Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.8% → 99.9%

Time: 17.7s

Alternatives: 23

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* z (- 1.0 (log t))) (fma (+ a -0.5) b (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (z * (1.0 - log(t))) + fma((a + -0.5), b, (x + y));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(z * Float64(1.0 - log(t))) + fma(Float64(a + -0.5), b, Float64(x + y)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

   2. associate--l+ 99.9%

      \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

   3. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

   4. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

   5. *-lft-identity 99.9%

      \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   7. *-commutative 99.9%

      \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   8. distribute-rgt-out-- 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   9. metadata-eval 99.9%

      \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   10. fma-define 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

   11. sub-neg 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

   12. metadata-eval 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := b \cdot \left(a - 0.5\right)\\ t_3 := t\_2 + \left(z - t\_1\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+224}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+117}:\\ \;\;\;\;\left(z + \left(\left(x + y\right) - t\_1\right)\right) + -0.5 \cdot b\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+46}:\\ \;\;\;\;\left(x + y\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* b (- a 0.5))) (t_3 (+ t_2 (- z t_1))))
   (if (<= z -7.2e+224)
     t_3
     (if (<= z -3.1e+117)
       (+ (+ z (- (+ x y) t_1)) (* -0.5 b))
       (if (<= z 1.6e+46) (+ (+ x y) t_2) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = b * (a - 0.5);
	double t_3 = t_2 + (z - t_1);
	double tmp;
	if (z <= -7.2e+224) {
		tmp = t_3;
	} else if (z <= -3.1e+117) {
		tmp = (z + ((x + y) - t_1)) + (-0.5 * b);
	} else if (z <= 1.6e+46) {
		tmp = (x + y) + t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = b * (a - 0.5d0)
    t_3 = t_2 + (z - t_1)
    if (z <= (-7.2d+224)) then
        tmp = t_3
    else if (z <= (-3.1d+117)) then
        tmp = (z + ((x + y) - t_1)) + ((-0.5d0) * b)
    else if (z <= 1.6d+46) then
        tmp = (x + y) + t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double t_2 = b * (a - 0.5);
	double t_3 = t_2 + (z - t_1);
	double tmp;
	if (z <= -7.2e+224) {
		tmp = t_3;
	} else if (z <= -3.1e+117) {
		tmp = (z + ((x + y) - t_1)) + (-0.5 * b);
	} else if (z <= 1.6e+46) {
		tmp = (x + y) + t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = b * (a - 0.5)
	t_3 = t_2 + (z - t_1)
	tmp = 0
	if z <= -7.2e+224:
		tmp = t_3
	elif z <= -3.1e+117:
		tmp = (z + ((x + y) - t_1)) + (-0.5 * b)
	elif z <= 1.6e+46:
		tmp = (x + y) + t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(b * Float64(a - 0.5))
	t_3 = Float64(t_2 + Float64(z - t_1))
	tmp = 0.0
	if (z <= -7.2e+224)
		tmp = t_3;
	elseif (z <= -3.1e+117)
		tmp = Float64(Float64(z + Float64(Float64(x + y) - t_1)) + Float64(-0.5 * b));
	elseif (z <= 1.6e+46)
		tmp = Float64(Float64(x + y) + t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = b * (a - 0.5);
	t_3 = t_2 + (z - t_1);
	tmp = 0.0;
	if (z <= -7.2e+224)
		tmp = t_3;
	elseif (z <= -3.1e+117)
		tmp = (z + ((x + y) - t_1)) + (-0.5 * b);
	elseif (z <= 1.6e+46)
		tmp = (x + y) + t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(z - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+224], t$95$3, If[LessEqual[z, -3.1e+117], N[(N[(z + N[(N[(x + y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+46], N[(N[(x + y), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e224 or 1.5999999999999999e46 < z

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.3%

      \[\leadsto \color{blue}{\left(\left(x + z\right) - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   if -7.2e224 < z < -3.09999999999999975e117

