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

Percentage Accurate: 95.2% → 98.0%

Time: 16.9s

Alternatives: 27

Speedup: 0.5×

• 35.9% 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: 95.2% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. sub-neg 0.0%

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

      5. metadata-eval 0.0%

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

      6. remove-double-neg 0.0%

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

      7. remove-double-neg 0.0%

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

      8. sub-neg 0.0%

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

      9. metadata-eval 0.0%

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

      10. associate--l+ 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around inf 50.0%

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

   5. Taylor expanded in y around 0 83.3%

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

      1. cancel-sign-sub-inv 83.3%

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

      2. metadata-eval 83.3%

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

      3. *-lft-identity 83.3%

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

      4. +-commutative 83.3%

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

   7. Simplified 83.3%

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

4. Final simplification 99.6%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 97.6%

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

   2. fma-def 98.8%

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

   3. +-commutative 98.8%

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

   4. associate--l+ 98.8%

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

   5. sub-neg 98.8%

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

   6. associate-+l- 98.8%

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

   7. fma-neg 98.8%

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

   8. sub-neg 98.8%

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

   9. metadata-eval 98.8%

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

   10. distribute-lft-neg-in 98.8%

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

   11. distribute-lft-neg-in 98.8%

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

   12. remove-double-neg 98.8%

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

   13. sub-neg 98.8%

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

   14. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 60.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-290}:\\ \;\;\;\;\left(x + z\right) + b \cdot -2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-30}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a)))) (t_2 (* y (- b z))))
   (if (<= y -3.9e+56)
     t_2
     (if (<= y -9.8e-243)
       t_1
       (if (<= y 4.4e-290)
         (+ (+ x z) (* b -2.0))
         (if (<= y 5.8e-225)
           t_1
           (if (<= y 2.8e-30) (+ x (+ z a)) (if (<= y 3.3e+97) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -3.9e+56) {
		tmp = t_2;
	} else if (y <= -9.8e-243) {
		tmp = t_1;
	} else if (y <= 4.4e-290) {
		tmp = (x + z) + (b * -2.0);
	} else if (y <= 5.8e-225) {
		tmp = t_1;
	} else if (y <= 2.8e-30) {
		tmp = x + (z + a);
	} else if (y <= 3.3e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + (t * (b - a))
    t_2 = y * (b - z)
    if (y <= (-3.9d+56)) then
        tmp = t_2
    else if (y <= (-9.8d-243)) then
        tmp = t_1
    else if (y <= 4.4d-290) then
        tmp = (x + z) + (b * (-2.0d0))
    else if (y <= 5.8d-225) then
        tmp = t_1
    else if (y <= 2.8d-30) then
        tmp = x + (z + a)
    else if (y <= 3.3d+97) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -3.9e+56) {
		tmp = t_2;
	} else if (y <= -9.8e-243) {
		tmp = t_1;
	} else if (y <= 4.4e-290) {
		tmp = (x + z) + (b * -2.0);
	} else if (y <= 5.8e-225) {
		tmp = t_1;
	} else if (y <= 2.8e-30) {
		tmp = x + (z + a);
	} else if (y <= 3.3e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -3.9e+56:
		tmp = t_2
	elif y <= -9.8e-243:
		tmp = t_1
	elif y <= 4.4e-290:
		tmp = (x + z) + (b * -2.0)
	elif y <= 5.8e-225:
		tmp = t_1
	elif y <= 2.8e-30:
		tmp = x + (z + a)
	elif y <= 3.3e+97:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3.9e+56)
		tmp = t_2;
	elseif (y <= -9.8e-243)
		tmp = t_1;
	elseif (y <= 4.4e-290)
		tmp = Float64(Float64(x + z) + Float64(b * -2.0));
	elseif (y <= 5.8e-225)
		tmp = t_1;
	elseif (y <= 2.8e-30)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 3.3e+97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * (b - a));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.9e+56)
		tmp = t_2;
	elseif (y <= -9.8e-243)
		tmp = t_1;
	elseif (y <= 4.4e-290)
		tmp = (x + z) + (b * -2.0);
	elseif (y <= 5.8e-225)
		tmp = t_1;
	elseif (y <= 2.8e-30)
		tmp = x + (z + a);
	elseif (y <= 3.3e+97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+56], t$95$2, If[LessEqual[y, -9.8e-243], t$95$1, If[LessEqual[y, 4.4e-290], N[(N[(x + z), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-225], t$95$1, If[LessEqual[y, 2.8e-30], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+97], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.89999999999999994e56 or 3.3000000000000001e97 < y

   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. Step-by-step derivation

      1. associate-+l- 95.4%

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

      2. *-commutative 95.4%

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

      3. *-commutative 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

      6. remove-double-neg 95.4%

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

      7. remove-double-neg 95.4%

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

      8. sub-neg 95.4%

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

      9. metadata-eval 95.4%

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

      10. associate--l+ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 74.4%

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

   if -3.89999999999999994e56 < y < -9.8e-243 or 4.4000000000000002e-290 < y < 5.7999999999999996e-225 or 2.79999999999999988e-30 < y < 3.3000000000000001e97

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.9%

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

      2. *-commutative 98.9%

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

      3. *-commutative 98.9%

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

      4. sub-neg 98.9%

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

      5. metadata-eval 98.9%

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

      6. remove-double-neg 98.9%

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

      7. remove-double-neg 98.9%

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

      8. sub-neg 98.9%

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

      9. metadata-eval 98.9%

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

      10. associate--l+ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around inf 81.7%

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

   5. Taylor expanded in z around 0 64.6%

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

   if -9.8e-243 < y < 4.4000000000000002e-290

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 99.9%

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

      8. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 99.9%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

      13. fma-def 99.9%

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

      14. sub-neg 99.9%

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

      15. associate-+l+ 99.9%

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

      16. metadata-eval 99.9%

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

      17. sub-neg 99.9%

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

      18. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in t around 0 87.9%

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

   6. Taylor expanded in a around 0 81.9%

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

   if 5.7999999999999996e-225 < y < 2.79999999999999988e-30

   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. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in t around 0 77.6%

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

   6. Taylor expanded in b around 0 68.6%

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

      1. associate-+r+ 68.6%

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

   8. Simplified 68.6%

      \[\leadsto \color{blue}{\left(a + z\right) + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-243}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-290}:\\ \;\;\;\;\left(x + z\right) + b \cdot -2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-225}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-30}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+97}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 4: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) - t \cdot a\\ t_2 := x - \left(y + -1\right) \cdot z\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-200}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-174}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x a) (* t a))) (t_2 (- x (* (+ y -1.0) z))))
   (if (<= z -1.7e+119)
     t_2
     (if (<= z -3.9e-200)
       (+ x (* t (- b a)))
       (if (<= z -1.9e-268)
         (* b (- (+ t y) 2.0))
         (if (<= z 1.2e-213)
           t_1
           (if (<= z 1.7e-174)
             (* (- y 2.0) b)
             (if (<= z 2.9e-28) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - (t * a);
	double t_2 = x - ((y + -1.0) * z);
	double tmp;
	if (z <= -1.7e+119) {
		tmp = t_2;
	} else if (z <= -3.9e-200) {
		tmp = x + (t * (b - a));
	} else if (z <= -1.9e-268) {
		tmp = b * ((t + y) - 2.0);
	} else if (z <= 1.2e-213) {
		tmp = t_1;
	} else if (z <= 1.7e-174) {
		tmp = (y - 2.0) * b;
	} else if (z <= 2.9e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (x + a) - (t * a)
    t_2 = x - ((y + (-1.0d0)) * z)
    if (z <= (-1.7d+119)) then
        tmp = t_2
    else if (z <= (-3.9d-200)) then
        tmp = x + (t * (b - a))
    else if (z <= (-1.9d-268)) then
        tmp = b * ((t + y) - 2.0d0)
    else if (z <= 1.2d-213) then
        tmp = t_1
    else if (z <= 1.7d-174) then
        tmp = (y - 2.0d0) * b
    else if (z <= 2.9d-28) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - (t * a);
	double t_2 = x - ((y + -1.0) * z);
	double tmp;
	if (z <= -1.7e+119) {
		tmp = t_2;
	} else if (z <= -3.9e-200) {
		tmp = x + (t * (b - a));
	} else if (z <= -1.9e-268) {
		tmp = b * ((t + y) - 2.0);
	} else if (z <= 1.2e-213) {
		tmp = t_1;
	} else if (z <= 1.7e-174) {
		tmp = (y - 2.0) * b;
	} else if (z <= 2.9e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) - (t * a)
	t_2 = x - ((y + -1.0) * z)
	tmp = 0
	if z <= -1.7e+119:
		tmp = t_2
	elif z <= -3.9e-200:
		tmp = x + (t * (b - a))
	elif z <= -1.9e-268:
		tmp = b * ((t + y) - 2.0)
	elif z <= 1.2e-213:
		tmp = t_1
	elif z <= 1.7e-174:
		tmp = (y - 2.0) * b
	elif z <= 2.9e-28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + a) - Float64(t * a))
	t_2 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (z <= -1.7e+119)
		tmp = t_2;
	elseif (z <= -3.9e-200)
		tmp = Float64(x + Float64(t * Float64(b - a)));
	elseif (z <= -1.9e-268)
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	elseif (z <= 1.2e-213)
		tmp = t_1;
	elseif (z <= 1.7e-174)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (z <= 2.9e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + a) - (t * a);
	t_2 = x - ((y + -1.0) * z);
	tmp = 0.0;
	if (z <= -1.7e+119)
		tmp = t_2;
	elseif (z <= -3.9e-200)
		tmp = x + (t * (b - a));
	elseif (z <= -1.9e-268)
		tmp = b * ((t + y) - 2.0);
	elseif (z <= 1.2e-213)
		tmp = t_1;
	elseif (z <= 1.7e-174)
		tmp = (y - 2.0) * b;
	elseif (z <= 2.9e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+119], t$95$2, If[LessEqual[z, -3.9e-200], N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-268], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-213], t$95$1, If[LessEqual[z, 1.7e-174], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, 2.9e-28], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.70000000000000007e119 or 2.90000000000000013e-28 < z

