Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.6% → 98.0%

Time: 11.6s

Alternatives: 23

Speedup: 0.8×

• 35.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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 - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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 - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 INFINITY) t_1 (* y (- b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (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 + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 86.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 86.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-256}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -4.3e+55)
     t_1
     (if (<= b -8.4e-40)
       (* a (- 1.0 t))
       (if (<= b -1.08e-75)
         (* y (- b z))
         (if (<= b -1.15e-256)
           (+ x a)
           (if (<= b 1.02e+55) (* z (- 1.0 y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -4.3e+55) {
		tmp = t_1;
	} else if (b <= -8.4e-40) {
		tmp = a * (1.0 - t);
	} else if (b <= -1.08e-75) {
		tmp = y * (b - z);
	} else if (b <= -1.15e-256) {
		tmp = x + a;
	} else if (b <= 1.02e+55) {
		tmp = z * (1.0 - y);
	} 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 = b * (t + (y + (-2.0d0)))
    if (b <= (-4.3d+55)) then
        tmp = t_1
    else if (b <= (-8.4d-40)) then
        tmp = a * (1.0d0 - t)
    else if (b <= (-1.08d-75)) then
        tmp = y * (b - z)
    else if (b <= (-1.15d-256)) then
        tmp = x + a
    else if (b <= 1.02d+55) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -4.3e+55) {
		tmp = t_1;
	} else if (b <= -8.4e-40) {
		tmp = a * (1.0 - t);
	} else if (b <= -1.08e-75) {
		tmp = y * (b - z);
	} else if (b <= -1.15e-256) {
		tmp = x + a;
	} else if (b <= 1.02e+55) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -4.3e+55:
		tmp = t_1
	elif b <= -8.4e-40:
		tmp = a * (1.0 - t)
	elif b <= -1.08e-75:
		tmp = y * (b - z)
	elif b <= -1.15e-256:
		tmp = x + a
	elif b <= 1.02e+55:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -4.3e+55)
		tmp = t_1;
	elseif (b <= -8.4e-40)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= -1.08e-75)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -1.15e-256)
		tmp = Float64(x + a);
	elseif (b <= 1.02e+55)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -4.3e+55)
		tmp = t_1;
	elseif (b <= -8.4e-40)
		tmp = a * (1.0 - t);
	elseif (b <= -1.08e-75)
		tmp = y * (b - z);
	elseif (b <= -1.15e-256)
		tmp = x + a;
	elseif (b <= 1.02e+55)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.3e+55], t$95$1, If[LessEqual[b, -8.4e-40], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.08e-75], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-256], N[(x + a), $MachinePrecision], If[LessEqual[b, 1.02e+55], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.2999999999999999e55 or 1.02000000000000002e55 < b

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 80.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 80.3%

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

   if -4.2999999999999999e55 < b < -8.40000000000000071e-40

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto a \cdot \left(1 + -1 \cdot \color{blue}{t}\right) \]

      3. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \color{blue}{-1} \cdot t\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + \color{blue}{t}\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + \color{blue}{-1 \cdot t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1} \cdot t\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 42.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 42.7%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -8.40000000000000071e-40 < b < -1.08e-75

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 73.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 73.5%

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

   if -1.08e-75 < b < -1.15e-256

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 97.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot \left(1 - t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 - t\right)}\right)\right) \]

      3. --lowering--.f64 69.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 69.8%

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

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

       2. +-lowering-+.f64 47.9%

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{a}\right) \]

   11. Simplified 47.9%

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

   if -1.15e-256 < b < 1.02000000000000002e55

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 56.6%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 56.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+186}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right) + \left(\left(x + z\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8e+186)
   (+ x (* (- (+ y t) 2.0) b))
   (+ (+ (* y (- b z)) (* b (+ t -2.0))) (+ (+ x z) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+186) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = ((y * (b - z)) + (b * (t + -2.0))) + ((x + z) + (a * (1.0 - 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 (b <= (-8d+186)) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = ((y * (b - z)) + (b * (t + (-2.0d0)))) + ((x + z) + (a * (1.0d0 - 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 (b <= -8e+186) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = ((y * (b - z)) + (b * (t + -2.0))) + ((x + z) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8e+186:
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = ((y * (b - z)) + (b * (t + -2.0))) + ((x + z) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8e+186)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t + -2.0))) + Float64(Float64(x + z) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8e+186)
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = ((y * (b - z)) + (b * (t + -2.0))) + ((x + z) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8e+186], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.99999999999999984e186

