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

Percentage Accurate: 95.5% → 98.1%

Time: 17.0s

Alternatives: 25

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% 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: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - (z * (y + -1.0))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = 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[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $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. Taylor expanded in t around inf 60.8%

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

4. Final simplification 98.4%

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

Alternative 2: 97.7% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (+ y (+ t -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((y + (t + -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(y + Float64(t + -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[(y + N[(t + -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 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-def 97.6%

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

   3. associate--l+ 97.6%

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

   4. sub-neg 97.6%

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

   5. metadata-eval 97.6%

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

   6. sub-neg 97.6%

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

   7. associate-+l- 97.6%

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

   8. fma-neg 98.0%

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

   9. sub-neg 98.0%

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

   10. metadata-eval 98.0%

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

   11. remove-double-neg 98.0%

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

   12. sub-neg 98.0%

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

   13. metadata-eval 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 70.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) + z \cdot \left(1 - y\right)\\ t_2 := \left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-285}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x a) (* z (- 1.0 y))))
        (t_2 (+ (+ z a) (* b (+ t (+ y -2.0))))))
   (if (<= b -1.1e-84)
     t_2
     (if (<= b -8.2e-184)
       t_1
       (if (<= b -1.1e-285)
         (- x (* a (+ t -1.0)))
         (if (<= b 2.7e+77) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) + (z * (1.0 - y));
	double t_2 = (z + a) + (b * (t + (y + -2.0)));
	double tmp;
	if (b <= -1.1e-84) {
		tmp = t_2;
	} else if (b <= -8.2e-184) {
		tmp = t_1;
	} else if (b <= -1.1e-285) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 2.7e+77) {
		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) + (z * (1.0d0 - y))
    t_2 = (z + a) + (b * (t + (y + (-2.0d0))))
    if (b <= (-1.1d-84)) then
        tmp = t_2
    else if (b <= (-8.2d-184)) then
        tmp = t_1
    else if (b <= (-1.1d-285)) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (b <= 2.7d+77) 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) + (z * (1.0 - y));
	double t_2 = (z + a) + (b * (t + (y + -2.0)));
	double tmp;
	if (b <= -1.1e-84) {
		tmp = t_2;
	} else if (b <= -8.2e-184) {
		tmp = t_1;
	} else if (b <= -1.1e-285) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 2.7e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) + (z * (1.0 - y))
	t_2 = (z + a) + (b * (t + (y + -2.0)))
	tmp = 0
	if b <= -1.1e-84:
		tmp = t_2
	elif b <= -8.2e-184:
		tmp = t_1
	elif b <= -1.1e-285:
		tmp = x - (a * (t + -1.0))
	elif b <= 2.7e+77:
		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(z * Float64(1.0 - y)))
	t_2 = Float64(Float64(z + a) + Float64(b * Float64(t + Float64(y + -2.0))))
	tmp = 0.0
	if (b <= -1.1e-84)
		tmp = t_2;
	elseif (b <= -8.2e-184)
		tmp = t_1;
	elseif (b <= -1.1e-285)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (b <= 2.7e+77)
		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) + (z * (1.0 - y));
	t_2 = (z + a) + (b * (t + (y + -2.0)));
	tmp = 0.0;
	if (b <= -1.1e-84)
		tmp = t_2;
	elseif (b <= -8.2e-184)
		tmp = t_1;
	elseif (b <= -1.1e-285)
		tmp = x - (a * (t + -1.0));
	elseif (b <= 2.7e+77)
		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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e-84], t$95$2, If[LessEqual[b, -8.2e-184], t$95$1, If[LessEqual[b, -1.1e-285], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+77], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0999999999999999e-84 or 2.6999999999999998e77 < b

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. fma-def 95.6%

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

      3. associate--l+ 95.6%

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

      4. sub-neg 95.6%

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

      5. metadata-eval 95.6%

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

      6. sub-neg 95.6%

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

      7. associate-+l- 95.6%

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

      8. fma-neg 96.3%

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

      9. sub-neg 96.3%

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

      10. metadata-eval 96.3%

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

      11. remove-double-neg 96.3%

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

      12. sub-neg 96.3%

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

      13. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 91.5%

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

      1. +-commutative 91.5%

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

      2. sub-neg 91.5%

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

      3. metadata-eval 91.5%

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

      4. neg-mul-1 91.5%

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

      5. unsub-neg 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 90.1%

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

      1. neg-mul-1 90.1%

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

   9. Simplified 90.1%

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

   10. Taylor expanded in x around 0 84.8%

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

       1. associate-+r+ 84.8%

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

       2. associate--l+ 84.8%

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

       3. sub-neg 84.8%

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

       4. metadata-eval 84.8%

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

   12. Simplified 84.8%

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

   if -1.0999999999999999e-84 < b < -8.2e-184 or -1.1e-285 < b < 2.6999999999999998e77

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. sub-neg 81.2%

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

      3. metadata-eval 81.2%

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

      4. neg-mul-1 81.2%

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

      5. unsub-neg 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in b around 0 76.4%

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

   if -8.2e-184 < b < -1.1e-285

   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. Taylor expanded in z around 0 82.6%

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

   3. Taylor expanded in b around 0 82.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-84}:\\ \;\;\;\;\left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-184}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-285}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+77}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \]

Alternative 4: 85.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+91}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + t_1\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+131}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= z -3.8e+91)
     (+ (- x (* y z)) (+ z t_1))
     (if (<= z 1.15e+131) (+ t_2 t_1) (+ t_2 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (z <= -3.8e+91) {
		tmp = (x - (y * z)) + (z + t_1);
	} else if (z <= 1.15e+131) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_2 + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (z <= (-3.8d+91)) then
        tmp = (x - (y * z)) + (z + t_1)
    else if (z <= 1.15d+131) then
        tmp = t_2 + t_1
    else
        tmp = t_2 + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (z <= -3.8e+91) {
		tmp = (x - (y * z)) + (z + t_1);
	} else if (z <= 1.15e+131) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_2 + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if z <= -3.8e+91:
		tmp = (x - (y * z)) + (z + t_1)
	elif z <= 1.15e+131:
		tmp = t_2 + t_1
	else:
		tmp = t_2 + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (z <= -3.8e+91)
		tmp = Float64(Float64(x - Float64(y * z)) + Float64(z + t_1));
	elseif (z <= 1.15e+131)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(t_2 + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (z <= -3.8e+91)
		tmp = (x - (y * z)) + (z + t_1);
	elseif (z <= 1.15e+131)
		tmp = t_2 + t_1;
	else
		tmp = t_2 + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+91], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+131], N[(t$95$2 + t$95$1), $MachinePrecision], N[(t$95$2 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999998e91

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 93.6%

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

   3. Taylor expanded in b around 0 91.6%

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

      1. sub-neg 91.6%

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

      2. mul-1-neg 91.6%

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

      3. unsub-neg 91.6%

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

      4. sub-neg 91.6%

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

      5. metadata-eval 91.6%

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

      6. distribute-neg-in 91.6%

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

      7. mul-1-neg 91.6%

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

      8. remove-double-neg 91.6%

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

      9. sub-neg 91.6%

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

      10. *-commutative 91.6%

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

      11. cancel-sign-sub-inv 91.6%

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

      12. +-commutative 91.6%

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

      13. distribute-neg-in 91.6%

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

      14. metadata-eval 91.6%

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

      15. sub-neg 91.6%

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

      16. *-commutative 91.6%

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

   5. Simplified 91.6%

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

   if -3.7999999999999998e91 < z < 1.14999999999999996e131

   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. Taylor expanded in z around 0 92.8%