   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. Step-by-step derivation

      1. associate-+l- 96.3%

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

      2. *-commutative 96.3%

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

      3. *-commutative 96.3%

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

      4. sub-neg 96.3%

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

      5. metadata-eval 96.3%

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

      6. remove-double-neg 96.3%

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

      7. remove-double-neg 96.3%

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

      8. sub-neg 96.3%

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

      9. metadata-eval 96.3%

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

      10. associate--l+ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 88.1%

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

   5. Taylor expanded in t around 0 76.2%

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

   if -1.70000000000000007e119 < z < -3.89999999999999999e-200

   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. Step-by-step derivation

      1. associate-+l- 98.5%

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

      2. *-commutative 98.5%

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

      3. *-commutative 98.5%

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

      4. sub-neg 98.5%

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

      5. metadata-eval 98.5%

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

      6. remove-double-neg 98.5%

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

      7. remove-double-neg 98.5%

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

      8. sub-neg 98.5%

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

      9. metadata-eval 98.5%

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

      10. associate--l+ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around inf 73.4%

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

   5. Taylor expanded in z around 0 60.6%

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

   if -3.89999999999999999e-200 < z < -1.9000000000000001e-268

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 72.6%

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

   if -1.9000000000000001e-268 < z < 1.19999999999999998e-213 or 1.7000000000000001e-174 < z < 2.90000000000000013e-28

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.0%

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

      2. *-commutative 98.0%

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

      3. *-commutative 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

      6. remove-double-neg 98.0%

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

      7. remove-double-neg 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. associate--l+ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around inf 73.6%

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

      1. sub-neg 73.6%

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

      2. metadata-eval 73.6%

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

      3. *-commutative 73.6%

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

      4. distribute-rgt-in 73.6%

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

      5. *-commutative 73.6%

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

      6. mul-1-neg 73.6%

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

      7. unsub-neg 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in z around 0 70.0%

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

   if 1.19999999999999998e-213 < z < 1.7000000000000001e-174

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 93.9%

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

   5. Taylor expanded in t around 0 93.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+119}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-200}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-213}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-174}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \end{array} \]

Alternative 5: 63.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a))))
        (t_2 (* y (- b z)))
        (t_3 (+ a (+ (+ x z) (* b -2.0)))))
   (if (<= y -2.4e+56)
     t_2
     (if (<= y -2.35e-138)
       t_1
       (if (<= y 3.4e-290)
         t_3
         (if (<= y 4.5e-227)
           t_1
           (if (<= y 6.5e-14) t_3 (if (<= y 4.8e+93) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + ((x + z) + (b * -2.0));
	double tmp;
	if (y <= -2.4e+56) {
		tmp = t_2;
	} else if (y <= -2.35e-138) {
		tmp = t_1;
	} else if (y <= 3.4e-290) {
		tmp = t_3;
	} else if (y <= 4.5e-227) {
		tmp = t_1;
	} else if (y <= 6.5e-14) {
		tmp = t_3;
	} else if (y <= 4.8e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x + (t * (b - a))
    t_2 = y * (b - z)
    t_3 = a + ((x + z) + (b * (-2.0d0)))
    if (y <= (-2.4d+56)) then
        tmp = t_2
    else if (y <= (-2.35d-138)) then
        tmp = t_1
    else if (y <= 3.4d-290) then
        tmp = t_3
    else if (y <= 4.5d-227) then
        tmp = t_1
    else if (y <= 6.5d-14) then
        tmp = t_3
    else if (y <= 4.8d+93) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + ((x + z) + (b * -2.0));
	double tmp;
	if (y <= -2.4e+56) {
		tmp = t_2;
	} else if (y <= -2.35e-138) {
		tmp = t_1;
	} else if (y <= 3.4e-290) {
		tmp = t_3;
	} else if (y <= 4.5e-227) {
		tmp = t_1;
	} else if (y <= 6.5e-14) {
		tmp = t_3;
	} else if (y <= 4.8e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	t_2 = y * (b - z)
	t_3 = a + ((x + z) + (b * -2.0))
	tmp = 0
	if y <= -2.4e+56:
		tmp = t_2
	elif y <= -2.35e-138:
		tmp = t_1
	elif y <= 3.4e-290:
		tmp = t_3
	elif y <= 4.5e-227:
		tmp = t_1
	elif y <= 6.5e-14:
		tmp = t_3
	elif y <= 4.8e+93:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(a + Float64(Float64(x + z) + Float64(b * -2.0)))
	tmp = 0.0
	if (y <= -2.4e+56)
		tmp = t_2;
	elseif (y <= -2.35e-138)
		tmp = t_1;
	elseif (y <= 3.4e-290)
		tmp = t_3;
	elseif (y <= 4.5e-227)
		tmp = t_1;
	elseif (y <= 6.5e-14)
		tmp = t_3;
	elseif (y <= 4.8e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * (b - a));
	t_2 = y * (b - z);
	t_3 = a + ((x + z) + (b * -2.0));
	tmp = 0.0;
	if (y <= -2.4e+56)
		tmp = t_2;
	elseif (y <= -2.35e-138)
		tmp = t_1;
	elseif (y <= 3.4e-290)
		tmp = t_3;
	elseif (y <= 4.5e-227)
		tmp = t_1;
	elseif (y <= 6.5e-14)
		tmp = t_3;
	elseif (y <= 4.8e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(N[(x + z), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+56], t$95$2, If[LessEqual[y, -2.35e-138], t$95$1, If[LessEqual[y, 3.4e-290], t$95$3, If[LessEqual[y, 4.5e-227], t$95$1, If[LessEqual[y, 6.5e-14], t$95$3, If[LessEqual[y, 4.8e+93], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000013e56 or 4.80000000000000021e93 < y

   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. Step-by-step derivation

      1. associate-+l- 95.4%

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

      2. *-commutative 95.4%

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

      3. *-commutative 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

      6. remove-double-neg 95.4%

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

      7. remove-double-neg 95.4%

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

      8. sub-neg 95.4%

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

      9. metadata-eval 95.4%

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

      10. associate--l+ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 74.4%

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

   if -2.40000000000000013e56 < y < -2.3500000000000001e-138 or 3.39999999999999984e-290 < y < 4.49999999999999993e-227 or 6.5000000000000001e-14 < y < 4.80000000000000021e93

   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. Step-by-step derivation

      1. associate-+l- 98.7%

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

      2. *-commutative 98.7%

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

      3. *-commutative 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

      6. remove-double-neg 98.7%

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

      7. remove-double-neg 98.7%

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

      8. sub-neg 98.7%

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

      9. metadata-eval 98.7%

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

      10. associate--l+ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 86.2%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -2.3500000000000001e-138 < y < 3.39999999999999984e-290 or 4.49999999999999993e-227 < y < 6.5000000000000001e-14

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in t around 0 75.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-138}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-290}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-227}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+93}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;y \cdot b - y \cdot z\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a)))) (t_2 (+ a (+ (+ x z) (* b -2.0)))))
   (if (<= y -4.6e+56)
     (- (* y b) (* y z))
     (if (<= y -5.8e-138)
       t_1
       (if (<= y 1.5e-289)
         t_2
         (if (<= y 4.2e-227)
           t_1
           (if (<= y 2.7e-13) t_2 (if (<= y 4.1e+92) t_1 (* y (- b z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = a + ((x + z) + (b * -2.0));
	double tmp;
	if (y <= -4.6e+56) {
		tmp = (y * b) - (y * z);
	} else if (y <= -5.8e-138) {
		tmp = t_1;
	} else if (y <= 1.5e-289) {
		tmp = t_2;
	} else if (y <= 4.2e-227) {
		tmp = t_1;
	} else if (y <= 2.7e-13) {
		tmp = t_2;
	} else if (y <= 4.1e+92) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (b - a))
    t_2 = a + ((x + z) + (b * (-2.0d0)))
    if (y <= (-4.6d+56)) then
        tmp = (y * b) - (y * z)
    else if (y <= (-5.8d-138)) then
        tmp = t_1
    else if (y <= 1.5d-289) then
        tmp = t_2
    else if (y <= 4.2d-227) then
        tmp = t_1
    else if (y <= 2.7d-13) then
        tmp = t_2
    else if (y <= 4.1d+92) then
        tmp = t_1
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = a + ((x + z) + (b * -2.0));
	double tmp;
	if (y <= -4.6e+56) {
		tmp = (y * b) - (y * z);
	} else if (y <= -5.8e-138) {
		tmp = t_1;
	} else if (y <= 1.5e-289) {
		tmp = t_2;
	} else if (y <= 4.2e-227) {
		tmp = t_1;
	} else if (y <= 2.7e-13) {
		tmp = t_2;
	} else if (y <= 4.1e+92) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	t_2 = a + ((x + z) + (b * -2.0))
	tmp = 0
	if y <= -4.6e+56:
		tmp = (y * b) - (y * z)
	elif y <= -5.8e-138:
		tmp = t_1
	elif y <= 1.5e-289:
		tmp = t_2
	elif y <= 4.2e-227:
		tmp = t_1
	elif y <= 2.7e-13:
		tmp = t_2
	elif y <= 4.1e+92:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	t_2 = Float64(a + Float64(Float64(x + z) + Float64(b * -2.0)))
	tmp = 0.0
	if (y <= -4.6e+56)
		tmp = Float64(Float64(y * b) - Float64(y * z));
	elseif (y <= -5.8e-138)
		tmp = t_1;
	elseif (y <= 1.5e-289)
		tmp = t_2;
	elseif (y <= 4.2e-227)
		tmp = t_1;
	elseif (y <= 2.7e-13)
		tmp = t_2;
	elseif (y <= 4.1e+92)
		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 + (t * (b - a));
	t_2 = a + ((x + z) + (b * -2.0));
	tmp = 0.0;
	if (y <= -4.6e+56)
		tmp = (y * b) - (y * z);
	elseif (y <= -5.8e-138)
		tmp = t_1;
	elseif (y <= 1.5e-289)
		tmp = t_2;
	elseif (y <= 4.2e-227)
		tmp = t_1;
	elseif (y <= 2.7e-13)
		tmp = t_2;
	elseif (y <= 4.1e+92)
		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[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(x + z), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+56], N[(N[(y * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-138], t$95$1, If[LessEqual[y, 1.5e-289], t$95$2, If[LessEqual[y, 4.2e-227], t$95$1, If[LessEqual[y, 2.7e-13], t$95$2, If[LessEqual[y, 4.1e+92], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.60000000000000029e56

