= -1.25e-135:
		tmp = (a * t) + (y * z)
	elif a <= 1.35e-35:
		tmp = x + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(t + Float64(b * z))))
	tmp = 0.0
	if (a <= -1.72e-59)
		tmp = t_1;
	elseif (a <= -1.25e-135)
		tmp = Float64(Float64(a * t) + Float64(y * z));
	elseif (a <= 1.35e-35)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (t + (b * z)));
	tmp = 0.0;
	if (a <= -1.72e-59)
		tmp = t_1;
	elseif (a <= -1.25e-135)
		tmp = (a * t) + (y * z);
	elseif (a <= 1.35e-35)
		tmp = x + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.72e-59], t$95$1, If[LessEqual[a, -1.25e-135], N[(N[(a * t), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-35], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.72e-59 or 1.3499999999999999e-35 < a

   1. Initial program 87.7%

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

      1. associate-+l+ 87.7%

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

      2. +-commutative 87.7%

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

      3. fma-define 87.7%

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

      4. associate-*l* 91.6%

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

      5. *-commutative 91.6%

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

      6. *-commutative 91.6%

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

      7. distribute-rgt-out 94.9%

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

      8. remove-double-neg 94.9%

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

      9. *-commutative 94.9%

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

      10. distribute-lft-neg-out 94.9%

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

      11. sub-neg 94.9%

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

      12. sub-neg 94.9%

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

      13. distribute-lft-neg-in 94.9%

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

      14. remove-double-neg 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 89.1%

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

   if -1.72e-59 < a < -1.25000000000000005e-135

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 95.9%

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

      5. *-commutative 95.9%

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

      6. *-commutative 95.9%

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

      7. distribute-rgt-out 95.9%

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

      8. remove-double-neg 95.9%

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

      9. *-commutative 95.9%

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

      10. distribute-lft-neg-out 95.9%

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

      11. sub-neg 95.9%

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

      12. sub-neg 95.9%

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

      13. distribute-lft-neg-in 95.9%

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

      14. remove-double-neg 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 91.6%

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

      1. *-commutative 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around inf 87.5%

      \[\leadsto z \cdot y + a \cdot \color{blue}{t} \]

   if -1.25000000000000005e-135 < a < 1.3499999999999999e-35

   1. Initial program 98.8%

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

      1. add-cbrt-cube 91.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 91.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 91.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 91.4%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in a around 0 84.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.72 \cdot 10^{-59}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + b \cdot z\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-138}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* b z)))))
   (if (<= a -3.5e-59)
     t_1
     (if (<= a -7.5e-138)
       (+ (* a t) (* y z))
       (if (<= a 7e+69) (+ x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (b * z));
	double tmp;
	if (a <= -3.5e-59) {
		tmp = t_1;
	} else if (a <= -7.5e-138) {
		tmp = (a * t) + (y * z);
	} else if (a <= 7e+69) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (b * z))
    if (a <= (-3.5d-59)) then
        tmp = t_1
    else if (a <= (-7.5d-138)) then
        tmp = (a * t) + (y * z)
    else if (a <= 7d+69) then
        tmp = x + (y * 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 a, double b) {
	double t_1 = a * (t + (b * z));
	double tmp;
	if (a <= -3.5e-59) {
		tmp = t_1;
	} else if (a <= -7.5e-138) {
		tmp = (a * t) + (y * z);
	} else if (a <= 7e+69) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (b * z))
	tmp = 0
	if a <= -3.5e-59:
		tmp = t_1
	elif a <= -7.5e-138:
		tmp = (a * t) + (y * z)
	elif a <= 7e+69:
		tmp = x + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(b * z)))
	tmp = 0.0
	if (a <= -3.5e-59)
		tmp = t_1;
	elseif (a <= -7.5e-138)
		tmp = Float64(Float64(a * t) + Float64(y * z));
	elseif (a <= 7e+69)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (b * z));
	tmp = 0.0;
	if (a <= -3.5e-59)
		tmp = t_1;
	elseif (a <= -7.5e-138)
		tmp = (a * t) + (y * z);
	elseif (a <= 7e+69)
		tmp = x + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-59], t$95$1, If[LessEqual[a, -7.5e-138], N[(N[(a * t), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+69], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5000000000000001e-59 or 6.99999999999999974e69 < a