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

   if 1.14999999999999996e131 < z

   1. Initial program 93.5%

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

   2. Taylor expanded in a around 0 90.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+91}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+131}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 5: 46.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-237}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-154}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-89}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 27500000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -2.15e+90)
     t_2
     (if (<= t -2.3e-110)
       t_1
       (if (<= t 9.2e-237)
         (+ x a)
         (if (<= t 1.7e-154)
           z
           (if (<= t 3.1e-89) (+ x a) (if (<= t 27500000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.15e+90) {
		tmp = t_2;
	} else if (t <= -2.3e-110) {
		tmp = t_1;
	} else if (t <= 9.2e-237) {
		tmp = x + a;
	} else if (t <= 1.7e-154) {
		tmp = z;
	} else if (t <= 3.1e-89) {
		tmp = x + a;
	} else if (t <= 27500000000.0) {
		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 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-2.15d+90)) then
        tmp = t_2
    else if (t <= (-2.3d-110)) then
        tmp = t_1
    else if (t <= 9.2d-237) then
        tmp = x + a
    else if (t <= 1.7d-154) then
        tmp = z
    else if (t <= 3.1d-89) then
        tmp = x + a
    else if (t <= 27500000000.0d0) 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 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.15e+90) {
		tmp = t_2;
	} else if (t <= -2.3e-110) {
		tmp = t_1;
	} else if (t <= 9.2e-237) {
		tmp = x + a;
	} else if (t <= 1.7e-154) {
		tmp = z;
	} else if (t <= 3.1e-89) {
		tmp = x + a;
	} else if (t <= 27500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.15e+90:
		tmp = t_2
	elif t <= -2.3e-110:
		tmp = t_1
	elif t <= 9.2e-237:
		tmp = x + a
	elif t <= 1.7e-154:
		tmp = z
	elif t <= 3.1e-89:
		tmp = x + a
	elif t <= 27500000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.15e+90)
		tmp = t_2;
	elseif (t <= -2.3e-110)
		tmp = t_1;
	elseif (t <= 9.2e-237)
		tmp = Float64(x + a);
	elseif (t <= 1.7e-154)
		tmp = z;
	elseif (t <= 3.1e-89)
		tmp = Float64(x + a);
	elseif (t <= 27500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.15e+90)
		tmp = t_2;
	elseif (t <= -2.3e-110)
		tmp = t_1;
	elseif (t <= 9.2e-237)
		tmp = x + a;
	elseif (t <= 1.7e-154)
		tmp = z;
	elseif (t <= 3.1e-89)
		tmp = x + a;
	elseif (t <= 27500000000.0)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+90], t$95$2, If[LessEqual[t, -2.3e-110], t$95$1, If[LessEqual[t, 9.2e-237], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.7e-154], z, If[LessEqual[t, 3.1e-89], N[(x + a), $MachinePrecision], If[LessEqual[t, 27500000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1499999999999999e90 or 2.75e10 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in t around inf 66.9%

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

   if -2.1499999999999999e90 < t < -2.3000000000000001e-110 or 3.09999999999999996e-89 < t < 2.75e10

   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. Taylor expanded in b around inf 53.8%

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

   3. Taylor expanded in t around 0 51.0%

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

   if -2.3000000000000001e-110 < t < 9.20000000000000046e-237 or 1.6999999999999999e-154 < t < 3.09999999999999996e-89

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 73.8%

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

   3. Taylor expanded in t around 0 73.8%

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

      1. sub-neg 73.8%

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

      2. metadata-eval 73.8%

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

      3. neg-mul-1 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in b around 0 52.5%

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

   if 9.20000000000000046e-237 < t < 1.6999999999999999e-154

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. fma-def 93.8%

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

      3. associate--l+ 93.8%

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

      4. sub-neg 93.8%

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

      5. metadata-eval 93.8%

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

      6. sub-neg 93.8%

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

      7. associate-+l- 93.8%

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

      8. fma-neg 93.8%

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

      9. sub-neg 93.8%

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

      10. metadata-eval 93.8%

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

      11. remove-double-neg 93.8%

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

      12. sub-neg 93.8%

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

      13. metadata-eval 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. sub-neg 93.8%

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

      3. metadata-eval 93.8%

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

      4. neg-mul-1 93.8%

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

      5. unsub-neg 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in y around 0 81.3%

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

      1. neg-mul-1 81.3%

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

   9. Simplified 81.3%

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

   10. Taylor expanded in z around inf 40.2%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-237}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-154}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-89}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 27500000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 6: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.02 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-209}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-113}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 30000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -2.02e+89)
     t_2
     (if (<= t -1.9e-112)
       t_1
       (if (<= t 6.8e-209)
         (+ x a)
         (if (<= t 2.15e-150)
           t_1
           (if (<= t 4.1e-113) (+ x a) (if (<= t 30000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.02e+89) {
		tmp = t_2;
	} else if (t <= -1.9e-112) {
		tmp = t_1;
	} else if (t <= 6.8e-209) {
		tmp = x + a;
	} else if (t <= 2.15e-150) {
		tmp = t_1;
	} else if (t <= 4.1e-113) {
		tmp = x + a;
	} else if (t <= 30000000000.0) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-2.02d+89)) then
        tmp = t_2
    else if (t <= (-1.9d-112)) then
        tmp = t_1
    else if (t <= 6.8d-209) then
        tmp = x + a
    else if (t <= 2.15d-150) then
        tmp = t_1
    else if (t <= 4.1d-113) then
        tmp = x + a
    else if (t <= 30000000000.0d0) 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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.02e+89) {
		tmp = t_2;
	} else if (t <= -1.9e-112) {
		tmp = t_1;
	} else if (t <= 6.8e-209) {
		tmp = x + a;
	} else if (t <= 2.15e-150) {
		tmp = t_1;
	} else if (t <= 4.1e-113) {
		tmp = x + a;
	} else if (t <= 30000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.02e+89:
		tmp = t_2
	elif t <= -1.9e-112:
		tmp = t_1
	elif t <= 6.8e-209:
		tmp = x + a
	elif t <= 2.15e-150:
		tmp = t_1
	elif t <= 4.1e-113:
		tmp = x + a
	elif t <= 30000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.02e+89)
		tmp = t_2;
	elseif (t <= -1.9e-112)
		tmp = t_1;
	elseif (t <= 6.8e-209)
		tmp = Float64(x + a);
	elseif (t <= 2.15e-150)
		tmp = t_1;
	elseif (t <= 4.1e-113)
		tmp = Float64(x + a);
	elseif (t <= 30000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.02e+89)
		tmp = t_2;
	elseif (t <= -1.9e-112)
		tmp = t_1;
	elseif (t <= 6.8e-209)
		tmp = x + a;
	elseif (t <= 2.15e-150)
		tmp = t_1;
	elseif (t <= 4.1e-113)
		tmp = x + a;
	elseif (t <= 30000000000.0)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.02e+89], t$95$2, If[LessEqual[t, -1.9e-112], t$95$1, If[LessEqual[t, 6.8e-209], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.15e-150], t$95$1, If[LessEqual[t, 4.1e-113], N[(x + a), $MachinePrecision], If[LessEqual[t, 30000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.02000000000000008e89 or 3e10 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in t around inf 66.9%

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

   if -2.02000000000000008e89 < t < -1.89999999999999997e-112 or 6.79999999999999976e-209 < t < 2.15000000000000002e-150 or 4.1e-113 < t < 3e10

   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. Taylor expanded in y around inf 53.7%

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

   if -1.89999999999999997e-112 < t < 6.79999999999999976e-209 or 2.15000000000000002e-150 < t < 4.1e-113

   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. Taylor expanded in z around 0 74.2%

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

   3. Taylor expanded in t around 0 74.2%

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

      1. sub-neg 74.2%

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

      2. metadata-eval 74.2%

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

      3. neg-mul-1 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in b around 0 53.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.02 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-209}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-113}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 30000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 7: 50.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-239}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-112}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 27500000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -7.5e+86)
     t_2
     (if (<= t -1.42e-111)
       t_1
       (if (<= t 4e-239)
         (+ x a)
         (if (<= t 5.2e-152)
           (* z (- 1.0 y))
           (if (<= t 3.8e-112) (+ x a) (if (<= t 27500000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+86) {
		tmp = t_2;
	} else if (t <= -1.42e-111) {
		tmp = t_1;
	} else if (t <= 4e-239) {
		tmp = x + a;
	} else if (t <= 5.2e-152) {
		tmp = z * (1.0 - y);
	} else if (t <= 3.8e-112) {
		tmp = x + a;
	} else if (t <= 27500000000.0) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-7.5d+86)) then
        tmp = t_2
    else if (t <= (-1.42d-111)) then
        tmp = t_1
    else if (t <= 4d-239) then
        tmp = x + a
    else if (t <= 5.2d-152) then
        tmp = z * (1.0d0 - y)
    else if (t <= 3.8d-112) then
        tmp = x + a
    else if (t <= 27500000000.0d0) 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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+86) {
		tmp = t_2;
	} else if (t <= -1.42e-111) {
		tmp = t_1;
	} else if (t <= 4e-239) {
		tmp = x + a;
	} else if (t <= 5.2e-152) {
		tmp = z * (1.0 - y);
	} else if (t <= 3.8e-112) {
		tmp = x + a;
	} else if (t <= 27500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.5e+86:
		tmp = t_2
	elif t <= -1.42e-111:
		tmp = t_1
	elif t <= 4e-239:
		tmp = x + a
	elif t <= 5.2e-152:
		tmp = z * (1.0 - y)
	elif t <= 3.8e-112:
		tmp = x + a
	elif t <= 27500000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.5e+86)
		tmp = t_2;
	elseif (t <= -1.42e-111)
		tmp = t_1;
	elseif (t <= 4e-239)
		tmp = Float64(x + a);
	elseif (t <= 5.2e-152)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 3.8e-112)
		tmp = Float64(x + a);
	elseif (t <= 27500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.5e+86)
		tmp = t_2;
	elseif (t <= -1.42e-111)
		tmp = t_1;
	elseif (t <= 4e-239)
		tmp = x + a;
	elseif (t <= 5.2e-152)
		tmp = z * (1.0 - y);
	elseif (t <= 3.8e-112)
		tmp = x + a;
	elseif (t <= 27500000000.0)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+86], t$95$2, If[LessEqual[t, -1.42e-111], t$95$1, If[LessEqual[t, 4e-239], N[(x + a), $MachinePrecision], If[LessEqual[t, 5.2e-152], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-112], N[(x + a), $MachinePrecision], If[LessEqual[t, 27500000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999997e86 or 2.75e10 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in t around inf 66.9%