   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. Step-by-step derivation

      1. associate-+l- 96.4%

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

      2. *-commutative 96.4%

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

      3. *-commutative 96.4%

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

      4. sub-neg 96.4%

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

      5. metadata-eval 96.4%

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

      6. remove-double-neg 96.4%

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

      7. remove-double-neg 96.4%

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

      8. sub-neg 96.4%

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

      9. metadata-eval 96.4%

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

      10. associate--l+ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around inf 78.5%

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

   5. Taylor expanded in b around 0 78.5%

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

   if -4.60000000000000029e56 < y < -5.79999999999999946e-138 or 1.4999999999999999e-289 < y < 4.1999999999999999e-227 or 2.70000000000000011e-13 < y < 4.10000000000000024e92

   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. Step-by-step derivation

      1. associate-+l- 98.7%

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

      2. *-commutative 98.7%

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

      3. *-commutative 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

      6. remove-double-neg 98.7%

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

      7. remove-double-neg 98.7%

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

      8. sub-neg 98.7%

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

      9. metadata-eval 98.7%

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

      10. associate--l+ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 86.2%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -5.79999999999999946e-138 < y < 1.4999999999999999e-289 or 4.1999999999999999e-227 < y < 2.70000000000000011e-13

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in t around 0 75.9%

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

   if 4.10000000000000024e92 < y

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.3%

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

      2. *-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. sub-neg 94.3%

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

      5. metadata-eval 94.3%

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

      6. remove-double-neg 94.3%

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

      7. remove-double-neg 94.3%

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

      8. sub-neg 94.3%

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

      9. metadata-eval 94.3%

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

      10. associate--l+ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 70.1%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;y \cdot b - y \cdot z\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-138}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-227}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+92}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 7: 64.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + b \cdot \left(t - 2\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot b - y \cdot z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+127}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 10^{+178}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* b (- t 2.0)))))
   (if (<= y -1.5e+36)
     (- (* y b) (* y z))
     (if (<= y 2.15e-100)
       t_1
       (if (<= y 1.5e-29)
         (+ a (+ (+ x z) (* b -2.0)))
         (if (<= y 4.1e-13)
           t_1
           (if (<= y 3.35e+127)
             (+ x (* t (- b a)))
             (if (<= y 1e+178) (- x (* (+ y -1.0) z)) (* y (- b z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (b * (t - 2.0));
	double tmp;
	if (y <= -1.5e+36) {
		tmp = (y * b) - (y * z);
	} else if (y <= 2.15e-100) {
		tmp = t_1;
	} else if (y <= 1.5e-29) {
		tmp = a + ((x + z) + (b * -2.0));
	} else if (y <= 4.1e-13) {
		tmp = t_1;
	} else if (y <= 3.35e+127) {
		tmp = x + (t * (b - a));
	} else if (y <= 1e+178) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + z) + (b * (t - 2.0d0))
    if (y <= (-1.5d+36)) then
        tmp = (y * b) - (y * z)
    else if (y <= 2.15d-100) then
        tmp = t_1
    else if (y <= 1.5d-29) then
        tmp = a + ((x + z) + (b * (-2.0d0)))
    else if (y <= 4.1d-13) then
        tmp = t_1
    else if (y <= 3.35d+127) then
        tmp = x + (t * (b - a))
    else if (y <= 1d+178) then
        tmp = x - ((y + (-1.0d0)) * z)
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (b * (t - 2.0));
	double tmp;
	if (y <= -1.5e+36) {
		tmp = (y * b) - (y * z);
	} else if (y <= 2.15e-100) {
		tmp = t_1;
	} else if (y <= 1.5e-29) {
		tmp = a + ((x + z) + (b * -2.0));
	} else if (y <= 4.1e-13) {
		tmp = t_1;
	} else if (y <= 3.35e+127) {
		tmp = x + (t * (b - a));
	} else if (y <= 1e+178) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (b * (t - 2.0))
	tmp = 0
	if y <= -1.5e+36:
		tmp = (y * b) - (y * z)
	elif y <= 2.15e-100:
		tmp = t_1
	elif y <= 1.5e-29:
		tmp = a + ((x + z) + (b * -2.0))
	elif y <= 4.1e-13:
		tmp = t_1
	elif y <= 3.35e+127:
		tmp = x + (t * (b - a))
	elif y <= 1e+178:
		tmp = x - ((y + -1.0) * z)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(b * Float64(t - 2.0)))
	tmp = 0.0
	if (y <= -1.5e+36)
		tmp = Float64(Float64(y * b) - Float64(y * z));
	elseif (y <= 2.15e-100)
		tmp = t_1;
	elseif (y <= 1.5e-29)
		tmp = Float64(a + Float64(Float64(x + z) + Float64(b * -2.0)));
	elseif (y <= 4.1e-13)
		tmp = t_1;
	elseif (y <= 3.35e+127)
		tmp = Float64(x + Float64(t * Float64(b - a)));
	elseif (y <= 1e+178)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	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) + (b * (t - 2.0));
	tmp = 0.0;
	if (y <= -1.5e+36)
		tmp = (y * b) - (y * z);
	elseif (y <= 2.15e-100)
		tmp = t_1;
	elseif (y <= 1.5e-29)
		tmp = a + ((x + z) + (b * -2.0));
	elseif (y <= 4.1e-13)
		tmp = t_1;
	elseif (y <= 3.35e+127)
		tmp = x + (t * (b - a));
	elseif (y <= 1e+178)
		tmp = x - ((y + -1.0) * z);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+36], N[(N[(y * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-100], t$95$1, If[LessEqual[y, 1.5e-29], N[(a + N[(N[(x + z), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-13], t$95$1, If[LessEqual[y, 3.35e+127], N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+178], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.5e36

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.6%

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

      2. *-commutative 96.6%

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

      3. *-commutative 96.6%

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

      4. sub-neg 96.6%

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

      5. metadata-eval 96.6%

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

      6. remove-double-neg 96.6%

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

      7. remove-double-neg 96.6%

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

      8. sub-neg 96.6%

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

      9. metadata-eval 96.6%

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

      10. associate--l+ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around inf 77.5%

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

   5. Taylor expanded in b around 0 77.6%

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

   if -1.5e36 < y < 2.14999999999999999e-100 or 1.5000000000000001e-29 < y < 4.1000000000000002e-13

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.2%

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

   5. Taylor expanded in a around 0 72.6%

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

   if 2.14999999999999999e-100 < y < 1.5000000000000001e-29

   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. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in t around 0 86.5%

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

   if 4.1000000000000002e-13 < y < 3.3499999999999998e127

   1. Initial program 94.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.2%

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

      2. *-commutative 94.2%

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

      3. *-commutative 94.2%

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

      4. sub-neg 94.2%

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

      5. metadata-eval 94.2%

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

      6. remove-double-neg 94.2%

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

      7. remove-double-neg 94.2%

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

      8. sub-neg 94.2%

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

      9. metadata-eval 94.2%

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

      10. associate--l+ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 71.9%

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

   5. Taylor expanded in z around 0 58.2%

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

   if 3.3499999999999998e127 < y < 1.0000000000000001e178

   1. Initial program 94.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.7%

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

      2. *-commutative 94.7%

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

      3. *-commutative 94.7%

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

      4. sub-neg 94.7%

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

      5. metadata-eval 94.7%

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

      6. remove-double-neg 94.7%

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

      7. remove-double-neg 94.7%

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

      8. sub-neg 94.7%

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

      9. metadata-eval 94.7%

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

      10. associate--l+ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 82.5%

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

   5. Taylor expanded in t around 0 82.0%

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

   if 1.0000000000000001e178 < y

   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. Step-by-step derivation

      1. associate-+l- 96.0%

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

      2. *-commutative 96.0%

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

      3. *-commutative 96.0%

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

      4. sub-neg 96.0%

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

      5. metadata-eval 96.0%

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

      6. remove-double-neg 96.0%

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

      7. remove-double-neg 96.0%

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

      8. sub-neg 96.0%

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

      9. metadata-eval 96.0%

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

      10. associate--l+ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot b - y \cdot z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-100}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+127}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 10^{+178}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 8: 83.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-11} \lor \neg \left(y \leq 1.1 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.22e-11) (not (<= y 1.1e+52)))
   (+ (- x (* (+ y -1.0) z)) (* y b))
   (+ (+ z (+ x (* b (- t 2.0)))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.22e-11) || !(y <= 1.1e+52)) {
		tmp = (x - ((y + -1.0) * z)) + (y * b);
	} else {
		tmp = (z + (x + (b * (t - 2.0)))) + (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 ((y <= (-1.22d-11)) .or. (.not. (y <= 1.1d+52))) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (y * b)
    else
        tmp = (z + (x + (b * (t - 2.0d0)))) + (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 ((y <= -1.22e-11) || !(y <= 1.1e+52)) {
		tmp = (x - ((y + -1.0) * z)) + (y * b);
	} else {
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.22e-11) or not (y <= 1.1e+52):
		tmp = (x - ((y + -1.0) * z)) + (y * b)
	else:
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.22e-11) || !(y <= 1.1e+52))
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(y * b));
	else
		tmp = Float64(Float64(z + Float64(x + Float64(b * Float64(t - 2.0)))) + 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 ((y <= -1.22e-11) || ~((y <= 1.1e+52)))
		tmp = (x - ((y + -1.0) * z)) + (y * b);
	else
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.22e-11], N[Not[LessEqual[y, 1.1e+52]], $MachinePrecision]], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2200000000000001e-11 or 1.1e52 < y