   1. Initial program 87.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 93.9%

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

   if -7.99999999999999984e186 < b

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right), \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + 1 \cdot z\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + z\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(z + x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 97.3%

      \[\leadsto \color{blue}{\left(b \cdot \left(t + -2\right) + y \cdot \left(b - z\right)\right) + \left(\left(z + x\right) + a \cdot \left(1 - t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+186}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right) + \left(\left(x + z\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(\left(t + \left(y + -2\right)\right) - t \cdot \frac{a}{b}\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\left(x + a \cdot \left(1 - t\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= b -7.4e+55)
     (* b (- (+ t (+ y -2.0)) (* t (/ a b))))
     (if (<= b 5.8e+94)
       (+ (+ x (* a (- 1.0 t))) t_1)
       (+ (* (- (+ y t) 2.0) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (b <= -7.4e+55) {
		tmp = b * ((t + (y + -2.0)) - (t * (a / b)));
	} else if (b <= 5.8e+94) {
		tmp = (x + (a * (1.0 - t))) + t_1;
	} else {
		tmp = (((y + t) - 2.0) * b) + 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 * (1.0d0 - y)
    if (b <= (-7.4d+55)) then
        tmp = b * ((t + (y + (-2.0d0))) - (t * (a / b)))
    else if (b <= 5.8d+94) then
        tmp = (x + (a * (1.0d0 - t))) + t_1
    else
        tmp = (((y + t) - 2.0d0) * b) + 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 * (1.0 - y);
	double tmp;
	if (b <= -7.4e+55) {
		tmp = b * ((t + (y + -2.0)) - (t * (a / b)));
	} else if (b <= 5.8e+94) {
		tmp = (x + (a * (1.0 - t))) + t_1;
	} else {
		tmp = (((y + t) - 2.0) * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if b <= -7.4e+55:
		tmp = b * ((t + (y + -2.0)) - (t * (a / b)))
	elif b <= 5.8e+94:
		tmp = (x + (a * (1.0 - t))) + t_1
	else:
		tmp = (((y + t) - 2.0) * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -7.4e+55)
		tmp = Float64(b * Float64(Float64(t + Float64(y + -2.0)) - Float64(t * Float64(a / b))));
	elseif (b <= 5.8e+94)
		tmp = Float64(Float64(x + Float64(a * Float64(1.0 - t))) + t_1);
	else
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -7.4e+55)
		tmp = b * ((t + (y + -2.0)) - (t * (a / b)));
	elseif (b <= 5.8e+94)
		tmp = (x + (a * (1.0 - t))) + t_1;
	else
		tmp = (((y + t) - 2.0) * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+55], N[(b * N[(N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+94], N[(N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4000000000000004e55

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \left(\left(t + y\right) - 2\right) + -1 \cdot \frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(-1 \cdot \left(\left(t + y\right) - 2\right) + -1 \cdot \frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \left(\left(t + y\right) - 2\right) + -1 \cdot \frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)\right)\right)} \]

      3. distribute-lft-out N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\left(\left(t + y\right) - 2\right) + \frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\left(\left(t + y\right) - 2\right) + \frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto b \cdot \left(\left(\left(t + y\right) - 2\right) + \color{blue}{\frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(\left(t + y\right) - 2\right) + \frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\left(t + y\right) - 2\right), \color{blue}{\left(\frac{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}{b}\right)}\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t + \left(y - 2\right)\right), \left(\frac{\color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}}{b}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \left(y - 2\right)\right), \left(\frac{\color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}}{b}\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(\frac{x - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}}{b}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(\frac{x - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)}}{b}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \left(\frac{x - \left(a \cdot \left(t - 1\right) + \color{blue}{z \cdot \left(y - 1\right)}\right)}{b}\right)\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{/.f64}\left(\left(x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right), \color{blue}{b}\right)\right)\right) \]

   5. Simplified 94.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + -2\right)\right) + \frac{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)}{b}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \color{blue}{\left(-1 \cdot \frac{a \cdot t}{b}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \left(-1 \cdot \left(\frac{a}{b} \cdot \color{blue}{t}\right)\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \left(\left(-1 \cdot \frac{a}{b}\right) \cdot \color{blue}{t}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \color{blue}{\left(-1 \cdot \frac{a}{b}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{a}{b}\right)}\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\frac{a}{b}\right)\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(0 - \color{blue}{\frac{a}{b}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a}{b}\right)}\right)\right)\right)\right) \]

      8. /-lowering-/.f64 87.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(a, \color{blue}{b}\right)\right)\right)\right)\right) \]

   8. Simplified 87.5%

      \[\leadsto b \cdot \left(\left(t + \left(y + -2\right)\right) + \color{blue}{t \cdot \left(0 - \frac{a}{b}\right)}\right) \]

   if -7.4000000000000004e55 < b < 5.7999999999999997e94

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 92.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   if 5.7999999999999997e94 < b