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

   if -7.4999999999999997e86 < t < -1.41999999999999991e-111 or 3.79999999999999995e-112 < t < 2.75e10

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 53.4%

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

   if -1.41999999999999991e-111 < t < 4.0000000000000003e-239 or 5.20000000000000026e-152 < t < 3.79999999999999995e-112

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 75.7%

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

   3. Taylor expanded in t around 0 75.7%

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

      1. sub-neg 75.7%

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

      2. metadata-eval 75.7%

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

      3. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in b around 0 55.0%

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

   if 4.0000000000000003e-239 < t < 5.20000000000000026e-152

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 60.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-239}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-112}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 27500000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 8: 53.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-112}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 1100000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+219}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8.8e+54)
     t_1
     (if (<= t 2e-112)
       (+ a (+ x z))
       (if (<= t 1100000000.0)
         (* y (- b z))
         (if (<= t 2.2e+106)
           t_1
           (if (<= t 4.5e+123)
             (* z (- 1.0 y))
             (if (<= t 2.4e+219) (- x (* t a)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8.8e+54) {
		tmp = t_1;
	} else if (t <= 2e-112) {
		tmp = a + (x + z);
	} else if (t <= 1100000000.0) {
		tmp = y * (b - z);
	} else if (t <= 2.2e+106) {
		tmp = t_1;
	} else if (t <= 4.5e+123) {
		tmp = z * (1.0 - y);
	} else if (t <= 2.4e+219) {
		tmp = x - (t * 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 = t * (b - a)
    if (t <= (-8.8d+54)) then
        tmp = t_1
    else if (t <= 2d-112) then
        tmp = a + (x + z)
    else if (t <= 1100000000.0d0) then
        tmp = y * (b - z)
    else if (t <= 2.2d+106) then
        tmp = t_1
    else if (t <= 4.5d+123) then
        tmp = z * (1.0d0 - y)
    else if (t <= 2.4d+219) then
        tmp = x - (t * 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 = t * (b - a);
	double tmp;
	if (t <= -8.8e+54) {
		tmp = t_1;
	} else if (t <= 2e-112) {
		tmp = a + (x + z);
	} else if (t <= 1100000000.0) {
		tmp = y * (b - z);
	} else if (t <= 2.2e+106) {
		tmp = t_1;
	} else if (t <= 4.5e+123) {
		tmp = z * (1.0 - y);
	} else if (t <= 2.4e+219) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -8.8e+54:
		tmp = t_1
	elif t <= 2e-112:
		tmp = a + (x + z)
	elif t <= 1100000000.0:
		tmp = y * (b - z)
	elif t <= 2.2e+106:
		tmp = t_1
	elif t <= 4.5e+123:
		tmp = z * (1.0 - y)
	elif t <= 2.4e+219:
		tmp = x - (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.8e+54)
		tmp = t_1;
	elseif (t <= 2e-112)
		tmp = Float64(a + Float64(x + z));
	elseif (t <= 1100000000.0)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 2.2e+106)
		tmp = t_1;
	elseif (t <= 4.5e+123)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 2.4e+219)
		tmp = Float64(x - Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.8e+54)
		tmp = t_1;
	elseif (t <= 2e-112)
		tmp = a + (x + z);
	elseif (t <= 1100000000.0)
		tmp = y * (b - z);
	elseif (t <= 2.2e+106)
		tmp = t_1;
	elseif (t <= 4.5e+123)
		tmp = z * (1.0 - y);
	elseif (t <= 2.4e+219)
		tmp = x - (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+54], t$95$1, If[LessEqual[t, 2e-112], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1100000000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+106], t$95$1, If[LessEqual[t, 4.5e+123], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+219], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.7999999999999996e54 or 1.1e9 < t < 2.19999999999999992e106 or 2.4e219 < t

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 71.8%

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

   if -8.7999999999999996e54 < t < 1.9999999999999999e-112

   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. +-commutative 98.2%

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

      2. fma-def 98.2%

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

      3. associate--l+ 98.2%

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

      4. sub-neg 98.2%

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

      5. metadata-eval 98.2%

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

      6. sub-neg 98.2%

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

      7. associate-+l- 98.2%

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

      8. fma-neg 98.2%

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

      9. sub-neg 98.2%

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

      10. metadata-eval 98.2%

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

      11. remove-double-neg 98.2%

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

      12. sub-neg 98.2%

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

      13. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. sub-neg 97.3%

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

      3. metadata-eval 97.3%

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

      4. neg-mul-1 97.3%

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

      5. unsub-neg 97.3%

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

   6. Simplified 97.3%

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

   7. Taylor expanded in y around 0 82.3%

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

      1. neg-mul-1 82.3%

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

   9. Simplified 82.3%

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

   10. Taylor expanded in b around 0 54.1%

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

   if 1.9999999999999999e-112 < t < 1.1e9

   1. Initial program 90.8%

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

   2. Taylor expanded in y around inf 64.9%

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

   if 2.19999999999999992e106 < t < 4.49999999999999983e123

   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. Taylor expanded in z around inf 86.9%

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

   if 4.49999999999999983e123 < t < 2.4e219

   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. Taylor expanded in z around 0 90.5%

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

   3. Taylor expanded in b around 0 76.8%

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

   4. Taylor expanded in t around inf 76.8%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-112}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 1100000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+219}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 9: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + z\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-281}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x z))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -8.2e-54)
     t_2
     (if (<= b -1.7e-116)
       t_1
       (if (<= b -2.8e-198)
         (* z (- 1.0 y))
         (if (<= b 9.4e-281) (- x (* t a)) (if (<= b 4.8e+102) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.2e-54) {
		tmp = t_2;
	} else if (b <= -1.7e-116) {
		tmp = t_1;
	} else if (b <= -2.8e-198) {
		tmp = z * (1.0 - y);
	} else if (b <= 9.4e-281) {
		tmp = x - (t * a);
	} else if (b <= 4.8e+102) {
		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 = a + (x + z)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-8.2d-54)) then
        tmp = t_2
    else if (b <= (-1.7d-116)) then
        tmp = t_1
    else if (b <= (-2.8d-198)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 9.4d-281) then
        tmp = x - (t * a)
    else if (b <= 4.8d+102) 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 = a + (x + z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.2e-54) {
		tmp = t_2;
	} else if (b <= -1.7e-116) {
		tmp = t_1;
	} else if (b <= -2.8e-198) {
		tmp = z * (1.0 - y);
	} else if (b <= 9.4e-281) {
		tmp = x - (t * a);
	} else if (b <= 4.8e+102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + z)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -8.2e-54:
		tmp = t_2
	elif b <= -1.7e-116:
		tmp = t_1
	elif b <= -2.8e-198:
		tmp = z * (1.0 - y)
	elif b <= 9.4e-281:
		tmp = x - (t * a)
	elif b <= 4.8e+102:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + z))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -8.2e-54)
		tmp = t_2;
	elseif (b <= -1.7e-116)
		tmp = t_1;
	elseif (b <= -2.8e-198)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 9.4e-281)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 4.8e+102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x + z);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -8.2e-54)
		tmp = t_2;
	elseif (b <= -1.7e-116)
		tmp = t_1;
	elseif (b <= -2.8e-198)
		tmp = z * (1.0 - y);
	elseif (b <= 9.4e-281)
		tmp = x - (t * a);
	elseif (b <= 4.8e+102)
		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[(a + N[(x + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e-54], t$95$2, If[LessEqual[b, -1.7e-116], t$95$1, If[LessEqual[b, -2.8e-198], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.4e-281], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+102], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.2000000000000001e-54 or 4.79999999999999989e102 < b