   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. Step-by-step derivation

      1. associate-+l- 95.4%

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

      2. *-commutative 95.4%

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

      3. *-commutative 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

      6. remove-double-neg 95.4%

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

      7. remove-double-neg 95.4%

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

      8. sub-neg 95.4%

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

      9. metadata-eval 95.4%

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

      10. associate--l+ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-rgt-neg-in 82.1%

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

   6. Simplified 82.1%

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

   if -1.2200000000000001e-11 < y < 1.1e52

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-11} \lor \neg \left(y \leq 1.1 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 9: 85.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+95} \lor \neg \left(z \leq 3.2 \cdot 10^{-73}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e+95) (not (<= z 3.2e-73)))
   (+ (- x (* (+ y -1.0) z)) (* t (- b a)))
   (+ (+ x (* b (- (+ t y) 2.0))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e+95) || !(z <= 3.2e-73)) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) + (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 ((z <= (-1.7d+95)) .or. (.not. (z <= 3.2d-73))) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (t * (b - a))
    else
        tmp = (x + (b * ((t + y) - 2.0d0))) + (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 ((z <= -1.7e+95) || !(z <= 3.2e-73)) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.7e+95) or not (z <= 3.2e-73):
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a))
	else:
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.7e+95) || !(z <= 3.2e-73))
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(t * Float64(b - a)));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) + 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 ((z <= -1.7e+95) || ~((z <= 3.2e-73)))
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	else
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.7e+95], N[Not[LessEqual[z, 3.2e-73]], $MachinePrecision]], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000011e95 or 3.19999999999999986e-73 < z

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.7%

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

      2. *-commutative 96.7%

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

      3. *-commutative 96.7%

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

      4. sub-neg 96.7%

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

      5. metadata-eval 96.7%

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

      6. remove-double-neg 96.7%

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

      7. remove-double-neg 96.7%

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

      8. sub-neg 96.7%

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

      9. metadata-eval 96.7%

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

      10. associate--l+ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around inf 89.2%

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

   if -1.70000000000000011e95 < z < 3.19999999999999986e-73

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.4%

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

      2. *-commutative 98.4%

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

      3. *-commutative 98.4%

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

      4. sub-neg 98.4%

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

      5. metadata-eval 98.4%

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

      6. remove-double-neg 98.4%

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

      7. remove-double-neg 98.4%

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

      8. sub-neg 98.4%

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

      9. metadata-eval 98.4%

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

      10. associate--l+ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 91.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+95} \lor \neg \left(z \leq 3.2 \cdot 10^{-73}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 10: 85.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+125} \lor \neg \left(z \leq 8.2 \cdot 10^{-69}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(x + \left(y - 2\right) \cdot b\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (or (<= z -2.3e+125) (not (<= z 8.2e-69)))
     (+ (- x (* (+ y -1.0) z)) t_1)
     (+ (+ a (+ x (* (- y 2.0) 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 ((z <= -2.3e+125) || !(z <= 8.2e-69)) {
		tmp = (x - ((y + -1.0) * z)) + t_1;
	} else {
		tmp = (a + (x + ((y - 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 = t * (b - a)
    if ((z <= (-2.3d+125)) .or. (.not. (z <= 8.2d-69))) then
        tmp = (x - ((y + (-1.0d0)) * z)) + t_1
    else
        tmp = (a + (x + ((y - 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 = t * (b - a);
	double tmp;
	if ((z <= -2.3e+125) || !(z <= 8.2e-69)) {
		tmp = (x - ((y + -1.0) * z)) + t_1;
	} else {
		tmp = (a + (x + ((y - 2.0) * b))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if (z <= -2.3e+125) or not (z <= 8.2e-69):
		tmp = (x - ((y + -1.0) * z)) + t_1
	else:
		tmp = (a + (x + ((y - 2.0) * b))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if ((z <= -2.3e+125) || !(z <= 8.2e-69))
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + t_1);
	else
		tmp = Float64(Float64(a + Float64(x + Float64(Float64(y - 2.0) * b))) + 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 ((z <= -2.3e+125) || ~((z <= 8.2e-69)))
		tmp = (x - ((y + -1.0) * z)) + t_1;
	else
		tmp = (a + (x + ((y - 2.0) * b))) + 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[Or[LessEqual[z, -2.3e+125], N[Not[LessEqual[z, 8.2e-69]], $MachinePrecision]], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a + N[(x + N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000013e125 or 8.1999999999999998e-69 < z

   1. Initial program 96.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.5%

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

      2. *-commutative 96.5%

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

      3. *-commutative 96.5%

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

      4. sub-neg 96.5%

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

      5. metadata-eval 96.5%

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

      6. remove-double-neg 96.5%

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

      7. remove-double-neg 96.5%

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

      8. sub-neg 96.5%

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

      9. metadata-eval 96.5%

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

      10. associate--l+ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 89.3%

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

   if -2.30000000000000013e125 < z < 8.1999999999999998e-69

   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. Step-by-step derivation

      1. sub-neg 98.5%

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

      2. +-commutative 98.5%

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

      3. associate-+l+ 98.5%

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

      4. *-commutative 98.5%

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

      5. distribute-rgt-neg-in 98.5%

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

      6. +-commutative 98.5%

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

      7. fma-def 98.6%

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

      8. neg-sub0 98.6%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 98.6%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 98.6%

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

      11. +-commutative 98.6%

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

      12. sub-neg 98.6%

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

      13. fma-def 98.6%

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

      14. sub-neg 98.6%

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

      15. associate-+l+ 98.6%

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

      16. metadata-eval 98.6%

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

      17. sub-neg 98.6%

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

      18. +-commutative 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in t around 0 99.3%

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

   5. Taylor expanded in z around 0 92.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+125} \lor \neg \left(z \leq 8.2 \cdot 10^{-69}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(x + \left(y - 2\right) \cdot b\right)\right) + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 11: 45.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-297}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-205}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+119}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -2.2e+97)
     t_2
     (if (<= t -4.2e-284)
       t_1
       (if (<= t 6e-297)
         (* y b)
         (if (<= t 1.75e-205)
           (+ x z)
           (if (<= t 1.15e-66) t_1 (if (<= t 1.15e+119) (+ x z) t_2))))))))

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 = t * (b - a);
	double tmp;
	if (t <= -2.2e+97) {
		tmp = t_2;
	} else if (t <= -4.2e-284) {
		tmp = t_1;
	} else if (t <= 6e-297) {
		tmp = y * b;
	} else if (t <= 1.75e-205) {
		tmp = x + z;
	} else if (t <= 1.15e-66) {
		tmp = t_1;
	} else if (t <= 1.15e+119) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	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 = t * (b - a)
    if (t <= (-2.2d+97)) then
        tmp = t_2
    else if (t <= (-4.2d-284)) then
        tmp = t_1
    else if (t <= 6d-297) then
        tmp = y * b
    else if (t <= 1.75d-205) then
        tmp = x + z
    else if (t <= 1.15d-66) then
        tmp = t_1
    else if (t <= 1.15d+119) then
        tmp = x + z
    else
        tmp = t_2
    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 = t * (b - a);
	double tmp;
	if (t <= -2.2e+97) {
		tmp = t_2;
	} else if (t <= -4.2e-284) {
		tmp = t_1;
	} else if (t <= 6e-297) {
		tmp = y * b;
	} else if (t <= 1.75e-205) {
		tmp = x + z;
	} else if (t <= 1.15e-66) {
		tmp = t_1;
	} else if (t <= 1.15e+119) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.2e+97:
		tmp = t_2
	elif t <= -4.2e-284:
		tmp = t_1
	elif t <= 6e-297:
		tmp = y * b
	elif t <= 1.75e-205:
		tmp = x + z
	elif t <= 1.15e-66:
		tmp = t_1
	elif t <= 1.15e+119:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.2e+97)
		tmp = t_2;
	elseif (t <= -4.2e-284)
		tmp = t_1;
	elseif (t <= 6e-297)
		tmp = Float64(y * b);
	elseif (t <= 1.75e-205)
		tmp = Float64(x + z);
	elseif (t <= 1.15e-66)
		tmp = t_1;
	elseif (t <= 1.15e+119)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.2e+97)
		tmp = t_2;
	elseif (t <= -4.2e-284)
		tmp = t_1;
	elseif (t <= 6e-297)
		tmp = y * b;
	elseif (t <= 1.75e-205)
		tmp = x + z;
	elseif (t <= 1.15e-66)
		tmp = t_1;
	elseif (t <= 1.15e+119)
		tmp = x + z;
	else
		tmp = t_2;
	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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+97], t$95$2, If[LessEqual[t, -4.2e-284], t$95$1, If[LessEqual[t, 6e-297], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.75e-205], N[(x + z), $MachinePrecision], If[LessEqual[t, 1.15e-66], t$95$1, If[LessEqual[t, 1.15e+119], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.2000000000000001e97 or 1.15e119 < t