   1. Initial program 86.1%

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

      1. associate-+l+ 86.1%

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

      2. +-commutative 86.1%

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

      3. fma-define 86.1%

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

      4. associate-*l* 91.1%

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

      5. *-commutative 91.1%

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

      6. *-commutative 91.1%

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

      7. distribute-rgt-out 94.8%

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

      8. remove-double-neg 94.8%

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

      9. *-commutative 94.8%

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

      10. distribute-lft-neg-out 94.8%

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

      11. sub-neg 94.8%

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

      12. sub-neg 94.8%

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

      13. distribute-lft-neg-in 94.8%

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

      14. remove-double-neg 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around 0 92.2%

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

   6. Taylor expanded in x around 0 78.1%

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

   if -3.5000000000000001e-59 < a < -7.4999999999999995e-138

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 95.9%

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

      5. *-commutative 95.9%

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

      6. *-commutative 95.9%

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

      7. distribute-rgt-out 95.9%

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

      8. remove-double-neg 95.9%

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

      9. *-commutative 95.9%

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

      10. distribute-lft-neg-out 95.9%

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

      11. sub-neg 95.9%

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

      12. sub-neg 95.9%

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

      13. distribute-lft-neg-in 95.9%

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

      14. remove-double-neg 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 91.6%

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

      1. *-commutative 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around inf 87.5%

      \[\leadsto z \cdot y + a \cdot \color{blue}{t} \]

   if -7.4999999999999995e-138 < a < 6.99999999999999974e69

   1. Initial program 99.0%

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

      1. add-cbrt-cube 90.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 90.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 90.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 90.0%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in a around 0 79.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-138}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+57} \lor \neg \left(z \leq 1.55 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9.5e+125)
   (* y z)
   (if (or (<= z -5.7e+57) (not (<= z 1.55e+79)))
     (* z (* b a))
     (+ x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.5e+125) {
		tmp = y * z;
	} else if ((z <= -5.7e+57) || !(z <= 1.55e+79)) {
		tmp = z * (b * a);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-9.5d+125)) then
        tmp = y * z
    else if ((z <= (-5.7d+57)) .or. (.not. (z <= 1.55d+79))) then
        tmp = z * (b * a)
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.5e+125) {
		tmp = y * z;
	} else if ((z <= -5.7e+57) || !(z <= 1.55e+79)) {
		tmp = z * (b * a);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9.5e+125:
		tmp = y * z
	elif (z <= -5.7e+57) or not (z <= 1.55e+79):
		tmp = z * (b * a)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.5e+125)
		tmp = Float64(y * z);
	elseif ((z <= -5.7e+57) || !(z <= 1.55e+79))
		tmp = Float64(z * Float64(b * a));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9.5e+125)
		tmp = y * z;
	elseif ((z <= -5.7e+57) || ~((z <= 1.55e+79)))
		tmp = z * (b * a);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.5e+125], N[(y * z), $MachinePrecision], If[Or[LessEqual[z, -5.7e+57], N[Not[LessEqual[z, 1.55e+79]], $MachinePrecision]], N[(z * N[(b * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000041e125

   1. Initial program 83.1%

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

      1. associate-+l+ 83.1%

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

      2. +-commutative 83.1%

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

      3. fma-define 83.1%

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

      4. associate-*l* 94.1%

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

      5. *-commutative 94.1%

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

      6. *-commutative 94.1%

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

      7. distribute-rgt-out 97.0%

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

      8. remove-double-neg 97.0%

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

      9. *-commutative 97.0%

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

      10. distribute-lft-neg-out 97.0%

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

      11. sub-neg 97.0%

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

      12. sub-neg 97.0%

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

      13. distribute-lft-neg-in 97.0%

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

      14. remove-double-neg 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around inf 91.2%

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

      1. *-commutative 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in t around inf 68.9%

      \[\leadsto z \cdot y + a \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf 53.9%