   1. Initial program 92.9%

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

   2. Taylor expanded in b around inf 74.7%

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

   if -8.2000000000000001e-54 < b < -1.69999999999999996e-116 or 9.4000000000000005e-281 < b < 4.79999999999999989e102

   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. +-commutative 98.8%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. sub-neg 82.3%

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

      3. metadata-eval 82.3%

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

      4. neg-mul-1 82.3%

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

      5. unsub-neg 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in y around 0 65.6%

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

      1. neg-mul-1 65.6%

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

   9. Simplified 65.6%

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

   10. Taylor expanded in b around 0 55.3%

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

   if -1.69999999999999996e-116 < b < -2.7999999999999999e-198

   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. Taylor expanded in z around inf 57.6%

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

   if -2.7999999999999999e-198 < b < 9.4000000000000005e-281

   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. Taylor expanded in z around 0 74.9%

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

   3. Taylor expanded in b around 0 74.9%

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

   4. Taylor expanded in t around inf 67.2%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-281}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+102}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 10: 64.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(t + -1\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* a (+ t -1.0)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -6.8e-63)
     t_2
     (if (<= b 2.5e-183)
       t_1
       (if (<= b 1.8e-127) (- (+ x a) (* y z)) (if (<= b 2.4e+55) 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 + -1.0));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -6.8e-63) {
		tmp = t_2;
	} else if (b <= 2.5e-183) {
		tmp = t_1;
	} else if (b <= 1.8e-127) {
		tmp = (x + a) - (y * z);
	} else if (b <= 2.4e+55) {
		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 + (-1.0d0)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-6.8d-63)) then
        tmp = t_2
    else if (b <= 2.5d-183) then
        tmp = t_1
    else if (b <= 1.8d-127) then
        tmp = (x + a) - (y * z)
    else if (b <= 2.4d+55) 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 + -1.0));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -6.8e-63) {
		tmp = t_2;
	} else if (b <= 2.5e-183) {
		tmp = t_1;
	} else if (b <= 1.8e-127) {
		tmp = (x + a) - (y * z);
	} else if (b <= 2.4e+55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (a * (t + -1.0))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -6.8e-63:
		tmp = t_2
	elif b <= 2.5e-183:
		tmp = t_1
	elif b <= 1.8e-127:
		tmp = (x + a) - (y * z)
	elif b <= 2.4e+55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(a * Float64(t + -1.0)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -6.8e-63)
		tmp = t_2;
	elseif (b <= 2.5e-183)
		tmp = t_1;
	elseif (b <= 1.8e-127)
		tmp = Float64(Float64(x + a) - Float64(y * z));
	elseif (b <= 2.4e+55)
		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 + -1.0));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -6.8e-63)
		tmp = t_2;
	elseif (b <= 2.5e-183)
		tmp = t_1;
	elseif (b <= 1.8e-127)
		tmp = (x + a) - (y * z);
	elseif (b <= 2.4e+55)
		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[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-63], t$95$2, If[LessEqual[b, 2.5e-183], t$95$1, If[LessEqual[b, 1.8e-127], N[(N[(x + a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.79999999999999997e-63 or 2.3999999999999999e55 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 86.0%

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

   3. Taylor expanded in a around 0 78.3%

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

   if -6.79999999999999997e-63 < b < 2.5000000000000001e-183 or 1.8e-127 < b < 2.3999999999999999e55

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 66.7%

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

   3. Taylor expanded in b around 0 61.3%

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

   if 2.5000000000000001e-183 < b < 1.8e-127

   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. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 92.2%

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

      1. +-commutative 92.2%

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

      2. sub-neg 92.2%

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

      3. metadata-eval 92.2%

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

      4. neg-mul-1 92.2%

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

      5. unsub-neg 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in b around 0 92.2%

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

   8. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   10. Simplified 88.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-183}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 11: 69.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -52000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{-285}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x a) (* z (- 1.0 y)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -52000.0)
     t_2
     (if (<= b -2.1e-179)
       t_1
       (if (<= b -3.25e-285)
         (- x (* a (+ t -1.0)))
         (if (<= b 4.8e+102) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) + (z * (1.0 - y));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -52000.0) {
		tmp = t_2;
	} else if (b <= -2.1e-179) {
		tmp = t_1;
	} else if (b <= -3.25e-285) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 4.8e+102) {
		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) + (z * (1.0d0 - y))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-52000.0d0)) then
        tmp = t_2
    else if (b <= (-2.1d-179)) then
        tmp = t_1
    else if (b <= (-3.25d-285)) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (b <= 4.8d+102) 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) + (z * (1.0 - y));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -52000.0) {
		tmp = t_2;
	} else if (b <= -2.1e-179) {
		tmp = t_1;
	} else if (b <= -3.25e-285) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 4.8e+102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) + (z * (1.0 - y))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -52000.0:
		tmp = t_2
	elif b <= -2.1e-179:
		tmp = t_1
	elif b <= -3.25e-285:
		tmp = x - (a * (t + -1.0))
	elif b <= 4.8e+102:
		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(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -52000.0)
		tmp = t_2;
	elseif (b <= -2.1e-179)
		tmp = t_1;
	elseif (b <= -3.25e-285)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (b <= 4.8e+102)
		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) + (z * (1.0 - y));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -52000.0)
		tmp = t_2;
	elseif (b <= -2.1e-179)
		tmp = t_1;
	elseif (b <= -3.25e-285)
		tmp = x - (a * (t + -1.0));
	elseif (b <= 4.8e+102)
		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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -52000.0], t$95$2, If[LessEqual[b, -2.1e-179], t$95$1, If[LessEqual[b, -3.25e-285], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+102], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -52000 or 4.79999999999999989e102 < b

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 88.8%

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

   3. Taylor expanded in a around 0 84.4%

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

   if -52000 < b < -2.0999999999999999e-179 or -3.25e-285 < b < 4.79999999999999989e102

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. sub-neg 82.0%

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

      3. metadata-eval 82.0%

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

      4. neg-mul-1 82.0%

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

      5. unsub-neg 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in b around 0 72.0%

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

   if -2.0999999999999999e-179 < b < -3.25e-285

   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. Taylor expanded in z around 0 82.6%

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

   3. Taylor expanded in b around 0 82.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -52000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-179}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{-285}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+102}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 12: 84.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -70000 \lor \neg \left(b \leq 3.2 \cdot 10^{+77}\right):\\ \;\;\;\;\left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -70000.0) (not (<= b 3.2e+77)))
   (+ (+ z a) (* b (+ t (+ y -2.0))))
   (+ (- x (* y z)) (+ z (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -70000.0) || !(b <= 3.2e+77)) {
		tmp = (z + a) + (b * (t + (y + -2.0)));
	} else {
		tmp = (x - (y * z)) + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-70000.0d0)) .or. (.not. (b <= 3.2d+77))) then
        tmp = (z + a) + (b * (t + (y + (-2.0d0))))
    else
        tmp = (x - (y * z)) + (z + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -70000.0) || !(b <= 3.2e+77)) {
		tmp = (z + a) + (b * (t + (y + -2.0)));
	} else {
		tmp = (x - (y * z)) + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -70000.0) or not (b <= 3.2e+77):
		tmp = (z + a) + (b * (t + (y + -2.0)))
	else:
		tmp = (x - (y * z)) + (z + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -70000.0) || !(b <= 3.2e+77))
		tmp = Float64(Float64(z + a) + Float64(b * Float64(t + Float64(y + -2.0))));
	else
		tmp = Float64(Float64(x - Float64(y * z)) + Float64(z + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -70000.0) || ~((b <= 3.2e+77)))
		tmp = (z + a) + (b * (t + (y + -2.0)));
	else
		tmp = (x - (y * z)) + (z + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -70000.0], N[Not[LessEqual[b, 3.2e+77]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7e4 or 3.2000000000000002e77 < b