   1. Initial program 96.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 92.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 92.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(\left(t + \left(y + -2\right)\right) - t \cdot \frac{a}{b}\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5 \cdot 10^{+67}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\left(x + a \cdot \left(1 - t\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -5e+67)
     (+ x t_2)
     (if (<= b 5.8e+94) (+ (+ x (* a (- 1.0 t))) t_1) (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5e+67) {
		tmp = x + t_2;
	} else if (b <= 5.8e+94) {
		tmp = (x + (a * (1.0 - t))) + t_1;
	} else {
		tmp = t_2 + 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) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-5d+67)) then
        tmp = x + t_2
    else if (b <= 5.8d+94) then
        tmp = (x + (a * (1.0d0 - t))) + t_1
    else
        tmp = t_2 + 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 * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5e+67) {
		tmp = x + t_2;
	} else if (b <= 5.8e+94) {
		tmp = (x + (a * (1.0 - t))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -5e+67:
		tmp = x + t_2
	elif b <= 5.8e+94:
		tmp = (x + (a * (1.0 - t))) + t_1
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -5e+67)
		tmp = Float64(x + t_2);
	elseif (b <= 5.8e+94)
		tmp = Float64(Float64(x + Float64(a * Float64(1.0 - t))) + t_1);
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -5e+67)
		tmp = x + t_2;
	elseif (b <= 5.8e+94)
		tmp = (x + (a * (1.0 - t))) + t_1;
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5e+67], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, 5.8e+94], N[(N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.99999999999999976e67

   1. Initial program 89.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.9%

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

   if -4.99999999999999976e67 < b < 5.7999999999999997e94

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.2%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   if 5.7999999999999997e94 < b

   1. Initial program 96.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 92.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 92.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+67}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(1 - t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.9e+68)
     (+ x t_2)
     (if (<= b 8.2e+84) (+ (* a (- 1.0 t)) t_1) (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.9e+68) {
		tmp = x + t_2;
	} else if (b <= 8.2e+84) {
		tmp = (a * (1.0 - t)) + t_1;
	} else {
		tmp = t_2 + 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) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-1.9d+68)) then
        tmp = x + t_2
    else if (b <= 8.2d+84) then
        tmp = (a * (1.0d0 - t)) + t_1
    else
        tmp = t_2 + 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 * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.9e+68) {
		tmp = x + t_2;
	} else if (b <= 8.2e+84) {
		tmp = (a * (1.0 - t)) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.9e+68:
		tmp = x + t_2
	elif b <= 8.2e+84:
		tmp = (a * (1.0 - t)) + t_1
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.9e+68)
		tmp = Float64(x + t_2);
	elseif (b <= 8.2e+84)
		tmp = Float64(Float64(a * Float64(1.0 - t)) + t_1);
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.9e+68)
		tmp = x + t_2;
	elseif (b <= 8.2e+84)
		tmp = (a * (1.0 - t)) + t_1;
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.9e+68], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, 8.2e+84], N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9e68

   1. Initial program 89.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.9%

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

   if -1.9e68 < b < 8.2000000000000006e84

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 - t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 - t\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      5. --lowering--.f64 71.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 71.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)} \]

   if 8.2000000000000006e84 < b

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 90.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 90.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+68}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+56}:\\ \;\;\;\;t\_1 + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.7e+68)
     (+ x t_2)
     (if (<= b 2.7e+56) (+ t_1 (* z (- 1.0 y))) (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.7e+68) {
		tmp = x + t_2;
	} else if (b <= 2.7e+56) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = t_2 + 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) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-2.7d+68)) then
        tmp = x + t_2
    else if (b <= 2.7d+56) then
        tmp = t_1 + (z * (1.0d0 - y))
    else
        tmp = t_2 + 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 * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.7e+68) {
		tmp = x + t_2;
	} else if (b <= 2.7e+56) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2.7e+68:
		tmp = x + t_2
	elif b <= 2.7e+56:
		tmp = t_1 + (z * (1.0 - y))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.7e+68)
		tmp = Float64(x + t_2);
	elseif (b <= 2.7e+56)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.7e+68)
		tmp = x + t_2;
	elseif (b <= 2.7e+56)
		tmp = t_1 + (z * (1.0 - y));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.7e+68], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, 2.7e+56], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.69999999999999991e68