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

       1. *-commutative 53.9%

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

   11. Simplified 53.9%

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

   if -9.50000000000000041e125 < z < -5.6999999999999998e57 or 1.5499999999999999e79 < z

   1. Initial program 85.7%

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

      1. add-cbrt-cube 69.6%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 69.6%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 69.6%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 69.6%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in z around inf 82.6%

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

      1. +-commutative 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in a around inf 61.1%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -5.6999999999999998e57 < z < 1.5499999999999999e79

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 69.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+57} \lor \neg \left(z \leq 1.55 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= y -4.5e+76)
     t_1
     (if (<= y -2.15e-58)
       (* z (* b a))
       (if (<= y 1.6e+49) (+ x (* a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (y <= -4.5e+76) {
		tmp = t_1;
	} else if (y <= -2.15e-58) {
		tmp = z * (b * a);
	} else if (y <= 1.6e+49) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (y <= (-4.5d+76)) then
        tmp = t_1
    else if (y <= (-2.15d-58)) then
        tmp = z * (b * a)
    else if (y <= 1.6d+49) then
        tmp = x + (a * 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 a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (y <= -4.5e+76) {
		tmp = t_1;
	} else if (y <= -2.15e-58) {
		tmp = z * (b * a);
	} else if (y <= 1.6e+49) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if y <= -4.5e+76:
		tmp = t_1
	elif y <= -2.15e-58:
		tmp = z * (b * a)
	elif y <= 1.6e+49:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (y <= -4.5e+76)
		tmp = t_1;
	elseif (y <= -2.15e-58)
		tmp = Float64(z * Float64(b * a));
	elseif (y <= 1.6e+49)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (y <= -4.5e+76)
		tmp = t_1;
	elseif (y <= -2.15e-58)
		tmp = z * (b * a);
	elseif (y <= 1.6e+49)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+76], t$95$1, If[LessEqual[y, -2.15e-58], N[(z * N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+49], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999997e76 or 1.60000000000000007e49 < y

   1. Initial program 95.0%

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

      1. add-cbrt-cube 85.3%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 85.3%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 85.3%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 85.3%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in a around 0 71.9%

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

   if -4.4999999999999997e76 < y < -2.15e-58

   1. Initial program 92.0%

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

      1. add-cbrt-cube 65.2%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 65.2%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 65.2%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 65.2%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in z around inf 76.9%

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

      1. +-commutative 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in a around inf 61.0%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -2.15e-58 < y < 1.60000000000000007e49

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 62.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+76}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-59} \lor \neg \left(a \leq 1.65 \cdot 10^{-35}\right):\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.3e-59) (not (<= a 1.65e-35)))
   (+ x (* a (+ t (* b z))))
   (+ x (+ (* a t) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.3e-59) || !(a <= 1.65e-35)) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = x + ((a * t) + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-5.3d-59)) .or. (.not. (a <= 1.65d-35))) then
        tmp = x + (a * (t + (b * z)))
    else
        tmp = x + ((a * t) + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.3e-59) || !(a <= 1.65e-35)) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = x + ((a * t) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.3e-59) or not (a <= 1.65e-35):
		tmp = x + (a * (t + (b * z)))
	else:
		tmp = x + ((a * t) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.3e-59) || !(a <= 1.65e-35))
		tmp = Float64(x + Float64(a * Float64(t + Float64(b * z))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -5.3e-59) || ~((a <= 1.65e-35)))
		tmp = x + (a * (t + (b * z)));
	else
		tmp = x + ((a * t) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.3e-59], N[Not[LessEqual[a, 1.65e-35]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.3000000000000003e-59 or 1.65e-35 < a

   1. Initial program 87.7%

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

      1. associate-+l+ 87.7%

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

      2. +-commutative 87.7%

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

      3. fma-define 87.7%

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

      4. associate-*l* 91.6%

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

      5. *-commutative 91.6%

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

      6. *-commutative 91.6%

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

      7. distribute-rgt-out 94.9%

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

      8. remove-double-neg 94.9%

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

      9. *-commutative 94.9%

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

      10. distribute-lft-neg-out 94.9%

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

      11. sub-neg 94.9%

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

      12. sub-neg 94.9%

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

      13. distribute-lft-neg-in 94.9%

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

      14. remove-double-neg 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 89.1%