   1. Initial program 92.2%

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

      1. +-commutative 92.2%

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

      2. fma-def 94.8%

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

      3. associate--l+ 94.8%

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

      4. sub-neg 94.8%

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

      5. metadata-eval 94.8%

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

      6. sub-neg 94.8%

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

      7. associate-+l- 94.8%

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

      8. fma-neg 95.7%

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

      9. sub-neg 95.7%

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

      10. metadata-eval 95.7%

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

      11. remove-double-neg 95.7%

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

      12. sub-neg 95.7%

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

      13. metadata-eval 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. sub-neg 93.1%

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

      3. metadata-eval 93.1%

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

      4. neg-mul-1 93.1%

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

      5. unsub-neg 93.1%

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

   6. Simplified 93.1%

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

   7. Taylor expanded in y around 0 94.1%

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

      1. neg-mul-1 94.1%

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

   9. Simplified 94.1%

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

   10. Taylor expanded in x around 0 89.4%

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

       1. associate-+r+ 89.4%

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

       2. associate--l+ 89.4%

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

       3. sub-neg 89.4%

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

       4. metadata-eval 89.4%

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

   12. Simplified 89.4%

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

   if -7e4 < b < 3.2000000000000002e77

   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. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in b around 0 91.9%

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

      1. sub-neg 91.9%

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

      2. mul-1-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. sub-neg 91.9%

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

      5. metadata-eval 91.9%

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

      6. distribute-neg-in 91.9%

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

      7. mul-1-neg 91.9%

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

      8. remove-double-neg 91.9%

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

      9. sub-neg 91.9%

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

      10. *-commutative 91.9%

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

      11. cancel-sign-sub-inv 91.9%

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

      12. +-commutative 91.9%

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

      13. distribute-neg-in 91.9%

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

      14. metadata-eval 91.9%

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

      15. sub-neg 91.9%

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

      16. *-commutative 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -70000 \lor \neg \left(b \leq 3.2 \cdot 10^{+77}\right):\\ \;\;\;\;\left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 13: 85.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+81}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -6.8e-63)
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (if (<= b 8e+81)
       (+ (- x (* y z)) (+ z t_1))
       (+ (+ z a) (* b (+ t (+ y -2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -6.8e-63) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (b <= 8e+81) {
		tmp = (x - (y * z)) + (z + t_1);
	} else {
		tmp = (z + a) + (b * (t + (y + -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-6.8d-63)) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else if (b <= 8d+81) then
        tmp = (x - (y * z)) + (z + t_1)
    else
        tmp = (z + a) + (b * (t + (y + (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -6.8e-63) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (b <= 8e+81) {
		tmp = (x - (y * z)) + (z + t_1);
	} else {
		tmp = (z + a) + (b * (t + (y + -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -6.8e-63:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	elif b <= 8e+81:
		tmp = (x - (y * z)) + (z + t_1)
	else:
		tmp = (z + a) + (b * (t + (y + -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -6.8e-63)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	elseif (b <= 8e+81)
		tmp = Float64(Float64(x - Float64(y * z)) + Float64(z + t_1));
	else
		tmp = Float64(Float64(z + a) + Float64(b * Float64(t + Float64(y + -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -6.8e-63)
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	elseif (b <= 8e+81)
		tmp = (x - (y * z)) + (z + t_1);
	else
		tmp = (z + a) + (b * (t + (y + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-63], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 8e+81], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.79999999999999997e-63

   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. Taylor expanded in z around 0 86.0%

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

   if -6.79999999999999997e-63 < b < 7.99999999999999937e81

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 99.2%

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

   3. Taylor expanded in b around 0 95.4%

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

      1. sub-neg 95.4%

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

      2. mul-1-neg 95.4%

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

      3. unsub-neg 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

      6. distribute-neg-in 95.4%

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

      7. mul-1-neg 95.4%

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

      8. remove-double-neg 95.4%

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

      9. sub-neg 95.4%

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

      10. *-commutative 95.4%

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

      11. cancel-sign-sub-inv 95.4%

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

      12. +-commutative 95.4%

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

      13. distribute-neg-in 95.4%

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

      14. metadata-eval 95.4%

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

      15. sub-neg 95.4%

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

      16. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   if 7.99999999999999937e81 < b

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. fma-def 93.0%

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

      3. associate--l+ 93.0%

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

      4. sub-neg 93.0%

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

      5. metadata-eval 93.0%

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

      6. sub-neg 93.0%

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

      7. associate-+l- 93.0%

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

      8. fma-neg 93.0%

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

      9. sub-neg 93.0%

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

      10. metadata-eval 93.0%

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

      11. remove-double-neg 93.0%

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

      12. sub-neg 93.0%

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

      13. metadata-eval 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in t around 0 90.7%

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

      1. +-commutative 90.7%

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

      2. sub-neg 90.7%

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

      3. metadata-eval 90.7%

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

      4. neg-mul-1 90.7%

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

      5. unsub-neg 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around 0 93.4%

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

      1. neg-mul-1 93.4%

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

   9. Simplified 93.4%

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

   10. Taylor expanded in x around 0 92.7%

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

       1. associate-+r+ 92.7%

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

       2. associate--l+ 92.7%

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

       3. sub-neg 92.7%

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

       4. metadata-eval 92.7%

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

   12. Simplified 92.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+81}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \]

Alternative 14: 61.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(t + -1\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -0.000105:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* a (+ t -1.0)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -0.000105)
     t_2
     (if (<= b 9.8e-183)
       t_1
       (if (<= b 5.4e-129)
         (- (+ x a) (* y z))
         (if (<= b 2.25e+61) 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 + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -0.000105) {
		tmp = t_2;
	} else if (b <= 9.8e-183) {
		tmp = t_1;
	} else if (b <= 5.4e-129) {
		tmp = (x + a) - (y * z);
	} else if (b <= 2.25e+61) {
		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 + (-1.0d0)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-0.000105d0)) then
        tmp = t_2
    else if (b <= 9.8d-183) then
        tmp = t_1
    else if (b <= 5.4d-129) then
        tmp = (x + a) - (y * z)
    else if (b <= 2.25d+61) 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 + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -0.000105) {
		tmp = t_2;
	} else if (b <= 9.8e-183) {
		tmp = t_1;
	} else if (b <= 5.4e-129) {
		tmp = (x + a) - (y * z);
	} else if (b <= 2.25e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (a * (t + -1.0))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -0.000105:
		tmp = t_2
	elif b <= 9.8e-183:
		tmp = t_1
	elif b <= 5.4e-129:
		tmp = (x + a) - (y * z)
	elif b <= 2.25e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(a * Float64(t + -1.0)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -0.000105)
		tmp = t_2;
	elseif (b <= 9.8e-183)
		tmp = t_1;
	elseif (b <= 5.4e-129)
		tmp = Float64(Float64(x + a) - Float64(y * z));
	elseif (b <= 2.25e+61)
		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 + -1.0));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -0.000105)
		tmp = t_2;
	elseif (b <= 9.8e-183)
		tmp = t_1;
	elseif (b <= 5.4e-129)
		tmp = (x + a) - (y * z);
	elseif (b <= 2.25e+61)
		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[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.000105], t$95$2, If[LessEqual[b, 9.8e-183], t$95$1, If[LessEqual[b, 5.4e-129], N[(N[(x + a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e-4 or 2.25e61 < b

   1. Initial program 92.6%

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

   2. Taylor expanded in b around inf 76.1%

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

   if -1.05e-4 < b < 9.799999999999999e-183 or 5.39999999999999998e-129 < b < 2.25e61

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.2%

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

   3. Taylor expanded in b around 0 60.5%

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

   if 9.799999999999999e-183 < b < 5.39999999999999998e-129

   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. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 92.2%

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

      1. +-commutative 92.2%

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

      2. sub-neg 92.2%

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

      3. metadata-eval 92.2%

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

      4. neg-mul-1 92.2%

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

      5. unsub-neg 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in b around 0 92.2%