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in a around 0 87.1%

      \[\leadsto \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + \color{blue}{-0.5 \cdot b} \]
   6. Step-by-step derivation

      1. *-commutative 87.1%

         \[\leadsto \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + \color{blue}{b \cdot -0.5} \]

   7. Simplified 87.1%

      \[\leadsto \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + \color{blue}{b \cdot -0.5} \]

   if -3.09999999999999975e117 < z < 1.5999999999999999e46

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 96.6%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+224}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+117}:\\ \;\;\;\;\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + -0.5 \cdot b\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+46}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq 7 \cdot 10^{+200}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+223}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \frac{1 - \log t}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+247}:\\ \;\;\;\;y + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - z \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= z 7e+200)
     (+ (+ x y) t_1)
     (if (<= z 8.2e+223)
       (* (* z b) (/ (- 1.0 (log t)) b))
       (if (<= z 5.8e+247) (+ y t_1) (+ x (- z (* z (log t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 7e+200) {
		tmp = (x + y) + t_1;
	} else if (z <= 8.2e+223) {
		tmp = (z * b) * ((1.0 - log(t)) / b);
	} else if (z <= 5.8e+247) {
		tmp = y + t_1;
	} else {
		tmp = x + (z - (z * log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (z <= 7d+200) then
        tmp = (x + y) + t_1
    else if (z <= 8.2d+223) then
        tmp = (z * b) * ((1.0d0 - log(t)) / b)
    else if (z <= 5.8d+247) then
        tmp = y + t_1
    else
        tmp = x + (z - (z * log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 7e+200) {
		tmp = (x + y) + t_1;
	} else if (z <= 8.2e+223) {
		tmp = (z * b) * ((1.0 - Math.log(t)) / b);
	} else if (z <= 5.8e+247) {
		tmp = y + t_1;
	} else {
		tmp = x + (z - (z * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if z <= 7e+200:
		tmp = (x + y) + t_1
	elif z <= 8.2e+223:
		tmp = (z * b) * ((1.0 - math.log(t)) / b)
	elif z <= 5.8e+247:
		tmp = y + t_1
	else:
		tmp = x + (z - (z * math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= 7e+200)
		tmp = Float64(Float64(x + y) + t_1);
	elseif (z <= 8.2e+223)
		tmp = Float64(Float64(z * b) * Float64(Float64(1.0 - log(t)) / b));
	elseif (z <= 5.8e+247)
		tmp = Float64(y + t_1);
	else
		tmp = Float64(x + Float64(z - Float64(z * log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= 7e+200)
		tmp = (x + y) + t_1;
	elseif (z <= 8.2e+223)
		tmp = (z * b) * ((1.0 - log(t)) / b);
	elseif (z <= 5.8e+247)
		tmp = y + t_1;
	else
		tmp = x + (z - (z * log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 7e+200], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 8.2e+223], N[(N[(z * b), $MachinePrecision] * N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+247], N[(y + t$95$1), $MachinePrecision], N[(x + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 7.00000000000000013e200

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 7.00000000000000013e200 < z < 8.2e223

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 31.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 31.6%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 33.6%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in b around inf 71.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a + \frac{z \cdot \left(1 - \log t\right)}{b}\right) - 0.5\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 71.8%

         \[\leadsto b \cdot \color{blue}{\left(a + \left(\frac{z \cdot \left(1 - \log t\right)}{b} - 0.5\right)\right)} \]

      2. associate-/l* 71.4%

         \[\leadsto b \cdot \left(a + \left(\color{blue}{z \cdot \frac{1 - \log t}{b}} - 0.5\right)\right) \]

   9. Simplified 71.4%

      \[\leadsto \color{blue}{b \cdot \left(a + \left(z \cdot \frac{1 - \log t}{b} - 0.5\right)\right)} \]