   1. Initial program 89.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.9%

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

   if -2.69999999999999991e68 < b < 2.7000000000000001e56

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 - t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 - t\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      5. --lowering--.f64 71.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 71.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)} \]

   if 2.7000000000000001e56 < b

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot \left(1 - t\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot -1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(-1 + t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 - t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      16. --lowering--.f64 84.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+68}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-281}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -2.2e+55)
     t_1
     (if (<= b 3.4e-281)
       (+ x (* a (- 1.0 t)))
       (if (<= b 4.7e+55) (* z (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -2.2e+55) {
		tmp = t_1;
	} else if (b <= 3.4e-281) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.7e+55) {
		tmp = z * (1.0 - y);
	} 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 = b * (t + (y + (-2.0d0)))
    if (b <= (-2.2d+55)) then
        tmp = t_1
    else if (b <= 3.4d-281) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 4.7d+55) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -2.2e+55) {
		tmp = t_1;
	} else if (b <= 3.4e-281) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.7e+55) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -2.2e+55:
		tmp = t_1
	elif b <= 3.4e-281:
		tmp = x + (a * (1.0 - t))
	elif b <= 4.7e+55:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -2.2e+55)
		tmp = t_1;
	elseif (b <= 3.4e-281)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 4.7e+55)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -2.2e+55)
		tmp = t_1;
	elseif (b <= 3.4e-281)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 4.7e+55)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+55], t$95$1, If[LessEqual[b, 3.4e-281], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+55], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2000000000000001e55 or 4.7000000000000001e55 < b

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 80.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 80.3%

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

   if -2.2000000000000001e55 < b < 3.4e-281

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 92.2%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot \left(1 - t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 - t\right)}\right)\right) \]

      3. --lowering--.f64 61.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 61.1%

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]

   if 3.4e-281 < b < 4.7000000000000001e55

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 60.3%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 60.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2.15e+68)
     t_1
     (if (<= b 1.7e+91) (+ (* a (- 1.0 t)) (* z (- 1.0 y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.15e+68) {
		tmp = t_1;
	} else if (b <= 1.7e+91) {
		tmp = (a * (1.0 - t)) + (z * (1.0 - y));
	} 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 + t) - 2.0d0) * b)
    if (b <= (-2.15d+68)) then
        tmp = t_1
    else if (b <= 1.7d+91) then
        tmp = (a * (1.0d0 - t)) + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.15e+68) {
		tmp = t_1;
	} else if (b <= 1.7e+91) {
		tmp = (a * (1.0 - t)) + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -2.15e+68:
		tmp = t_1
	elif b <= 1.7e+91:
		tmp = (a * (1.0 - t)) + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2.15e+68)
		tmp = t_1;
	elseif (b <= 1.7e+91)
		tmp = Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -2.15e+68)
		tmp = t_1;
	elseif (b <= 1.7e+91)
		tmp = (a * (1.0 - t)) + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+68], t$95$1, If[LessEqual[b, 1.7e+91], N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1500000000000001e68 or 1.7e91 < b

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 87.5%

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

   if -2.1500000000000001e68 < b < 1.7e91

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 - t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 - t\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      5. --lowering--.f64 71.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 71.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7e+41)
     t_1
     (if (<= t -5.2e-127)
       (* z (- 1.0 y))
       (if (<= t 1.65e+31) (* y (- b z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7e+41) {
		tmp = t_1;
	} else if (t <= -5.2e-127) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.65e+31) {
		tmp = y * (b - 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 = t * (b - a)
    if (t <= (-7d+41)) then
        tmp = t_1
    else if (t <= (-5.2d-127)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 1.65d+31) then
        tmp = y * (b - 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 = t * (b - a);
	double tmp;
	if (t <= -7e+41) {
		tmp = t_1;
	} else if (t <= -5.2e-127) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.65e+31) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -7e+41:
		tmp = t_1
	elif t <= -5.2e-127:
		tmp = z * (1.0 - y)
	elif t <= 1.65e+31:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7e+41)
		tmp = t_1;
	elseif (t <= -5.2e-127)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 1.65e+31)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -7e+41)
		tmp = t_1;
	elseif (t <= -5.2e-127)
		tmp = z * (1.0 - y);
	elseif (t <= 1.65e+31)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+41], t$95$1, If[LessEqual[t, -5.2e-127], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+31], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.9999999999999998e41 or 1.64999999999999996e31 < t

   1. Initial program 95.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 69.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 69.1%

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

   if -6.9999999999999998e41 < t < -5.19999999999999982e-127

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 47.8%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -5.19999999999999982e-127 < t < 1.64999999999999996e31