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

   8. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   10. Simplified 88.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.000105:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-183}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+61}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 15: 21.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-158}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+69}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.55e+103)
   x
   (if (<= x -1.32e-99)
     a
     (if (<= x -1.45e-289)
       z
       (if (<= x 1.7e-158) a (if (<= x 2.1e-6) z (if (<= x 8e+69) a x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.55e+103) {
		tmp = x;
	} else if (x <= -1.32e-99) {
		tmp = a;
	} else if (x <= -1.45e-289) {
		tmp = z;
	} else if (x <= 1.7e-158) {
		tmp = a;
	} else if (x <= 2.1e-6) {
		tmp = z;
	} else if (x <= 8e+69) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.55d+103)) then
        tmp = x
    else if (x <= (-1.32d-99)) then
        tmp = a
    else if (x <= (-1.45d-289)) then
        tmp = z
    else if (x <= 1.7d-158) then
        tmp = a
    else if (x <= 2.1d-6) then
        tmp = z
    else if (x <= 8d+69) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.55e+103) {
		tmp = x;
	} else if (x <= -1.32e-99) {
		tmp = a;
	} else if (x <= -1.45e-289) {
		tmp = z;
	} else if (x <= 1.7e-158) {
		tmp = a;
	} else if (x <= 2.1e-6) {
		tmp = z;
	} else if (x <= 8e+69) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.55e+103:
		tmp = x
	elif x <= -1.32e-99:
		tmp = a
	elif x <= -1.45e-289:
		tmp = z
	elif x <= 1.7e-158:
		tmp = a
	elif x <= 2.1e-6:
		tmp = z
	elif x <= 8e+69:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.55e+103)
		tmp = x;
	elseif (x <= -1.32e-99)
		tmp = a;
	elseif (x <= -1.45e-289)
		tmp = z;
	elseif (x <= 1.7e-158)
		tmp = a;
	elseif (x <= 2.1e-6)
		tmp = z;
	elseif (x <= 8e+69)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.55e+103)
		tmp = x;
	elseif (x <= -1.32e-99)
		tmp = a;
	elseif (x <= -1.45e-289)
		tmp = z;
	elseif (x <= 1.7e-158)
		tmp = a;
	elseif (x <= 2.1e-6)
		tmp = z;
	elseif (x <= 8e+69)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.55e+103], x, If[LessEqual[x, -1.32e-99], a, If[LessEqual[x, -1.45e-289], z, If[LessEqual[x, 1.7e-158], a, If[LessEqual[x, 2.1e-6], z, If[LessEqual[x, 8e+69], a, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5500000000000001e103 or 8.0000000000000006e69 < x

   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. Taylor expanded in x around inf 40.6%

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

   if -2.5500000000000001e103 < x < -1.31999999999999999e-99 or -1.45000000000000003e-289 < x < 1.7e-158 or 2.0999999999999998e-6 < x < 8.0000000000000006e69

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 45.1%

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

   3. Taylor expanded in t around 0 20.4%

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

   if -1.31999999999999999e-99 < x < -1.45000000000000003e-289 or 1.7e-158 < x < 2.0999999999999998e-6

   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. +-commutative 95.4%

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

      2. fma-def 96.9%

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

      3. associate--l+ 96.9%

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

      4. sub-neg 96.9%

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

      5. metadata-eval 96.9%

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

      6. sub-neg 96.9%

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

      7. associate-+l- 96.9%

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

      8. fma-neg 96.9%

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

      9. sub-neg 96.9%

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

      10. metadata-eval 96.9%

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

      11. remove-double-neg 96.9%

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

      12. sub-neg 96.9%

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

      13. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 86.8%

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

      1. +-commutative 86.8%

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

      2. sub-neg 86.8%

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

      3. metadata-eval 86.8%

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

      4. neg-mul-1 86.8%

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

      5. unsub-neg 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in y around 0 82.1%

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

      1. neg-mul-1 82.1%

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

   9. Simplified 82.1%

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

   10. Taylor expanded in z around inf 24.5%

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

4. Final simplification 28.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-158}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+69}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 20.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-101}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-145}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 0.057:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.1e+103)
   x
   (if (<= x -1.22e-101)
     a
     (if (<= x -2.1e-289)
       z
       (if (<= x 2.4e-145)
         a
         (if (<= x 0.057) (* -2.0 b) (if (<= x 3.5e+72) a x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+103) {
		tmp = x;
	} else if (x <= -1.22e-101) {
		tmp = a;
	} else if (x <= -2.1e-289) {
		tmp = z;
	} else if (x <= 2.4e-145) {
		tmp = a;
	} else if (x <= 0.057) {
		tmp = -2.0 * b;
	} else if (x <= 3.5e+72) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.1d+103)) then
        tmp = x
    else if (x <= (-1.22d-101)) then
        tmp = a
    else if (x <= (-2.1d-289)) then
        tmp = z
    else if (x <= 2.4d-145) then
        tmp = a
    else if (x <= 0.057d0) then
        tmp = (-2.0d0) * b
    else if (x <= 3.5d+72) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+103) {
		tmp = x;
	} else if (x <= -1.22e-101) {
		tmp = a;
	} else if (x <= -2.1e-289) {
		tmp = z;
	} else if (x <= 2.4e-145) {
		tmp = a;
	} else if (x <= 0.057) {
		tmp = -2.0 * b;
	} else if (x <= 3.5e+72) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.1e+103:
		tmp = x
	elif x <= -1.22e-101:
		tmp = a
	elif x <= -2.1e-289:
		tmp = z
	elif x <= 2.4e-145:
		tmp = a
	elif x <= 0.057:
		tmp = -2.0 * b
	elif x <= 3.5e+72:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.1e+103)
		tmp = x;
	elseif (x <= -1.22e-101)
		tmp = a;
	elseif (x <= -2.1e-289)
		tmp = z;
	elseif (x <= 2.4e-145)
		tmp = a;
	elseif (x <= 0.057)
		tmp = Float64(-2.0 * b);
	elseif (x <= 3.5e+72)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.1e+103)
		tmp = x;
	elseif (x <= -1.22e-101)
		tmp = a;
	elseif (x <= -2.1e-289)
		tmp = z;
	elseif (x <= 2.4e-145)
		tmp = a;
	elseif (x <= 0.057)
		tmp = -2.0 * b;
	elseif (x <= 3.5e+72)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.1e+103], x, If[LessEqual[x, -1.22e-101], a, If[LessEqual[x, -2.1e-289], z, If[LessEqual[x, 2.4e-145], a, If[LessEqual[x, 0.057], N[(-2.0 * b), $MachinePrecision], If[LessEqual[x, 3.5e+72], a, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1000000000000002e103 or 3.5000000000000001e72 < x

   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. Taylor expanded in x around inf 40.6%

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

   if -2.1000000000000002e103 < x < -1.2199999999999999e-101 or -2.0999999999999998e-289 < x < 2.40000000000000015e-145 or 0.0570000000000000021 < x < 3.5000000000000001e72

   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. Taylor expanded in a around inf 43.6%

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

   3. Taylor expanded in t around 0 20.3%

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

   if -1.2199999999999999e-101 < x < -2.0999999999999998e-289

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. fma-def 93.1%

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

      3. associate--l+ 93.1%

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

      4. sub-neg 93.1%

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

      5. metadata-eval 93.1%

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

      6. sub-neg 93.1%

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

      7. associate-+l- 93.1%

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

      8. fma-neg 93.1%

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

      9. sub-neg 93.1%

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

      10. metadata-eval 93.1%

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

      11. remove-double-neg 93.1%

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

      12. sub-neg 93.1%

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

      13. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. sub-neg 80.4%

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

      3. metadata-eval 80.4%

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

      4. neg-mul-1 80.4%

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

      5. unsub-neg 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in y around 0 80.5%

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

      1. neg-mul-1 80.5%

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

   9. Simplified 80.5%

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

   10. Taylor expanded in z around inf 31.1%

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

   if 2.40000000000000015e-145 < x < 0.0570000000000000021

   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. Taylor expanded in b around inf 66.9%