   10. Taylor expanded in z around inf 43.0%

       \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{1}{b} - \frac{\log t}{b}\right)\right)} \]
   11. Step-by-step derivation

       1. div-sub 43.0%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\frac{1 - \log t}{b}}\right) \]

       2. associate-*r* 80.6%

          \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \frac{1 - \log t}{b}} \]

   12. Simplified 80.6%

       \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \frac{1 - \log t}{b}} \]

   if 8.2e223 < z < 5.8000000000000004e247

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.7%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 78.9%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]

   if 5.8000000000000004e247 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.5%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.5%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 87.6%

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

   6. Taylor expanded in y around 0 81.5%

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

      1. distribute-rgt-out-- 87.8%

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

      2. *-un-lft-identity 87.8%

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

      3. *-commutative 87.8%

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

      4. sub-neg 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

   8. Applied egg-rr 81.7%

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

      1. distribute-rgt-neg-out 81.7%

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

      2. unsub-neg 81.7%

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

   10. Applied egg-rr 81.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+200}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+223}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \frac{1 - \log t}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+247}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq 1.18 \cdot 10^{+201}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+247}:\\ \;\;\;\;y + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - z \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= z 1.18e+201)
     (+ (+ x y) t_1)
     (if (<= z 1.66e+226)
       (* z (- 1.0 (log t)))
       (if (<= z 4.7e+247) (+ y t_1) (+ x (- z (* z (log t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 1.18e+201) {
		tmp = (x + y) + t_1;
	} else if (z <= 1.66e+226) {
		tmp = z * (1.0 - log(t));
	} else if (z <= 4.7e+247) {
		tmp = y + t_1;
	} else {
		tmp = x + (z - (z * log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (z <= 1.18d+201) then
        tmp = (x + y) + t_1
    else if (z <= 1.66d+226) then
        tmp = z * (1.0d0 - log(t))
    else if (z <= 4.7d+247) then
        tmp = y + t_1
    else
        tmp = x + (z - (z * log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 1.18e+201) {
		tmp = (x + y) + t_1;
	} else if (z <= 1.66e+226) {
		tmp = z * (1.0 - Math.log(t));
	} else if (z <= 4.7e+247) {
		tmp = y + t_1;
	} else {
		tmp = x + (z - (z * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if z <= 1.18e+201:
		tmp = (x + y) + t_1
	elif z <= 1.66e+226:
		tmp = z * (1.0 - math.log(t))
	elif z <= 4.7e+247:
		tmp = y + t_1
	else:
		tmp = x + (z - (z * math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= 1.18e+201)
		tmp = Float64(Float64(x + y) + t_1);
	elseif (z <= 1.66e+226)
		tmp = Float64(z * Float64(1.0 - log(t)));
	elseif (z <= 4.7e+247)
		tmp = Float64(y + t_1);
	else
		tmp = Float64(x + Float64(z - Float64(z * log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= 1.18e+201)
		tmp = (x + y) + t_1;
	elseif (z <= 1.66e+226)
		tmp = z * (1.0 - log(t));
	elseif (z <= 4.7e+247)
		tmp = y + t_1;
	else
		tmp = x + (z - (z * log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1.18e+201], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 1.66e+226], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+247], N[(y + t$95$1), $MachinePrecision], N[(x + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 1.18e201

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 1.18e201 < z < 1.6600000000000001e226

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 29.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 29.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 29.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 29.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 29.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 29.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 31.1%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in a around 0 73.7%

      \[\leadsto \color{blue}{-0.5 \cdot b + z \cdot \left(1 - \log t\right)} \]

   8. Taylor expanded in b around 0 73.7%

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

   if 1.6600000000000001e226 < z < 4.7000000000000002e247

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 100.0%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 97.4%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]

   if 4.7000000000000002e247 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.5%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.5%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 87.6%