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.8%

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

      2. *-commutative 91.8%

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

      3. *-commutative 91.8%

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

      4. sub-neg 91.8%

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

      5. metadata-eval 91.8%

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

      6. remove-double-neg 91.8%

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

      7. remove-double-neg 91.8%

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

      8. sub-neg 91.8%

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

      9. metadata-eval 91.8%

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

      10. associate--l+ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around inf 70.1%

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

   if -2.2000000000000001e97 < t < -4.19999999999999982e-284 or 1.75e-205 < t < 1.14999999999999996e-66

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 47.9%

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

   if -4.19999999999999982e-284 < t < 5.9999999999999999e-297

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 75.6%

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

   5. Taylor expanded in y around inf 75.7%

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

   if 5.9999999999999999e-297 < t < 1.75e-205 or 1.14999999999999996e-66 < t < 1.15e119

   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. Step-by-step derivation

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. remove-double-neg 99.9%

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

      7. remove-double-neg 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 65.6%

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

   5. Taylor expanded in t around 0 59.2%

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

   6. Taylor expanded in y around 0 49.6%

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   7. Step-by-step derivation

      1. sub-neg 49.6%

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

      2. neg-mul-1 49.6%

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

      3. remove-double-neg 49.6%

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

      4. +-commutative 49.6%

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

   8. Simplified 49.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-284}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-297}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-205}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+119}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 12: 66.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) - \left(y + -1\right) \cdot z\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-174}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x a) (* (+ y -1.0) z))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -2.45e+62)
     t_2
     (if (<= b -5e-114)
       t_1
       (if (<= b -5e-174)
         (+ x (* t (- b a)))
         (if (<= b 1.82e+177) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - ((y + -1.0) * z);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.45e+62) {
		tmp = t_2;
	} else if (b <= -5e-114) {
		tmp = t_1;
	} else if (b <= -5e-174) {
		tmp = x + (t * (b - a));
	} else if (b <= 1.82e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (x + a) - ((y + (-1.0d0)) * z)
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-2.45d+62)) then
        tmp = t_2
    else if (b <= (-5d-114)) then
        tmp = t_1
    else if (b <= (-5d-174)) then
        tmp = x + (t * (b - a))
    else if (b <= 1.82d+177) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - ((y + -1.0) * z);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.45e+62) {
		tmp = t_2;
	} else if (b <= -5e-114) {
		tmp = t_1;
	} else if (b <= -5e-174) {
		tmp = x + (t * (b - a));
	} else if (b <= 1.82e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) - ((y + -1.0) * z)
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.45e+62:
		tmp = t_2
	elif b <= -5e-114:
		tmp = t_1
	elif b <= -5e-174:
		tmp = x + (t * (b - a))
	elif b <= 1.82e+177:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + a) - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.45e+62)
		tmp = t_2;
	elseif (b <= -5e-114)
		tmp = t_1;
	elseif (b <= -5e-174)
		tmp = Float64(x + Float64(t * Float64(b - a)));
	elseif (b <= 1.82e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + a) - ((y + -1.0) * z);
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.45e+62)
		tmp = t_2;
	elseif (b <= -5e-114)
		tmp = t_1;
	elseif (b <= -5e-174)
		tmp = x + (t * (b - a));
	elseif (b <= 1.82e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+62], t$95$2, If[LessEqual[b, -5e-114], t$95$1, If[LessEqual[b, -5e-174], N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.82e+177], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4499999999999998e62 or 1.82e177 < b

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. sub-neg 95.6%

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

      5. metadata-eval 95.6%

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

      6. remove-double-neg 95.6%

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

      7. remove-double-neg 95.6%

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

      8. sub-neg 95.6%

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

      9. metadata-eval 95.6%

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

      10. associate--l+ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in b around inf 76.9%

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

   if -2.4499999999999998e62 < b < -4.99999999999999989e-114 or -5.0000000000000002e-174 < b < 1.82e177

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.2%

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

      2. *-commutative 98.2%

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

      3. *-commutative 98.2%

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

      4. sub-neg 98.2%

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

      5. metadata-eval 98.2%

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

      6. remove-double-neg 98.2%

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

      7. remove-double-neg 98.2%

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

      8. sub-neg 98.2%

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

      9. metadata-eval 98.2%

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

      10. associate--l+ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in a around inf 84.7%

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

      1. sub-neg 84.7%

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

      2. metadata-eval 84.7%

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

      3. *-commutative 84.7%

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

      4. distribute-rgt-in 84.7%

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

      5. *-commutative 84.7%

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

      6. mul-1-neg 84.7%

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

      7. unsub-neg 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around 0 73.5%

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

   if -4.99999999999999989e-114 < b < -5.0000000000000002e-174

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 100.0%

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

   5. Taylor expanded in z around 0 81.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-114}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-174}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{+177}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 13: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-146} \lor \neg \left(z \leq 4.4 \cdot 10^{-127}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e-146) (not (<= z 4.4e-127)))
   (+ (- x (* (+ y -1.0) z)) (* t (- b a)))
   (+ (+ x (* y b)) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e-146) || !(z <= 4.4e-127)) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else {
		tmp = (x + (y * b)) + (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 ((z <= (-9d-146)) .or. (.not. (z <= 4.4d-127))) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (t * (b - a))
    else
        tmp = (x + (y * b)) + (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 ((z <= -9e-146) || !(z <= 4.4e-127)) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else {
		tmp = (x + (y * b)) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9e-146) or not (z <= 4.4e-127):
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a))
	else:
		tmp = (x + (y * b)) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9e-146) || !(z <= 4.4e-127))
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(t * Float64(b - a)));
	else
		tmp = Float64(Float64(x + Float64(y * b)) + 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 ((z <= -9e-146) || ~((z <= 4.4e-127)))
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	else
		tmp = (x + (y * b)) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e-146], N[Not[LessEqual[z, 4.4e-127]], $MachinePrecision]], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000001e-146 or 4.4000000000000003e-127 < z

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.2%

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

      2. *-commutative 97.2%

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

      3. *-commutative 97.2%

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

      4. sub-neg 97.2%

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

      5. metadata-eval 97.2%

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

      6. remove-double-neg 97.2%

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

      7. remove-double-neg 97.2%

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

      8. sub-neg 97.2%

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

      9. metadata-eval 97.2%

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

      10. associate--l+ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 83.4%

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

   if -9.0000000000000001e-146 < z < 4.4000000000000003e-127

   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. Step-by-step derivation

      1. associate-+l- 98.7%

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

      2. *-commutative 98.7%

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

      3. *-commutative 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

      6. remove-double-neg 98.7%

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

      7. remove-double-neg 98.7%

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

      8. sub-neg 98.7%

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

      9. metadata-eval 98.7%

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

      10. associate--l+ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 98.7%

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

   5. Taylor expanded in y around inf 86.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-146} \lor \neg \left(z \leq 4.4 \cdot 10^{-127}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 14: 68.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;y \cdot b - y \cdot z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+127}:\\ \;\;\;\;\left(x + z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+178}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e+56)
   (- (* y b) (* y z))
   (if (<= y 3.05e+127)
     (+ (+ x z) (* t (- b a)))
     (if (<= y 1.1e+178) (- (+ x a) (* (+ y -1.0) z)) (* y (- b z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e+56) {
		tmp = (y * b) - (y * z);
	} else if (y <= 3.05e+127) {
		tmp = (x + z) + (t * (b - a));
	} else if (y <= 1.1e+178) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.35d+56)) then
        tmp = (y * b) - (y * z)
    else if (y <= 3.05d+127) then
        tmp = (x + z) + (t * (b - a))
    else if (y <= 1.1d+178) then
        tmp = (x + a) - ((y + (-1.0d0)) * z)
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e+56) {
		tmp = (y * b) - (y * z);
	} else if (y <= 3.05e+127) {
		tmp = (x + z) + (t * (b - a));
	} else if (y <= 1.1e+178) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e+56:
		tmp = (y * b) - (y * z)
	elif y <= 3.05e+127:
		tmp = (x + z) + (t * (b - a))
	elif y <= 1.1e+178:
		tmp = (x + a) - ((y + -1.0) * z)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.35e+56)
		tmp = Float64(Float64(y * b) - Float64(y * z));
	elseif (y <= 3.05e+127)
		tmp = Float64(Float64(x + z) + Float64(t * Float64(b - a)));
	elseif (y <= 1.1e+178)
		tmp = Float64(Float64(x + a) - Float64(Float64(y + -1.0) * z));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.35e+56)
		tmp = (y * b) - (y * z);
	elseif (y <= 3.05e+127)
		tmp = (x + z) + (t * (b - a));
	elseif (y <= 1.1e+178)
		tmp = (x + a) - ((y + -1.0) * z);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.35e+56], N[(N[(y * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e+127], N[(N[(x + z), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+178], N[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000005e56