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

   3. Taylor expanded in t around 0 51.4%

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

   4. Taylor expanded in y around 0 22.5%

      \[\leadsto \color{blue}{-2 \cdot b} \]
   5. Step-by-step derivation

      1. *-commutative 22.5%

         \[\leadsto \color{blue}{b \cdot -2} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{b \cdot -2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-101}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-145}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 0.057:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 25.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+56}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-239}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 64000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.8e+56)
   (* t b)
   (if (<= t 1.06e-293)
     x
     (if (<= t 2.45e-239)
       a
       (if (<= t 8.2e-152) z (if (<= t 64000000.0) a (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.8e+56) {
		tmp = t * b;
	} else if (t <= 1.06e-293) {
		tmp = x;
	} else if (t <= 2.45e-239) {
		tmp = a;
	} else if (t <= 8.2e-152) {
		tmp = z;
	} else if (t <= 64000000.0) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.8d+56)) then
        tmp = t * b
    else if (t <= 1.06d-293) then
        tmp = x
    else if (t <= 2.45d-239) then
        tmp = a
    else if (t <= 8.2d-152) then
        tmp = z
    else if (t <= 64000000.0d0) then
        tmp = a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.8e+56) {
		tmp = t * b;
	} else if (t <= 1.06e-293) {
		tmp = x;
	} else if (t <= 2.45e-239) {
		tmp = a;
	} else if (t <= 8.2e-152) {
		tmp = z;
	} else if (t <= 64000000.0) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.8e+56:
		tmp = t * b
	elif t <= 1.06e-293:
		tmp = x
	elif t <= 2.45e-239:
		tmp = a
	elif t <= 8.2e-152:
		tmp = z
	elif t <= 64000000.0:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.8e+56)
		tmp = Float64(t * b);
	elseif (t <= 1.06e-293)
		tmp = x;
	elseif (t <= 2.45e-239)
		tmp = a;
	elseif (t <= 8.2e-152)
		tmp = z;
	elseif (t <= 64000000.0)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.8e+56)
		tmp = t * b;
	elseif (t <= 1.06e-293)
		tmp = x;
	elseif (t <= 2.45e-239)
		tmp = a;
	elseif (t <= 8.2e-152)
		tmp = z;
	elseif (t <= 64000000.0)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.8e+56], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.06e-293], x, If[LessEqual[t, 2.45e-239], a, If[LessEqual[t, 8.2e-152], z, If[LessEqual[t, 64000000.0], a, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.79999999999999989e56 or 6.4e7 < t

   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. +-commutative 95.1%

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

      2. fma-def 97.6%

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

      3. associate--l+ 97.6%

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

      4. sub-neg 97.6%

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

      5. metadata-eval 97.6%

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

      6. sub-neg 97.6%

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

      7. associate-+l- 97.6%

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

      8. fma-neg 98.4%

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

      9. sub-neg 98.4%

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

      10. metadata-eval 98.4%

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

      11. remove-double-neg 98.4%

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

      12. sub-neg 98.4%

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

      13. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. sub-neg 72.0%

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

      3. metadata-eval 72.0%

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

      4. neg-mul-1 72.0%

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

      5. unsub-neg 72.0%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in t around inf 36.9%

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

   if -7.79999999999999989e56 < t < 1.05999999999999994e-293

   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. Taylor expanded in x around inf 23.1%

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

   if 1.05999999999999994e-293 < t < 2.45000000000000016e-239 or 8.2000000000000002e-152 < t < 6.4e7

   1. Initial program 92.5%

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

   2. Taylor expanded in a around inf 34.3%

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

   3. Taylor expanded in t around 0 33.8%

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

   if 2.45000000000000016e-239 < t < 8.2000000000000002e-152

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. fma-def 94.1%

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

      3. associate--l+ 94.1%

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

      4. sub-neg 94.1%

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

      5. metadata-eval 94.1%

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

      6. sub-neg 94.1%

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

      7. associate-+l- 94.1%

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

      8. fma-neg 94.1%

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

      9. sub-neg 94.1%

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

      10. metadata-eval 94.1%

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

      11. remove-double-neg 94.1%

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

      12. sub-neg 94.1%

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

      13. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. sub-neg 94.1%

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

      3. metadata-eval 94.1%

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

      4. neg-mul-1 94.1%

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

      5. unsub-neg 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in y around 0 77.0%

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

      1. neg-mul-1 77.0%

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

   9. Simplified 77.0%

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

   10. Taylor expanded in z around inf 38.1%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+56}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-239}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 64000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 18: 32.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+117}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= y -9.6e+117)
     (* y b)
     (if (<= y 7.2e-201)
       t_1
       (if (<= y 1.6e-153)
         z
         (if (<= y 1.9e-29) t_1 (if (<= y 5.4e+71) (* t b) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (y <= -9.6e+117) {
		tmp = y * b;
	} else if (y <= 7.2e-201) {
		tmp = t_1;
	} else if (y <= 1.6e-153) {
		tmp = z;
	} else if (y <= 1.9e-29) {
		tmp = t_1;
	} else if (y <= 5.4e+71) {
		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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (y <= (-9.6d+117)) then
        tmp = y * b
    else if (y <= 7.2d-201) then
        tmp = t_1
    else if (y <= 1.6d-153) then
        tmp = z
    else if (y <= 1.9d-29) then
        tmp = t_1
    else if (y <= 5.4d+71) 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 t_1 = a * (1.0 - t);
	double tmp;
	if (y <= -9.6e+117) {
		tmp = y * b;
	} else if (y <= 7.2e-201) {
		tmp = t_1;
	} else if (y <= 1.6e-153) {
		tmp = z;
	} else if (y <= 1.9e-29) {
		tmp = t_1;
	} else if (y <= 5.4e+71) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if y <= -9.6e+117:
		tmp = y * b
	elif y <= 7.2e-201:
		tmp = t_1
	elif y <= 1.6e-153:
		tmp = z
	elif y <= 1.9e-29:
		tmp = t_1
	elif y <= 5.4e+71:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (y <= -9.6e+117)
		tmp = Float64(y * b);
	elseif (y <= 7.2e-201)
		tmp = t_1;
	elseif (y <= 1.6e-153)
		tmp = z;
	elseif (y <= 1.9e-29)
		tmp = t_1;
	elseif (y <= 5.4e+71)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (y <= -9.6e+117)
		tmp = y * b;
	elseif (y <= 7.2e-201)
		tmp = t_1;
	elseif (y <= 1.6e-153)
		tmp = z;
	elseif (y <= 1.9e-29)
		tmp = t_1;
	elseif (y <= 5.4e+71)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+117], N[(y * b), $MachinePrecision], If[LessEqual[y, 7.2e-201], t$95$1, If[LessEqual[y, 1.6e-153], z, If[LessEqual[y, 1.9e-29], t$95$1, If[LessEqual[y, 5.4e+71], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5999999999999996e117 or 5.39999999999999993e71 < y

   1. Initial program 92.0%

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

   2. Taylor expanded in b around inf 53.7%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   if -9.5999999999999996e117 < y < 7.20000000000000063e-201 or 1.6e-153 < y < 1.89999999999999988e-29

   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. Taylor expanded in a around inf 41.5%

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

   if 7.20000000000000063e-201 < y < 1.6e-153

   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. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. neg-mul-1 100.0%

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

      5. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in z around inf 60.7%

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

   if 1.89999999999999988e-29 < y < 5.39999999999999993e71

   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. +-commutative 95.4%

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

      2. fma-def 95.5%

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

      3. associate--l+ 95.5%

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

      4. sub-neg 95.5%

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

      5. metadata-eval 95.5%

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

      6. sub-neg 95.5%

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

      7. associate-+l- 95.5%

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

      8. fma-neg 95.5%

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

      9. sub-neg 95.5%

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

      10. metadata-eval 95.5%

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

      11. remove-double-neg 95.5%

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

      12. sub-neg 95.5%

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

      13. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 91.6%

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

      1. +-commutative 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

      4. neg-mul-1 91.6%

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

      5. unsub-neg 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in t around inf 42.9%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+117}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 19: 24.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e+80)
   (* y b)
   (if (<= b -1.9e-55)
     (* t b)
     (if (<= b 1.18e-39) x (if (<= b 2.9e+55) a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+80) {
		tmp = y * b;
	} else if (b <= -1.9e-55) {
		tmp = t * b;
	} else if (b <= 1.18e-39) {
		tmp = x;
	} else if (b <= 2.9e+55) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7d+80)) then
        tmp = y * b
    else if (b <= (-1.9d-55)) then
        tmp = t * b
    else if (b <= 1.18d-39) then
        tmp = x
    else if (b <= 2.9d+55) then
        tmp = a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+80) {
		tmp = y * b;
	} else if (b <= -1.9e-55) {
		tmp = t * b;
	} else if (b <= 1.18e-39) {
		tmp = x;
	} else if (b <= 2.9e+55) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+80:
		tmp = y * b
	elif b <= -1.9e-55:
		tmp = t * b
	elif b <= 1.18e-39:
		tmp = x
	elif b <= 2.9e+55:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+80)
		tmp = Float64(y * b);
	elseif (b <= -1.9e-55)
		tmp = Float64(t * b);
	elseif (b <= 1.18e-39)
		tmp = x;
	elseif (b <= 2.9e+55)
		tmp = a;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e+80)
		tmp = y * b;
	elseif (b <= -1.9e-55)
		tmp = t * b;
	elseif (b <= 1.18e-39)
		tmp = x;
	elseif (b <= 2.9e+55)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+80], N[(y * b), $MachinePrecision], If[LessEqual[b, -1.9e-55], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.18e-39], x, If[LessEqual[b, 2.9e+55], a, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.99999999999999987e80 or 2.8999999999999999e55 < b