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

   6. Taylor expanded in y around 0 81.5%

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

      1. distribute-rgt-out-- 87.8%

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

      2. *-un-lft-identity 87.8%

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

      3. *-commutative 87.8%

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

      4. sub-neg 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

   8. Applied egg-rr 81.7%

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

      1. distribute-rgt-neg-out 81.7%

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

      2. unsub-neg 81.7%

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

   10. Applied egg-rr 81.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.18 \cdot 10^{+201}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+247}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq 2.2 \cdot 10^{+198}:\\ \;\;\;\;\left(x + y\right) + t\_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+248}:\\ \;\;\;\;y + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))) (t_2 (* b (- a 0.5))))
   (if (<= z 2.2e+198)
     (+ (+ x y) t_2)
     (if (<= z 2.4e+227) t_1 (if (<= z 2.4e+248) (+ y t_2) (+ t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double t_2 = b * (a - 0.5);
	double tmp;
	if (z <= 2.2e+198) {
		tmp = (x + y) + t_2;
	} else if (z <= 2.4e+227) {
		tmp = t_1;
	} else if (z <= 2.4e+248) {
		tmp = y + t_2;
	} else {
		tmp = t_1 + 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    t_2 = b * (a - 0.5d0)
    if (z <= 2.2d+198) then
        tmp = (x + y) + t_2
    else if (z <= 2.4d+227) then
        tmp = t_1
    else if (z <= 2.4d+248) then
        tmp = y + t_2
    else
        tmp = t_1 + 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 t_1 = z * (1.0 - Math.log(t));
	double t_2 = b * (a - 0.5);
	double tmp;
	if (z <= 2.2e+198) {
		tmp = (x + y) + t_2;
	} else if (z <= 2.4e+227) {
		tmp = t_1;
	} else if (z <= 2.4e+248) {
		tmp = y + t_2;
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	t_2 = b * (a - 0.5)
	tmp = 0
	if z <= 2.2e+198:
		tmp = (x + y) + t_2
	elif z <= 2.4e+227:
		tmp = t_1
	elif z <= 2.4e+248:
		tmp = y + t_2
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= 2.2e+198)
		tmp = Float64(Float64(x + y) + t_2);
	elseif (z <= 2.4e+227)
		tmp = t_1;
	elseif (z <= 2.4e+248)
		tmp = Float64(y + t_2);
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= 2.2e+198)
		tmp = (x + y) + t_2;
	elseif (z <= 2.4e+227)
		tmp = t_1;
	elseif (z <= 2.4e+248)
		tmp = y + t_2;
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 2.2e+198], N[(N[(x + y), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[z, 2.4e+227], t$95$1, If[LessEqual[z, 2.4e+248], N[(y + t$95$2), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 2.2e198

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 2.2e198 < z < 2.3999999999999998e227

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 29.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 29.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 29.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 29.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 29.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 29.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 31.1%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in a around 0 73.7%

      \[\leadsto \color{blue}{-0.5 \cdot b + z \cdot \left(1 - \log t\right)} \]

   8. Taylor expanded in b around 0 73.7%

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

   if 2.3999999999999998e227 < z < 2.4e248

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 100.0%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 97.4%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]

   if 2.4e248 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.5%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.5%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 87.6%

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

   6. Taylor expanded in y around 0 81.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+198}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+227}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+248}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+242} \lor \neg \left(z \leq 1.6 \cdot 10^{+46}\right):\\ \;\;\;\;t\_1 + \left(z - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= z -7.5e+242) (not (<= z 1.6e+46)))
     (+ t_1 (- z (* z (log t))))
     (+ (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((z <= -7.5e+242) || !(z <= 1.6e+46)) {
		tmp = t_1 + (z - (z * log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((z <= (-7.5d+242)) .or. (.not. (z <= 1.6d+46))) then
        tmp = t_1 + (z - (z * log(t)))
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((z <= -7.5e+242) || !(z <= 1.6e+46)) {
		tmp = t_1 + (z - (z * Math.log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (z <= -7.5e+242) or not (z <= 1.6e+46):
		tmp = t_1 + (z - (z * math.log(t)))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((z <= -7.5e+242) || !(z <= 1.6e+46))
		tmp = Float64(t_1 + Float64(z - Float64(z * log(t))));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((z <= -7.5e+242) || ~((z <= 1.6e+46)))
		tmp = t_1 + (z - (z * log(t)));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -7.5e+242], N[Not[LessEqual[z, 1.6e+46]], $MachinePrecision]], N[(t$95$1 + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999961e242 or 1.5999999999999999e46 < z