   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. Step-by-step derivation

      1. associate-+l- 96.4%

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

      2. *-commutative 96.4%

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

      3. *-commutative 96.4%

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

      4. sub-neg 96.4%

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

      5. metadata-eval 96.4%

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

      6. remove-double-neg 96.4%

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

      7. remove-double-neg 96.4%

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

      8. sub-neg 96.4%

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

      9. metadata-eval 96.4%

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

      10. associate--l+ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around inf 78.5%

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

   5. Taylor expanded in b around 0 78.5%

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

   if -1.35000000000000005e56 < y < 3.05000000000000023e127

   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. Step-by-step derivation

      1. associate-+l- 98.6%

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

      2. *-commutative 98.6%

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

      3. *-commutative 98.6%

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

      4. sub-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. remove-double-neg 98.6%

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

      7. remove-double-neg 98.6%

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

      8. sub-neg 98.6%

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

      9. metadata-eval 98.6%

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

      10. associate--l+ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in t around inf 78.1%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. cancel-sign-sub-inv 73.2%

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

      2. metadata-eval 73.2%

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

      3. *-lft-identity 73.2%

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

      4. +-commutative 73.2%

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

   7. Simplified 73.2%

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

   if 3.05000000000000023e127 < y < 1.09999999999999999e178

   1. Initial program 94.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.7%

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

      2. *-commutative 94.7%

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

      3. *-commutative 94.7%

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

      4. sub-neg 94.7%

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

      5. metadata-eval 94.7%

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

      6. remove-double-neg 94.7%

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

      7. remove-double-neg 94.7%

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

      8. sub-neg 94.7%

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

      9. metadata-eval 94.7%

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

      10. associate--l+ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around inf 89.7%

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

      1. sub-neg 89.7%

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

      2. metadata-eval 89.7%

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

      3. *-commutative 89.7%

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

      4. distribute-rgt-in 89.7%

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

      5. *-commutative 89.7%

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

      6. mul-1-neg 89.7%

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

      7. unsub-neg 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in t around 0 89.7%

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

   if 1.09999999999999999e178 < y

   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. Step-by-step derivation

      1. associate-+l- 96.0%

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

      2. *-commutative 96.0%

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

      3. *-commutative 96.0%

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

      4. sub-neg 96.0%

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

      5. metadata-eval 96.0%

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

      6. remove-double-neg 96.0%

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

      7. remove-double-neg 96.0%

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

      8. sub-neg 96.0%

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

      9. metadata-eval 96.0%

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

      10. associate--l+ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 80.3%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;y \cdot b - y \cdot z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+127}:\\ \;\;\;\;\left(x + z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+178}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 15: 68.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+118} \lor \neg \left(z \leq 2.9 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e+118) (not (<= z 2.9e-28)))
   (- (+ x a) (* (+ y -1.0) z))
   (+ (+ x (* y b)) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+118) || !(z <= 2.9e-28)) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else {
		tmp = (x + (y * b)) + (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 ((z <= (-2.3d+118)) .or. (.not. (z <= 2.9d-28))) then
        tmp = (x + a) - ((y + (-1.0d0)) * z)
    else
        tmp = (x + (y * b)) + (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 ((z <= -2.3e+118) || !(z <= 2.9e-28)) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else {
		tmp = (x + (y * b)) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e+118) or not (z <= 2.9e-28):
		tmp = (x + a) - ((y + -1.0) * z)
	else:
		tmp = (x + (y * b)) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e+118) || !(z <= 2.9e-28))
		tmp = Float64(Float64(x + a) - Float64(Float64(y + -1.0) * z));
	else
		tmp = Float64(Float64(x + Float64(y * b)) + 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 ((z <= -2.3e+118) || ~((z <= 2.9e-28)))
		tmp = (x + a) - ((y + -1.0) * z);
	else
		tmp = (x + (y * b)) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e+118], N[Not[LessEqual[z, 2.9e-28]], $MachinePrecision]], N[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000016e118 or 2.90000000000000013e-28 < z

   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. Step-by-step derivation

      1. associate-+l- 96.3%

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

      2. *-commutative 96.3%

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

      3. *-commutative 96.3%

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

      4. sub-neg 96.3%

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

      5. metadata-eval 96.3%

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

      6. remove-double-neg 96.3%

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

      7. remove-double-neg 96.3%

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

      8. sub-neg 96.3%

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

      9. metadata-eval 96.3%

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

      10. associate--l+ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. metadata-eval 86.4%

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

      3. *-commutative 86.4%

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

      4. distribute-rgt-in 86.4%

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

      5. *-commutative 86.4%

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

      6. mul-1-neg 86.4%

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

      7. unsub-neg 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in t around 0 80.3%

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

   if -2.30000000000000016e118 < z < 2.90000000000000013e-28

   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. Step-by-step derivation

      1. associate-+l- 98.6%

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

      2. *-commutative 98.6%

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

      3. *-commutative 98.6%

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

      4. sub-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. remove-double-neg 98.6%

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

      7. remove-double-neg 98.6%

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

      8. sub-neg 98.6%

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

      9. metadata-eval 98.6%

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

      10. associate--l+ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 91.0%

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

   5. Taylor expanded in y around inf 76.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+118} \lor \neg \left(z \leq 2.9 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 16: 71.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-11} \lor \neg \left(y \leq 8.8 \cdot 10^{+48}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.22e-11) (not (<= y 8.8e+48)))
   (+ (- x (* (+ y -1.0) z)) (* y b))
   (+ (+ x z) (* t (- b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.22e-11) || !(y <= 8.8e+48)) {
		tmp = (x - ((y + -1.0) * z)) + (y * b);
	} else {
		tmp = (x + z) + (t * (b - 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 ((y <= (-1.22d-11)) .or. (.not. (y <= 8.8d+48))) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (y * b)
    else
        tmp = (x + z) + (t * (b - 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 ((y <= -1.22e-11) || !(y <= 8.8e+48)) {
		tmp = (x - ((y + -1.0) * z)) + (y * b);
	} else {
		tmp = (x + z) + (t * (b - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.22e-11) or not (y <= 8.8e+48):
		tmp = (x - ((y + -1.0) * z)) + (y * b)
	else:
		tmp = (x + z) + (t * (b - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.22e-11) || !(y <= 8.8e+48))
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(y * b));
	else
		tmp = Float64(Float64(x + z) + Float64(t * Float64(b - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.22e-11) || ~((y <= 8.8e+48)))
		tmp = (x - ((y + -1.0) * z)) + (y * b);
	else
		tmp = (x + z) + (t * (b - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.22e-11], N[Not[LessEqual[y, 8.8e+48]], $MachinePrecision]], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2200000000000001e-11 or 8.7999999999999997e48 < y

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.5%

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

      2. *-commutative 95.5%

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

      3. *-commutative 95.5%

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

      4. sub-neg 95.5%

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

      5. metadata-eval 95.5%

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

      6. remove-double-neg 95.5%

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

      7. remove-double-neg 95.5%

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

      8. sub-neg 95.5%

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

      9. metadata-eval 95.5%

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

      10. associate--l+ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-rgt-neg-in 81.5%

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

   6. Simplified 81.5%

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

   if -1.2200000000000001e-11 < y < 8.7999999999999997e48

   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. Step-by-step derivation

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. remove-double-neg 99.9%

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

      7. remove-double-neg 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 78.8%

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

   5. Taylor expanded in y around 0 78.2%

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

      1. cancel-sign-sub-inv 78.2%

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

      2. metadata-eval 78.2%

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

      3. *-lft-identity 78.2%

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

      4. +-commutative 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-11} \lor \neg \left(y \leq 8.8 \cdot 10^{+48}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 17: 56.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-27}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+51}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.8e+35)
     t_1
     (if (<= y 1e-27)
       (+ x (+ z a))
       (if (<= y 1.16e+50) (* t (- b a)) (if (<= y 8.8e+51) a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e+35) {
		tmp = t_1;
	} else if (y <= 1e-27) {
		tmp = x + (z + a);
	} else if (y <= 1.16e+50) {
		tmp = t * (b - a);
	} else if (y <= 8.8e+51) {
		tmp = 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 = y * (b - z)
    if (y <= (-1.8d+35)) then
        tmp = t_1
    else if (y <= 1d-27) then
        tmp = x + (z + a)
    else if (y <= 1.16d+50) then
        tmp = t * (b - a)
    else if (y <= 8.8d+51) then
        tmp = 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 = y * (b - z);
	double tmp;
	if (y <= -1.8e+35) {
		tmp = t_1;
	} else if (y <= 1e-27) {
		tmp = x + (z + a);
	} else if (y <= 1.16e+50) {
		tmp = t * (b - a);
	} else if (y <= 8.8e+51) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.8e+35:
		tmp = t_1
	elif y <= 1e-27:
		tmp = x + (z + a)
	elif y <= 1.16e+50:
		tmp = t * (b - a)
	elif y <= 8.8e+51:
		tmp = a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.8e+35)
		tmp = t_1;
	elseif (y <= 1e-27)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 1.16e+50)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 8.8e+51)
		tmp = a;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.8e+35)
		tmp = t_1;
	elseif (y <= 1e-27)
		tmp = x + (z + a);
	elseif (y <= 1.16e+50)
		tmp = t * (b - a);
	elseif (y <= 8.8e+51)
		tmp = a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+35], t$95$1, If[LessEqual[y, 1e-27], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+50], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+51], a, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8e35 or 8.79999999999999967e51 < y