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 47.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.76 \cdot 10^{-102}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.7e+22)
     t_1
     (if (<= t -1.76e-102) (+ x a) (if (<= t 7e+28) (* b (+ y -2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.7e+22) {
		tmp = t_1;
	} else if (t <= -1.76e-102) {
		tmp = x + a;
	} else if (t <= 7e+28) {
		tmp = b * (y + -2.0);
	} 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 = t * (b - a)
    if (t <= (-4.7d+22)) then
        tmp = t_1
    else if (t <= (-1.76d-102)) then
        tmp = x + a
    else if (t <= 7d+28) then
        tmp = b * (y + (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.7e+22) {
		tmp = t_1;
	} else if (t <= -1.76e-102) {
		tmp = x + a;
	} else if (t <= 7e+28) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.7e+22:
		tmp = t_1
	elif t <= -1.76e-102:
		tmp = x + a
	elif t <= 7e+28:
		tmp = b * (y + -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.7e+22)
		tmp = t_1;
	elseif (t <= -1.76e-102)
		tmp = Float64(x + a);
	elseif (t <= 7e+28)
		tmp = Float64(b * Float64(y + -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.7e+22)
		tmp = t_1;
	elseif (t <= -1.76e-102)
		tmp = x + a;
	elseif (t <= 7e+28)
		tmp = b * (y + -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e+22], t$95$1, If[LessEqual[t, -1.76e-102], N[(x + a), $MachinePrecision], If[LessEqual[t, 7e+28], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.70000000000000021e22 or 6.9999999999999999e28 < t

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 67.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 67.0%

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

   if -4.70000000000000021e22 < t < -1.7599999999999999e-102

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot \left(1 - t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 - t\right)}\right)\right) \]

      3. --lowering--.f64 43.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 43.2%

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

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

       2. +-lowering-+.f64 41.8%

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{a}\right) \]

   11. Simplified 41.8%

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

   if -1.7599999999999999e-102 < t < 6.9999999999999999e28

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right), \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + 1 \cdot z\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + z\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(z + x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 99.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(t + -2\right) + y \cdot \left(b - z\right)\right) + \left(\left(z + x\right) + a \cdot \left(1 - t\right)\right)} \]

   6. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(x + z\right)\right), \color{blue}{\left(-2 \cdot b + y \cdot \left(b - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(x + z\right)\right), \left(\color{blue}{-2 \cdot b} + y \cdot \left(b - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \left(-2 \cdot \color{blue}{b} + y \cdot \left(b - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(-2 \cdot b\right), \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(b \cdot -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 100.0%

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

   9. Taylor expanded in b around inf

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

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

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y - 2\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + -2\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(-2 + \color{blue}{y}\right)\right) \]

       5. +-lowering-+.f64 40.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-2, \color{blue}{y}\right)\right) \]

   11. Simplified 40.0%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.76 \cdot 10^{-102}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+56}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -7.2e+54) t_1 (if (<= b 6.3e+56) (+ x (* z (- 1.0 y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.2e+54) {
		tmp = t_1;
	} else if (b <= 6.3e+56) {
		tmp = x + (z * (1.0 - y));
	} 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 + t) - 2.0d0) * b)
    if (b <= (-7.2d+54)) then
        tmp = t_1
    else if (b <= 6.3d+56) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.2e+54) {
		tmp = t_1;
	} else if (b <= 6.3e+56) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -7.2e+54:
		tmp = t_1
	elif b <= 6.3e+56:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -7.2e+54)
		tmp = t_1;
	elseif (b <= 6.3e+56)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -7.2e+54)
		tmp = t_1;
	elseif (b <= 6.3e+56)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+54], t$95$1, If[LessEqual[b, 6.3e+56], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000003e54 or 6.3000000000000001e56 < b

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 84.8%

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

   if -7.2000000000000003e54 < b < 6.3000000000000001e56

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 92.6%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      3. --lowering--.f64 65.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 65.7%

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 24.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 60:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+19) (* t b) (if (<= b 3.8e-291) x (if (<= b 60.0) z (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+19) {
		tmp = t * b;
	} else if (b <= 3.8e-291) {
		tmp = x;
	} else if (b <= 60.0) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	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 (b <= (-2d+19)) then
        tmp = t * b
    else if (b <= 3.8d-291) then
        tmp = x
    else if (b <= 60.0d0) then
        tmp = z
    else
        tmp = y * b
    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 (b <= -2e+19) {
		tmp = t * b;
	} else if (b <= 3.8e-291) {
		tmp = x;
	} else if (b <= 60.0) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+19:
		tmp = t * b
	elif b <= 3.8e-291:
		tmp = x
	elif b <= 60.0:
		tmp = z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+19)
		tmp = Float64(t * b);
	elseif (b <= 3.8e-291)
		tmp = x;
	elseif (b <= 60.0)
		tmp = z;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+19)
		tmp = t * b;
	elseif (b <= 3.8e-291)
		tmp = x;
	elseif (b <= 60.0)
		tmp = z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+19], N[(t * b), $MachinePrecision], If[LessEqual[b, 3.8e-291], x, If[LessEqual[b, 60.0], z, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2e19