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.6%

      \[\leadsto \color{blue}{\left(\left(x + z\right) - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in x around 0 89.0%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   if -7.49999999999999961e242 < z < 1.5999999999999999e46

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.1%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+242} \lor \neg \left(z \leq 1.6 \cdot 10^{+46}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq 1.08 \cdot 10^{+201}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+233} \lor \neg \left(z \leq 4.8 \cdot 10^{+247}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= z 1.08e+201)
     (+ (+ x y) t_1)
     (if (or (<= z 4.6e+233) (not (<= z 4.8e+247)))
       (* z (- 1.0 (log t)))
       (+ y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 1.08e+201) {
		tmp = (x + y) + t_1;
	} else if ((z <= 4.6e+233) || !(z <= 4.8e+247)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (z <= 1.08d+201) then
        tmp = (x + y) + t_1
    else if ((z <= 4.6d+233) .or. (.not. (z <= 4.8d+247))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 1.08e+201) {
		tmp = (x + y) + t_1;
	} else if ((z <= 4.6e+233) || !(z <= 4.8e+247)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if z <= 1.08e+201:
		tmp = (x + y) + t_1
	elif (z <= 4.6e+233) or not (z <= 4.8e+247):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= 1.08e+201)
		tmp = Float64(Float64(x + y) + t_1);
	elseif ((z <= 4.6e+233) || !(z <= 4.8e+247))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= 1.08e+201)
		tmp = (x + y) + t_1;
	elseif ((z <= 4.6e+233) || ~((z <= 4.8e+247)))
		tmp = z * (1.0 - log(t));
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1.08e+201], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[z, 4.6e+233], N[Not[LessEqual[z, 4.8e+247]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.08000000000000006e201

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 1.08000000000000006e201 < z < 4.60000000000000001e233 or 4.8e247 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 43.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 43.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 43.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 43.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 43.2%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 45.5%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 45.5%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 45.5%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 45.4%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 42.4%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in a around 0 79.8%

      \[\leadsto \color{blue}{-0.5 \cdot b + z \cdot \left(1 - \log t\right)} \]