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

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

      2. *-commutative 95.1%

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

      3. *-commutative 95.1%

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

      4. sub-neg 95.1%

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

      5. metadata-eval 95.1%

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

      6. remove-double-neg 95.1%

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

      7. remove-double-neg 95.1%

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

      8. sub-neg 95.1%

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

      9. metadata-eval 95.1%

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

      10. associate--l+ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 71.8%

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

   if -1.8e35 < y < 1e-27

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.4%

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

   5. Taylor expanded in t around 0 66.2%

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

   6. Taylor expanded in b around 0 57.8%

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

      1. associate-+r+ 57.8%

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

   8. Simplified 57.8%

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

   if 1e-27 < y < 1.16e50

   1. Initial program 99.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. remove-double-neg 99.7%

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

      7. remove-double-neg 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

      10. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 50.6%

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

   if 1.16e50 < y < 8.79999999999999967e51

   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. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in a around inf 100.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 10^{-27}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+51}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 18: 37.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-75}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -4.4e+37)
     t_1
     (if (<= y 6.5e-75)
       (+ x z)
       (if (<= y 4.2e+127)
         (* a (- 1.0 t))
         (if (<= y 2.1e+196) t_1 (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -4.4e+37) {
		tmp = t_1;
	} else if (y <= 6.5e-75) {
		tmp = x + z;
	} else if (y <= 4.2e+127) {
		tmp = a * (1.0 - t);
	} else if (y <= 2.1e+196) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-4.4d+37)) then
        tmp = t_1
    else if (y <= 6.5d-75) then
        tmp = x + z
    else if (y <= 4.2d+127) then
        tmp = a * (1.0d0 - t)
    else if (y <= 2.1d+196) then
        tmp = t_1
    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 t_1 = z * -y;
	double tmp;
	if (y <= -4.4e+37) {
		tmp = t_1;
	} else if (y <= 6.5e-75) {
		tmp = x + z;
	} else if (y <= 4.2e+127) {
		tmp = a * (1.0 - t);
	} else if (y <= 2.1e+196) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -4.4e+37:
		tmp = t_1
	elif y <= 6.5e-75:
		tmp = x + z
	elif y <= 4.2e+127:
		tmp = a * (1.0 - t)
	elif y <= 2.1e+196:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -4.4e+37)
		tmp = t_1;
	elseif (y <= 6.5e-75)
		tmp = Float64(x + z);
	elseif (y <= 4.2e+127)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 2.1e+196)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -4.4e+37)
		tmp = t_1;
	elseif (y <= 6.5e-75)
		tmp = x + z;
	elseif (y <= 4.2e+127)
		tmp = a * (1.0 - t);
	elseif (y <= 2.1e+196)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -4.4e+37], t$95$1, If[LessEqual[y, 6.5e-75], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.2e+127], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+196], t$95$1, N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000001e37 or 4.19999999999999983e127 < y < 2.10000000000000015e196

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

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

      2. *-commutative 95.1%

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

      3. *-commutative 95.1%

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

      4. sub-neg 95.1%

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

      5. metadata-eval 95.1%

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

      6. remove-double-neg 95.1%

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

      7. remove-double-neg 95.1%

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

      8. sub-neg 95.1%

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

      9. metadata-eval 95.1%

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

      10. associate--l+ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around inf 53.1%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   5. Taylor expanded in y around inf 53.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. *-commutative 53.1%

         \[\leadsto -\color{blue}{z \cdot y} \]

      3. distribute-rgt-neg-in 53.1%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]

   7. Simplified 53.1%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]

   if -4.4000000000000001e37 < y < 6.5000000000000002e-75

   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. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 83.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]

   6. Taylor expanded in y around 0 49.5%

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   7. Step-by-step derivation

      1. sub-neg 49.5%

         \[\leadsto \color{blue}{x + \left(--1 \cdot z\right)} \]

      2. neg-mul-1 49.5%

         \[\leadsto x + \left(-\color{blue}{\left(-z\right)}\right) \]

      3. remove-double-neg 49.5%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 49.5%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 49.5%

      \[\leadsto \color{blue}{z + x} \]

   if 6.5000000000000002e-75 < y < 4.19999999999999983e127

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.5%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.5%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.5%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.5%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.5%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.5%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 39.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if 2.10000000000000015e196 < y

   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. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{y} \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-75}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+196}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 19: 38.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -5.8e+35)
     t_1
     (if (<= y 4.2e-41)
       (+ x z)
       (if (<= y 3.05e+127) (* t (- b a)) (if (<= y 7.5e+200) t_1 (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -5.8e+35) {
		tmp = t_1;
	} else if (y <= 4.2e-41) {
		tmp = x + z;
	} else if (y <= 3.05e+127) {
		tmp = t * (b - a);
	} else if (y <= 7.5e+200) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-5.8d+35)) then
        tmp = t_1
    else if (y <= 4.2d-41) then
        tmp = x + z
    else if (y <= 3.05d+127) then
        tmp = t * (b - a)
    else if (y <= 7.5d+200) then
        tmp = t_1
    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 t_1 = z * -y;
	double tmp;
	if (y <= -5.8e+35) {
		tmp = t_1;
	} else if (y <= 4.2e-41) {
		tmp = x + z;
	} else if (y <= 3.05e+127) {
		tmp = t * (b - a);
	} else if (y <= 7.5e+200) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -5.8e+35:
		tmp = t_1
	elif y <= 4.2e-41:
		tmp = x + z
	elif y <= 3.05e+127:
		tmp = t * (b - a)
	elif y <= 7.5e+200:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -5.8e+35)
		tmp = t_1;
	elseif (y <= 4.2e-41)
		tmp = Float64(x + z);
	elseif (y <= 3.05e+127)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 7.5e+200)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -5.8e+35)
		tmp = t_1;
	elseif (y <= 4.2e-41)
		tmp = x + z;
	elseif (y <= 3.05e+127)
		tmp = t * (b - a);
	elseif (y <= 7.5e+200)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -5.8e+35], t$95$1, If[LessEqual[y, 4.2e-41], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.05e+127], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+200], t$95$1, N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999989e35 or 3.05000000000000023e127 < y < 7.50000000000000062e200

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around inf 53.1%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   5. Taylor expanded in y around inf 53.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. *-commutative 53.1%

         \[\leadsto -\color{blue}{z \cdot y} \]

      3. distribute-rgt-neg-in 53.1%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]

   7. Simplified 53.1%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]

   if -5.79999999999999989e35 < y < 4.20000000000000025e-41

   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. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 82.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in t around 0 50.9%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]

   6. Taylor expanded in y around 0 49.1%

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   7. Step-by-step derivation

      1. sub-neg 49.1%

         \[\leadsto \color{blue}{x + \left(--1 \cdot z\right)} \]

      2. neg-mul-1 49.1%

         \[\leadsto x + \left(-\color{blue}{\left(-z\right)}\right) \]

      3. remove-double-neg 49.1%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 49.1%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 49.1%

      \[\leadsto \color{blue}{z + x} \]

   if 4.20000000000000025e-41 < y < 3.05000000000000023e127

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 94.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 94.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 94.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 94.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 94.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 43.4%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if 7.50000000000000062e200 < y

   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. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{y} \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+200}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 20: 49.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-75}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 10^{+53}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.05e+35)
     t_1
     (if (<= y 2.5e-75) (+ x z) (if (<= y 1e+53) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.05e+35) {
		tmp = t_1;
	} else if (y <= 2.5e-75) {
		tmp = x + z;
	} else if (y <= 1e+53) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.05d+35)) then
        tmp = t_1
    else if (y <= 2.5d-75) then
        tmp = x + z
    else if (y <= 1d+53) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.05e+35) {
		tmp = t_1;
	} else if (y <= 2.5e-75) {
		tmp = x + z;
	} else if (y <= 1e+53) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.05e+35:
		tmp = t_1
	elif y <= 2.5e-75:
		tmp = x + z
	elif y <= 1e+53:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.05e+35)
		tmp = t_1;
	elseif (y <= 2.5e-75)
		tmp = Float64(x + z);
	elseif (y <= 1e+53)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.05e+35)
		tmp = t_1;
	elseif (y <= 2.5e-75)
		tmp = x + z;
	elseif (y <= 1e+53)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+35], t$95$1, If[LessEqual[y, 2.5e-75], N[(x + z), $MachinePrecision], If[LessEqual[y, 1e+53], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0499999999999999e35 or 9.9999999999999999e52 < y

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 71.8%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.0499999999999999e35 < y < 2.49999999999999989e-75

   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. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 83.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]

   6. Taylor expanded in y around 0 49.5%

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   7. Step-by-step derivation

      1. sub-neg 49.5%

         \[\leadsto \color{blue}{x + \left(--1 \cdot z\right)} \]

      2. neg-mul-1 49.5%

         \[\leadsto x + \left(-\color{blue}{\left(-z\right)}\right) \]

      3. remove-double-neg 49.5%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 49.5%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 49.5%

      \[\leadsto \color{blue}{z + x} \]

   if 2.49999999999999989e-75 < y < 9.9999999999999999e52

   1. Initial program 99.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 43.1%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-75}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 10^{+53}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 21: 37.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -1.15e+37)
     t_1
     (if (<= y 2.5e+23) (+ x z) (if (<= y 2.5e+198) t_1 (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -1.15e+37) {
		tmp = t_1;
	} else if (y <= 2.5e+23) {
		tmp = x + z;
	} else if (y <= 2.5e+198) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-1.15d+37)) then
        tmp = t_1
    else if (y <= 2.5d+23) then
        tmp = x + z
    else if (y <= 2.5d+198) then
        tmp = t_1
    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 t_1 = z * -y;
	double tmp;
	if (y <= -1.15e+37) {
		tmp = t_1;
	} else if (y <= 2.5e+23) {
		tmp = x + z;
	} else if (y <= 2.5e+198) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -1.15e+37:
		tmp = t_1
	elif y <= 2.5e+23:
		tmp = x + z
	elif y <= 2.5e+198:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -1.15e+37)
		tmp = t_1;
	elseif (y <= 2.5e+23)
		tmp = Float64(x + z);
	elseif (y <= 2.5e+198)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -1.15e+37)
		tmp = t_1;
	elseif (y <= 2.5e+23)
		tmp = x + z;
	elseif (y <= 2.5e+198)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.15e+37], t$95$1, If[LessEqual[y, 2.5e+23], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.5e+198], t$95$1, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000001e37 or 2.5e23 < y < 2.50000000000000024e198