   1. Initial program 90.7%

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

   2. Taylor expanded in b around inf 80.8%

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

   3. Taylor expanded in y around inf 44.4%

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

      1. *-commutative 44.4%

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

   5. Simplified 44.4%

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

   if -6.99999999999999987e80 < b < -1.8999999999999998e-55

   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. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 90.3%

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

      1. +-commutative 90.3%

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

      2. sub-neg 90.3%

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

      3. metadata-eval 90.3%

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

      4. neg-mul-1 90.3%

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

      5. unsub-neg 90.3%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in t around inf 30.6%

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

   if -1.8999999999999998e-55 < b < 1.17999999999999993e-39

   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. Taylor expanded in x around inf 26.4%

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

   if 1.17999999999999993e-39 < b < 2.8999999999999999e55

   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. Taylor expanded in a around inf 56.2%

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

   3. Taylor expanded in t around 0 32.2%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 20: 55.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-112}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 9000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.75e+56)
     t_1
     (if (<= t 2.8e-112)
       (+ a (+ x z))
       (if (<= t 9000000000.0) (* y (- b z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.75e+56) {
		tmp = t_1;
	} else if (t <= 2.8e-112) {
		tmp = a + (x + z);
	} else if (t <= 9000000000.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.75d+56)) then
        tmp = t_1
    else if (t <= 2.8d-112) then
        tmp = a + (x + z)
    else if (t <= 9000000000.0d0) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.75e+56) {
		tmp = t_1;
	} else if (t <= 2.8e-112) {
		tmp = a + (x + z);
	} else if (t <= 9000000000.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.75e+56:
		tmp = t_1
	elif t <= 2.8e-112:
		tmp = a + (x + z)
	elif t <= 9000000000.0:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.75e+56)
		tmp = t_1;
	elseif (t <= 2.8e-112)
		tmp = Float64(a + Float64(x + z));
	elseif (t <= 9000000000.0)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.75e+56)
		tmp = t_1;
	elseif (t <= 2.8e-112)
		tmp = a + (x + z);
	elseif (t <= 9000000000.0)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+56], t$95$1, If[LessEqual[t, 2.8e-112], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9000000000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e56 or 9e9 < t

   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. Taylor expanded in t around inf 66.4%

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

   if -1.75e56 < t < 2.80000000000000023e-112

   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. +-commutative 98.2%

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

      2. fma-def 98.2%

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

      3. associate--l+ 98.2%

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

      4. sub-neg 98.2%

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

      5. metadata-eval 98.2%

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

      6. sub-neg 98.2%

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

      7. associate-+l- 98.2%

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

      8. fma-neg 98.2%

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

      9. sub-neg 98.2%

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

      10. metadata-eval 98.2%

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

      11. remove-double-neg 98.2%

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

      12. sub-neg 98.2%

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

      13. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. sub-neg 97.3%

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

      3. metadata-eval 97.3%

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

      4. neg-mul-1 97.3%

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

      5. unsub-neg 97.3%

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

   6. Simplified 97.3%

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

   7. Taylor expanded in y around 0 82.3%

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

      1. neg-mul-1 82.3%

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

   9. Simplified 82.3%

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

   10. Taylor expanded in b around 0 54.1%

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

   if 2.80000000000000023e-112 < t < 9e9

   1. Initial program 90.8%

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

   2. Taylor expanded in y around inf 64.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-112}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 9000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 21: 61.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00095 \lor \neg \left(b \leq 7 \cdot 10^{+60}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.00095) (not (<= b 7e+60)))
   (* b (- (+ y t) 2.0))
   (- x (* a (+ t -1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.00095) || !(b <= 7e+60)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x - (a * (t + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.00095d0)) .or. (.not. (b <= 7d+60))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x - (a * (t + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.00095) || !(b <= 7e+60)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x - (a * (t + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.00095) or not (b <= 7e+60):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x - (a * (t + -1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.00095) || !(b <= 7e+60))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.00095) || ~((b <= 7e+60)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x - (a * (t + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.00095], N[Not[LessEqual[b, 7e+60]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.49999999999999998e-4 or 7.0000000000000004e60 < b

   1. Initial program 92.6%

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

   2. Taylor expanded in b around inf 76.1%

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

   if -9.49999999999999998e-4 < b < 7.0000000000000004e60

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 67.7%

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

   3. Taylor expanded in b around 0 59.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00095 \lor \neg \left(b \leq 7 \cdot 10^{+60}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \end{array} \]

Alternative 22: 40.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+69} \lor \neg \left(b \leq 6.2 \cdot 10^{+41}\right):\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.55e+69) (not (<= b 6.2e+41)))
   (* b (- 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 ((b <= -2.55e+69) || !(b <= 6.2e+41)) {
		tmp = b * (y - 2.0);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.55d+69)) .or. (.not. (b <= 6.2d+41))) then
        tmp = b * (y - 2.0d0)
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.55e+69) || !(b <= 6.2e+41)) {
		tmp = b * (y - 2.0);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.55e+69) or not (b <= 6.2e+41):
		tmp = b * (y - 2.0)
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.55e+69) || !(b <= 6.2e+41))
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.55e+69) || ~((b <= 6.2e+41)))
		tmp = b * (y - 2.0);
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.55e+69], N[Not[LessEqual[b, 6.2e+41]], $MachinePrecision]], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.54999999999999999e69 or 6.2e41 < b

   1. Initial program 91.6%

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

   2. Taylor expanded in b around inf 78.9%

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

   3. Taylor expanded in t around 0 56.3%

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

   if -2.54999999999999999e69 < b < 6.2e41

   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. Taylor expanded in a around inf 38.1%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+69} \lor \neg \left(b \leq 6.2 \cdot 10^{+41}\right):\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 23: 32.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+74} \lor \neg \left(b \leq 3.3 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e+74) (not (<= b 3.3e+61))) (* y b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e+74) || !(b <= 3.3e+61)) {
		tmp = y * b;
	} else {
		tmp = x + 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 ((b <= (-4.4d+74)) .or. (.not. (b <= 3.3d+61))) then
        tmp = y * b
    else
        tmp = x + 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 ((b <= -4.4e+74) || !(b <= 3.3e+61)) {
		tmp = y * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e+74) or not (b <= 3.3e+61):
		tmp = y * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e+74) || !(b <= 3.3e+61))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.4e+74) || ~((b <= 3.3e+61)))
		tmp = y * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e+74], N[Not[LessEqual[b, 3.3e+61]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4000000000000002e74 or 3.2999999999999998e61 < b

   1. Initial program 91.2%

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

   2. Taylor expanded in b around inf 81.6%

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

   3. Taylor expanded in y around inf 44.3%

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

      1. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   if -4.4000000000000002e74 < b < 3.2999999999999998e61

   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. Taylor expanded in z around 0 69.5%

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

   3. Taylor expanded in t around 0 41.5%

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

      1. sub-neg 41.5%

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

      2. metadata-eval 41.5%

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

      3. neg-mul-1 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in b around 0 36.0%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+74} \lor \neg \left(b \leq 3.3 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 24: 21.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+67}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.5e+103) x (if (<= x 9.6e+67) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.5e+103) {
		tmp = x;
	} else if (x <= 9.6e+67) {
		tmp = a;
	} 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 <= (-1.5d+103)) then
        tmp = x
    else if (x <= 9.6d+67) then
        tmp = a
    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 <= -1.5e+103) {
		tmp = x;
	} else if (x <= 9.6e+67) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.5e+103:
		tmp = x
	elif x <= 9.6e+67:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.5e+103)
		tmp = x;
	elseif (x <= 9.6e+67)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.5e+103)
		tmp = x;
	elseif (x <= 9.6e+67)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.5e+103], x, If[LessEqual[x, 9.6e+67], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e103 or 9.60000000000000007e67 < x

   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. Taylor expanded in x around inf 40.6%

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

   if -1.5e103 < x < 9.60000000000000007e67

   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. Taylor expanded in a around inf 36.8%

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

   3. Taylor expanded in t around 0 15.2%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+67}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 11.0% 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 96.1%

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

2. Taylor expanded in a around inf 29.9%

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

3. Taylor expanded in t around 0 11.8%

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

4. Final simplification 11.8%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023334 
(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)))