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 42.6%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 42.6%

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

   if -2e19 < b < 3.7999999999999998e-291

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 33.2%

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

   if 3.7999999999999998e-291 < b < 60

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 60.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 21.6%

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

   if 60 < b

   1. Initial program 96.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 49.3%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 49.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]

   8. Simplified 39.4%

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

Alternative 14: 62.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+94}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -1.3e+56) t_1 (if (<= b 7.2e+94) (+ x (* z (- 1.0 y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.3e+56) {
		tmp = t_1;
	} else if (b <= 7.2e+94) {
		tmp = x + (z * (1.0 - y));
	} 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 = b * (t + (y + (-2.0d0)))
    if (b <= (-1.3d+56)) then
        tmp = t_1
    else if (b <= 7.2d+94) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.3e+56) {
		tmp = t_1;
	} else if (b <= 7.2e+94) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -1.3e+56:
		tmp = t_1
	elif b <= 7.2e+94:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -1.3e+56)
		tmp = t_1;
	elseif (b <= 7.2e+94)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -1.3e+56)
		tmp = t_1;
	elseif (b <= 7.2e+94)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+56], t$95$1, If[LessEqual[b, 7.2e+94], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.30000000000000005e56 or 7.19999999999999985e94 < b

   1. Initial program 93.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 83.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 83.1%

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

   if -1.30000000000000005e56 < b < 7.19999999999999985e94

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 92.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      3. --lowering--.f64 64.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 64.8%

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 51.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.5e+27) t_1 (if (<= t 3.4e+31) (+ x (* y b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.5e+27) {
		tmp = t_1;
	} else if (t <= 3.4e+31) {
		tmp = x + (y * b);
	} 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 = t * (b - a)
    if (t <= (-3.5d+27)) then
        tmp = t_1
    else if (t <= 3.4d+31) then
        tmp = x + (y * b)
    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 = t * (b - a);
	double tmp;
	if (t <= -3.5e+27) {
		tmp = t_1;
	} else if (t <= 3.4e+31) {
		tmp = x + (y * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.5e+27:
		tmp = t_1
	elif t <= 3.4e+31:
		tmp = x + (y * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.5e+27)
		tmp = t_1;
	elseif (t <= 3.4e+31)
		tmp = Float64(x + Float64(y * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.5e+27)
		tmp = t_1;
	elseif (t <= 3.4e+31)
		tmp = x + (y * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+27], t$95$1, If[LessEqual[t, 3.4e+31], N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000002e27 or 3.3999999999999998e31 < t

   1. Initial program 95.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 68.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 68.5%

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

   if -3.5000000000000002e27 < t < 3.3999999999999998e31

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{b}\right)\right) \]

      2. *-lowering-*.f64 46.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right) \]

   8. Simplified 46.0%

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

Alternative 16: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -6.4e+30) t_1 (if (<= t 1.8e+31) (* y (- b z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6.4e+30) {
		tmp = t_1;
	} else if (t <= 1.8e+31) {
		tmp = y * (b - 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 = t * (b - a)
    if (t <= (-6.4d+30)) then
        tmp = t_1
    else if (t <= 1.8d+31) then
        tmp = y * (b - 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 = t * (b - a);
	double tmp;
	if (t <= -6.4e+30) {
		tmp = t_1;
	} else if (t <= 1.8e+31) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -6.4e+30:
		tmp = t_1
	elif t <= 1.8e+31:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.4e+30)
		tmp = t_1;
	elseif (t <= 1.8e+31)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.4e+30)
		tmp = t_1;
	elseif (t <= 1.8e+31)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e+30], t$95$1, If[LessEqual[t, 1.8e+31], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.39999999999999945e30 or 1.79999999999999998e31 < t

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 68.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 68.0%

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

   if -6.39999999999999945e30 < t < 1.79999999999999998e31

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 43.3%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 37.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+90}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+90)
   (* t b)
   (if (<= b 3.7e+84) (* a (- 1.0 t)) (* b (+ y -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+90) {
		tmp = t * b;
	} else if (b <= 3.7e+84) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (y + -2.0);
	}
	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 (b <= (-2.5d+90)) then
        tmp = t * b
    else if (b <= 3.7d+84) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (y + (-2.0d0))
    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 (b <= -2.5e+90) {
		tmp = t * b;
	} else if (b <= 3.7e+84) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+90:
		tmp = t * b
	elif b <= 3.7e+84:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (y + -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+90)
		tmp = Float64(t * b);
	elseif (b <= 3.7e+84)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+90)
		tmp = t * b;
	elseif (b <= 3.7e+84)
		tmp = a * (1.0 - t);
	else
		tmp = b * (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+90], N[(t * b), $MachinePrecision], If[LessEqual[b, 3.7e+84], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5000000000000002e90