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

   if -5.3000000000000003e-59 < a < 1.65e-35

   1. Initial program 99.0%

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

      1. associate-+l+ 99.0%

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

      2. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in b around 0 92.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-59} \lor \neg \left(a \leq 1.65 \cdot 10^{-35}\right):\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.15 \cdot 10^{-106} \lor \neg \left(a \leq 1.55 \cdot 10^{+72}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.15e-106) (not (<= a 1.55e+72)))
   (* a (+ t (* b z)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.15e-106) || !(a <= 1.55e+72)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4.15d-106)) .or. (.not. (a <= 1.55d+72))) then
        tmp = a * (t + (b * z))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.15e-106) || !(a <= 1.55e+72)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.15e-106) or not (a <= 1.55e+72):
		tmp = a * (t + (b * z))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.15e-106) || !(a <= 1.55e+72))
		tmp = Float64(a * Float64(t + Float64(b * z)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.15e-106) || ~((a <= 1.55e+72)))
		tmp = a * (t + (b * z));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.15e-106], N[Not[LessEqual[a, 1.55e+72]], $MachinePrecision]], N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.15000000000000023e-106 or 1.54999999999999994e72 < a

   1. Initial program 87.2%

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

      1. associate-+l+ 87.2%

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

      2. +-commutative 87.2%

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

      3. fma-define 87.2%

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

      4. associate-*l* 91.2%

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

      5. *-commutative 91.2%

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

      6. *-commutative 91.2%

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

      7. distribute-rgt-out 94.6%

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

      8. remove-double-neg 94.6%

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

      9. *-commutative 94.6%

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

      10. distribute-lft-neg-out 94.6%

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

      11. sub-neg 94.6%

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

      12. sub-neg 94.6%

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

      13. distribute-lft-neg-in 94.6%

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

      14. remove-double-neg 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around 0 88.9%

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

   6. Taylor expanded in x around 0 75.9%

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

   if -4.15000000000000023e-106 < a < 1.54999999999999994e72

   1. Initial program 99.1%

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

      1. add-cbrt-cube 90.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(a \cdot z\right)\right) \cdot \left(a \cdot z\right)}} \cdot b \]

      2. pow3 90.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{\color{blue}{{\left(a \cdot z\right)}^{3}}} \cdot b \]

      3. *-commutative 90.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{{\color{blue}{\left(z \cdot a\right)}}^{3}} \cdot b \]

   4. Applied egg-rr 90.0%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\sqrt[3]{{\left(z \cdot a\right)}^{3}}} \cdot b \]

   5. Taylor expanded in a around 0 79.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.15 \cdot 10^{-106} \lor \neg \left(a \leq 1.55 \cdot 10^{+72}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+105}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e+31) x (if (<= x 2.9e+105) (* a t) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+31) {
		tmp = x;
	} else if (x <= 2.9e+105) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.3d+31)) then
        tmp = x
    else if (x <= 2.9d+105) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+31) {
		tmp = x;
	} else if (x <= 2.9e+105) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e+31:
		tmp = x
	elif x <= 2.9e+105:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e+31)
		tmp = x;
	elseif (x <= 2.9e+105)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.3e+31)
		tmp = x;
	elseif (x <= 2.9e+105)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e+31], x, If[LessEqual[x, 2.9e+105], N[(a * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999992e31 or 2.9000000000000001e105 < x

   1. Initial program 90.5%

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

      1. associate-+l+ 90.5%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around 0 61.8%

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

   6. Taylor expanded in x around inf 57.1%

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

   if -3.29999999999999992e31 < x < 2.9000000000000001e105

   1. Initial program 93.1%

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

      1. associate-+l+ 93.1%

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

      2. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around 0 42.3%

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

   6. Taylor expanded in x around 0 36.1%

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

Alternative 12: 26.8% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 92.3%

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

   1. associate-+l+ 92.3%

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

   2. associate-*l* 93.2%

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

3. Simplified 93.2%

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

5. Taylor expanded in z around 0 48.7%

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

6. Taylor expanded in x around inf 24.5%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))