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 94.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 94.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 94.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 94.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 94.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 94.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 94.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 94.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 94.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around inf 46.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   5. Taylor expanded in y around inf 46.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. *-commutative 46.7%

         \[\leadsto -\color{blue}{z \cdot y} \]

      3. distribute-rgt-neg-in 46.7%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]

   7. Simplified 46.7%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} \]

   if -1.15000000000000001e37 < y < 2.5e23

   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. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 79.6%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in t around 0 47.5%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]

   6. Taylor expanded in y around 0 45.3%

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   7. Step-by-step derivation

      1. sub-neg 45.3%

         \[\leadsto \color{blue}{x + \left(--1 \cdot z\right)} \]

      2. neg-mul-1 45.3%

         \[\leadsto x + \left(-\color{blue}{\left(-z\right)}\right) \]

      3. remove-double-neg 45.3%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 45.3%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{z + x} \]

   if 2.50000000000000024e198 < y

   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. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{y} \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 22: 32.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8200000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 10^{-27}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+92}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8200000000.0)
   (* y b)
   (if (<= y 1e-27) (+ z a) (if (<= y 1.85e+92) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8200000000.0) {
		tmp = y * b;
	} else if (y <= 1e-27) {
		tmp = z + a;
	} else if (y <= 1.85e+92) {
		tmp = t * b;
	} 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 (y <= (-8200000000.0d0)) then
        tmp = y * b
    else if (y <= 1d-27) then
        tmp = z + a
    else if (y <= 1.85d+92) then
        tmp = t * b
    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 (y <= -8200000000.0) {
		tmp = y * b;
	} else if (y <= 1e-27) {
		tmp = z + a;
	} else if (y <= 1.85e+92) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8200000000.0:
		tmp = y * b
	elif y <= 1e-27:
		tmp = z + a
	elif y <= 1.85e+92:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8200000000.0)
		tmp = Float64(y * b);
	elseif (y <= 1e-27)
		tmp = Float64(z + a);
	elseif (y <= 1.85e+92)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8200000000.0)
		tmp = y * b;
	elseif (y <= 1e-27)
		tmp = z + a;
	elseif (y <= 1.85e+92)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8200000000.0], N[(y * b), $MachinePrecision], If[LessEqual[y, 1e-27], N[(z + a), $MachinePrecision], If[LessEqual[y, 1.85e+92], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2e9 or 1.84999999999999999e92 < y

   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. Step-by-step derivation

      1. associate-+l- 95.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in y around inf 36.1%

      \[\leadsto \color{blue}{y} \cdot b \]

   if -8.2e9 < y < 1e-27

   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. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in t around 0 67.1%

      \[\leadsto \color{blue}{a + \left(-2 \cdot b + \left(z + x\right)\right)} \]

   6. Taylor expanded in z around inf 37.5%

      \[\leadsto a + \color{blue}{z} \]

   if 1e-27 < y < 1.84999999999999999e92

   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. Step-by-step derivation

      1. associate-+l- 96.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in t around inf 27.2%

      \[\leadsto \color{blue}{t} \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8200000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 10^{-27}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+92}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 23: 24.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{+56}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8e+128) x (if (<= x 1e+56) (* y b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+128) {
		tmp = x;
	} else if (x <= 1e+56) {
		tmp = y * b;
	} 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 <= (-8d+128)) then
        tmp = x
    else if (x <= 1d+56) then
        tmp = y * b
    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 <= -8e+128) {
		tmp = x;
	} else if (x <= 1e+56) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8e+128:
		tmp = x
	elif x <= 1e+56:
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8e+128)
		tmp = x;
	elseif (x <= 1e+56)
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8e+128)
		tmp = x;
	elseif (x <= 1e+56)
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8e+128], x, If[LessEqual[x, 1e+56], N[(y * b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.0000000000000006e128 or 1.00000000000000009e56 < x

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 40.2%

      \[\leadsto \color{blue}{x} \]

   if -8.0000000000000006e128 < x < 1.00000000000000009e56

   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. Step-by-step derivation

      1. associate-+l- 96.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in y around inf 24.9%

      \[\leadsto \color{blue}{y} \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{+56}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 34.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+86}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+94}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.45e+86) (* y b) (if (<= y 3.5e+94) (+ x z) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+86) {
		tmp = y * b;
	} else if (y <= 3.5e+94) {
		tmp = x + 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 (y <= (-2.45d+86)) then
        tmp = y * b
    else if (y <= 3.5d+94) then
        tmp = x + 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 (y <= -2.45e+86) {
		tmp = y * b;
	} else if (y <= 3.5e+94) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.45e+86:
		tmp = y * b
	elif y <= 3.5e+94:
		tmp = x + z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.45e+86)
		tmp = Float64(y * b);
	elseif (y <= 3.5e+94)
		tmp = Float64(x + 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 (y <= -2.45e+86)
		tmp = y * b;
	elseif (y <= 3.5e+94)
		tmp = x + z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.45e+86], N[(y * b), $MachinePrecision], If[LessEqual[y, 3.5e+94], N[(x + z), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.45e86 or 3.4999999999999997e94 < y

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 40.3%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{y} \cdot b \]

   if -2.45e86 < y < 3.4999999999999997e94

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.3%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.3%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.3%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.3%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.3%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.3%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 79.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in t around 0 49.3%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]

   6. Taylor expanded in y around 0 40.8%

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   7. Step-by-step derivation

      1. sub-neg 40.8%

         \[\leadsto \color{blue}{x + \left(--1 \cdot z\right)} \]

      2. neg-mul-1 40.8%

         \[\leadsto x + \left(-\color{blue}{\left(-z\right)}\right) \]

      3. remove-double-neg 40.8%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 40.8%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 40.8%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+86}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+94}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 25: 20.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+121}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.8e+121) a (if (<= a 1e+41) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.8e+121) {
		tmp = a;
	} else if (a <= 1e+41) {
		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 <= (-7.8d+121)) then
        tmp = a
    else if (a <= 1d+41) 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 <= -7.8e+121) {
		tmp = a;
	} else if (a <= 1e+41) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.8e+121:
		tmp = a
	elif a <= 1e+41:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.8e+121)
		tmp = a;
	elseif (a <= 1e+41)
		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 <= -7.8e+121)
		tmp = a;
	elseif (a <= 1e+41)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.8e+121], a, If[LessEqual[a, 1e+41], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -7.79999999999999967e121 or 1.00000000000000001e41 < a

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 94.9%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 94.9%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 94.9%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 94.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 94.9%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 96.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 96.2%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 96.2%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 96.2%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 96.2%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 96.2%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 97.5%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 97.5%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 97.5%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 97.5%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 97.5%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 97.5%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 69.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in t around 0 34.8%

      \[\leadsto \color{blue}{a + \left(-2 \cdot b + \left(z + x\right)\right)} \]

   6. Taylor expanded in a around inf 25.1%

      \[\leadsto \color{blue}{a} \]

   if -7.79999999999999967e121 < a < 1.00000000000000001e41

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 24.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+121}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 26: 21.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.5e+150) z (if (<= z 3.15e+41) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.5e+150) {
		tmp = z;
	} else if (z <= 3.15e+41) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.5d+150)) then
        tmp = z
    else if (z <= 3.15d+41) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.5e+150) {
		tmp = z;
	} else if (z <= 3.15e+41) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.5e+150:
		tmp = z
	elif z <= 3.15e+41:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.5e+150)
		tmp = z;
	elseif (z <= 3.15e+41)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.5e+150)
		tmp = z;
	elseif (z <= 3.15e+41)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.5e+150], z, If[LessEqual[z, 3.15e+41], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000006e150 or 3.1499999999999999e41 < z

   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. Step-by-step derivation

      1. associate-+l- 95.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   5. Taylor expanded in y around 0 31.0%

      \[\leadsto \color{blue}{z} \]

   if -1.50000000000000006e150 < z < 3.1499999999999999e41

   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. Step-by-step derivation

      1. associate-+l- 98.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 24.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 27: 11.2% 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 97.6%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg 97.6%

      \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. +-commutative 97.6%

      \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   3. associate-+l+ 97.6%

      \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   4. *-commutative 97.6%

      \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   5. distribute-rgt-neg-in 97.6%

      \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   6. +-commutative 97.6%

      \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

   7. fma-def 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

   8. neg-sub0 98.0%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   9. associate--r- 98.0%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   10. neg-sub0 98.0%

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   11. +-commutative 98.0%

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   12. sub-neg 98.0%

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   13. fma-def 98.4%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

   14. sub-neg 98.4%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

   15. associate-+l+ 98.4%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

   16. metadata-eval 98.4%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

   17. sub-neg 98.4%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

   18. +-commutative 98.4%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

4. Taylor expanded in y around 0 64.8%

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

5. Taylor expanded in t around 0 41.5%

   \[\leadsto \color{blue}{a + \left(-2 \cdot b + \left(z + x\right)\right)} \]

6. Taylor expanded in a around inf 9.2%

   \[\leadsto \color{blue}{a} \]

7. Final simplification 9.2%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023230 
(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)))