   1. Initial program 88.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 91.2%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 51.3%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 51.3%

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

   if -2.5000000000000002e90 < b < 3.7e84

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto a \cdot \left(1 + -1 \cdot \color{blue}{t}\right) \]

      3. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \color{blue}{-1} \cdot t\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + \color{blue}{t}\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + \color{blue}{-1 \cdot t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1} \cdot t\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 31.8%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 31.8%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if 3.7e84 < b

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right), \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + 1 \cdot z\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + z\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(z + x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 90.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(t + -2\right) + y \cdot \left(b - z\right)\right) + \left(\left(z + x\right) + a \cdot \left(1 - t\right)\right)} \]

   6. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(x + z\right)\right), \color{blue}{\left(-2 \cdot b + y \cdot \left(b - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(x + z\right)\right), \left(\color{blue}{-2 \cdot b} + y \cdot \left(b - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \left(-2 \cdot \color{blue}{b} + y \cdot \left(b - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(-2 \cdot b\right), \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(b \cdot -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 80.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 80.9%

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

   9. Taylor expanded in b around inf

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

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

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y - 2\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + -2\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(-2 + \color{blue}{y}\right)\right) \]

       5. +-lowering-+.f64 62.3%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-2, \color{blue}{y}\right)\right) \]

   11. Simplified 62.3%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+90}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+61}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= t -9.5e+33) t_1 (if (<= t 7e+61) (+ x a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (t <= -9.5e+33) {
		tmp = t_1;
	} else if (t <= 7e+61) {
		tmp = x + a;
	} 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 * (1.0d0 - t)
    if (t <= (-9.5d+33)) then
        tmp = t_1
    else if (t <= 7d+61) then
        tmp = x + a
    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 * (1.0 - t);
	double tmp;
	if (t <= -9.5e+33) {
		tmp = t_1;
	} else if (t <= 7e+61) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if t <= -9.5e+33:
		tmp = t_1
	elif t <= 7e+61:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (t <= -9.5e+33)
		tmp = t_1;
	elseif (t <= 7e+61)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (t <= -9.5e+33)
		tmp = t_1;
	elseif (t <= 7e+61)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+33], t$95$1, If[LessEqual[t, 7e+61], N[(x + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000003e33 or 7.00000000000000036e61 < t

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto a \cdot \left(1 + -1 \cdot \color{blue}{t}\right) \]

      3. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \color{blue}{-1} \cdot t\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + \color{blue}{t}\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + \color{blue}{-1 \cdot t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1} \cdot t\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 48.5%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 48.5%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -9.5000000000000003e33 < t < 7.00000000000000036e61

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 68.4%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot \left(1 - t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 - t\right)}\right)\right) \]

      3. --lowering--.f64 32.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

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

       2. +-lowering-+.f64 32.6%

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{a}\right) \]

   11. Simplified 32.6%

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

Alternative 19: 33.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+105}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+19) (* t b) (if (<= b 1.06e+105) (+ x a) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+19) {
		tmp = t * b;
	} else if (b <= 1.06e+105) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	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 (b <= (-5.8d+19)) then
        tmp = t * b
    else if (b <= 1.06d+105) then
        tmp = x + a
    else
        tmp = y * b
    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 (b <= -5.8e+19) {
		tmp = t * b;
	} else if (b <= 1.06e+105) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.8e+19:
		tmp = t * b
	elif b <= 1.06e+105:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+19)
		tmp = Float64(t * b);
	elseif (b <= 1.06e+105)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.8e+19)
		tmp = t * b;
	elseif (b <= 1.06e+105)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+19], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.06e+105], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8e19

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 42.6%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 42.6%

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

   if -5.8e19 < b < 1.06e105

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x - a \cdot \left(t - 1\right)\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(-1 + t\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(-1 \cdot -1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(y - \color{blue}{1}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right)\right) \]

      22. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right)\right) \]

      23. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      26. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot \left(1 - t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 - t\right)}\right)\right) \]

      3. --lowering--.f64 50.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

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

       2. +-lowering-+.f64 30.0%

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{a}\right) \]

   11. Simplified 30.0%

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

   if 1.06e105 < b

   1. Initial program 95.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 55.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 55.5%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.2%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]

   8. Simplified 49.2%

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

Alternative 20: 26.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.2e+31) (* t b) (if (<= t 6e+33) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.2e+31) {
		tmp = t * b;
	} else if (t <= 6e+33) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	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 (t <= (-5.2d+31)) then
        tmp = t * b
    else if (t <= 6d+33) then
        tmp = x
    else
        tmp = t * b
    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 (t <= -5.2e+31) {
		tmp = t * b;
	} else if (t <= 6e+33) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.2e+31:
		tmp = t * b
	elif t <= 6e+33:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.2e+31)
		tmp = Float64(t * b);
	elseif (t <= 6e+33)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.2e+31)
		tmp = t * b;
	elseif (t <= 6e+33)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.2e+31], N[(t * b), $MachinePrecision], If[LessEqual[t, 6e+33], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e31 or 5.99999999999999967e33 < t

   1. Initial program 95.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 48.4%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 37.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 37.0%

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

   if -5.2e31 < t < 5.99999999999999967e33

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 24.8%

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

Alternative 21: 21.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+103}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.4e+54) x (if (<= x 5e+103) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.4e+54) {
		tmp = x;
	} else if (x <= 5e+103) {
		tmp = z;
	} 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 <= (-2.4d+54)) then
        tmp = x
    else if (x <= 5d+103) then
        tmp = z
    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 <= -2.4e+54) {
		tmp = x;
	} else if (x <= 5e+103) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.4e+54:
		tmp = x
	elif x <= 5e+103:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.4e+54)
		tmp = x;
	elseif (x <= 5e+103)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.4e+54)
		tmp = x;
	elseif (x <= 5e+103)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.4e+54], x, If[LessEqual[x, 5e+103], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999998e54 or 5e103 < x

   1. Initial program 95.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 37.0%

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

   if -2.39999999999999998e54 < x < 5e103

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 40.2%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 16.3%

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

Alternative 22: 20.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+111}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.7e+111) a (if (<= a 1.5e+223) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.7e+111) {
		tmp = a;
	} else if (a <= 1.5e+223) {
		tmp = x;
	} else {
		tmp = a;
	}
	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 <= (-3.7d+111)) then
        tmp = a
    else if (a <= 1.5d+223) then
        tmp = x
    else
        tmp = a
    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 <= -3.7e+111) {
		tmp = a;
	} else if (a <= 1.5e+223) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.7e+111:
		tmp = a
	elif a <= 1.5e+223:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.7e+111)
		tmp = a;
	elseif (a <= 1.5e+223)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.7e+111)
		tmp = a;
	elseif (a <= 1.5e+223)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.7e+111], a, If[LessEqual[a, 1.5e+223], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7000000000000003e111 or 1.50000000000000001e223 < a

   1. Initial program 89.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right), \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + 1 \cdot z\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + z\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(z + x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 89.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(t + -2\right) + y \cdot \left(b - z\right)\right) + \left(\left(z + x\right) + a \cdot \left(1 - t\right)\right)} \]

   6. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(x + z\right)\right), \color{blue}{\left(-2 \cdot b + y \cdot \left(b - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(x + z\right)\right), \left(\color{blue}{-2 \cdot b} + y \cdot \left(b - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \left(-2 \cdot \color{blue}{b} + y \cdot \left(b - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(-2 \cdot b\right), \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(b \cdot -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 55.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 55.7%

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

   9. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a} \]
   10. Step-by-step derivation

   11. Simplified 18.8%

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

   if -3.7000000000000003e111 < a < 1.50000000000000001e223

   1. Initial program 99.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 20.2%

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

Alternative 23: 11.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

   2. associate--l+ N/A

      \[\leadsto \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right), \color{blue}{\left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t - 2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(t + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \left(y \cdot \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \left(b - z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   11. associate--r+ N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right)\right) \]

   12. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \left(\left(x - -1 \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

   14. cancel-sign-sub-inv N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + 1 \cdot z\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

   16. *-lft-identity N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(x + z\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\left(z + x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

   19. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

   20. mul-1-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

   22. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

5. Simplified 95.3%

   \[\leadsto \color{blue}{\left(b \cdot \left(t + -2\right) + y \cdot \left(b - z\right)\right) + \left(\left(z + x\right) + a \cdot \left(1 - t\right)\right)} \]

6. Taylor expanded in t around 0

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

   1. associate-+r+ N/A

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

   2. associate-+r+ N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(a + \left(x + z\right)\right), \color{blue}{\left(-2 \cdot b + y \cdot \left(b - z\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(x + z\right)\right), \left(\color{blue}{-2 \cdot b} + y \cdot \left(b - z\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \left(-2 \cdot \color{blue}{b} + y \cdot \left(b - z\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(-2 \cdot b\right), \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\left(b \cdot -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \left(\color{blue}{y} \cdot \left(b - z\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right)\right) \]

   10. --lowering--.f64 73.2%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, -2\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

8. Simplified 73.2%

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

9. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a} \]
10. Step-by-step derivation

11. Simplified 7.1%

    \[\leadsto \color{blue}{a} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))