   8. Taylor expanded in b around 0 76.5%

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

   if 4.60000000000000001e233 < z < 4.8e247

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 100.0%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 97.4%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.08 \cdot 10^{+201}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+233} \lor \neg \left(z \leq 4.8 \cdot 10^{+247}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq 3.7 \cdot 10^{+199}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+235}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+248}:\\ \;\;\;\;y + t\_1\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= z 3.7e+199)
     (+ (+ x y) t_1)
     (if (<= z 9.5e+235)
       (* z (- 1.0 (log t)))
       (if (<= z 1.12e+248) (+ y t_1) (- z (* z (log t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 3.7e+199) {
		tmp = (x + y) + t_1;
	} else if (z <= 9.5e+235) {
		tmp = z * (1.0 - log(t));
	} else if (z <= 1.12e+248) {
		tmp = y + t_1;
	} else {
		tmp = z - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (z <= 3.7d+199) then
        tmp = (x + y) + t_1
    else if (z <= 9.5d+235) then
        tmp = z * (1.0d0 - log(t))
    else if (z <= 1.12d+248) then
        tmp = y + t_1
    else
        tmp = z - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= 3.7e+199) {
		tmp = (x + y) + t_1;
	} else if (z <= 9.5e+235) {
		tmp = z * (1.0 - Math.log(t));
	} else if (z <= 1.12e+248) {
		tmp = y + t_1;
	} else {
		tmp = z - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if z <= 3.7e+199:
		tmp = (x + y) + t_1
	elif z <= 9.5e+235:
		tmp = z * (1.0 - math.log(t))
	elif z <= 1.12e+248:
		tmp = y + t_1
	else:
		tmp = z - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= 3.7e+199)
		tmp = Float64(Float64(x + y) + t_1);
	elseif (z <= 9.5e+235)
		tmp = Float64(z * Float64(1.0 - log(t)));
	elseif (z <= 1.12e+248)
		tmp = Float64(y + t_1);
	else
		tmp = Float64(z - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= 3.7e+199)
		tmp = (x + y) + t_1;
	elseif (z <= 9.5e+235)
		tmp = z * (1.0 - log(t));
	elseif (z <= 1.12e+248)
		tmp = y + t_1;
	else
		tmp = z - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3.7e+199], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 9.5e+235], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+248], N[(y + t$95$1), $MachinePrecision], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 3.70000000000000021e199

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 3.70000000000000021e199 < z < 9.49999999999999966e235

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 29.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 29.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 29.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 29.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 29.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 29.9%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 29.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 31.1%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in a around 0 73.7%

      \[\leadsto \color{blue}{-0.5 \cdot b + z \cdot \left(1 - \log t\right)} \]

   8. Taylor expanded in b around 0 73.7%

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

   if 9.49999999999999966e235 < z < 1.11999999999999992e248

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 100.0%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 97.4%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]

   if 1.11999999999999992e248 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.6%

      \[\leadsto \color{blue}{\left(\left(x + z\right) - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in x around 0 90.5%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around 0 78.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+199}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+235}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+248}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 10^{+115}:\\ \;\;\;\;t\_1 + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) 1e+115) (+ t_1 (- (+ z x) (* z (log t)))) (+ (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e+115) {
		tmp = t_1 + ((z + x) - (z * log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= 1d+115) then
        tmp = t_1 + ((z + x) - (z * log(t)))
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e+115) {
		tmp = t_1 + ((z + x) - (z * Math.log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= 1e+115:
		tmp = t_1 + ((z + x) - (z * math.log(t)))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= 1e+115)
		tmp = Float64(t_1 + Float64(Float64(z + x) - Float64(z * log(t))));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= 1e+115)
		tmp = t_1 + ((z + x) - (z * log(t)));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 1e+115], N[(t$95$1 + N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1e115

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.8%

      \[\leadsto \color{blue}{\left(\left(x + z\right) - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   if 1e115 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.8%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+115}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.02 \cdot 10^{+201}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+222}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \frac{1 - \log t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(z - z \cdot \log t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.02e+201)
   (+ (+ x y) (* b (- a 0.5)))
   (if (<= z 1.9e+222)
     (* (* z b) (/ (- 1.0 (log t)) b))
     (+ x (+ y (- z (* z (log t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.02e+201) {
		tmp = (x + y) + (b * (a - 0.5));
	} else if (z <= 1.9e+222) {
		tmp = (z * b) * ((1.0 - log(t)) / b);
	} else {
		tmp = x + (y + (z - (z * log(t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.02d+201) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else if (z <= 1.9d+222) then
        tmp = (z * b) * ((1.0d0 - log(t)) / b)
    else
        tmp = x + (y + (z - (z * log(t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.02e+201) {
		tmp = (x + y) + (b * (a - 0.5));
	} else if (z <= 1.9e+222) {
		tmp = (z * b) * ((1.0 - Math.log(t)) / b);
	} else {
		tmp = x + (y + (z - (z * Math.log(t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.02e+201:
		tmp = (x + y) + (b * (a - 0.5))
	elif z <= 1.9e+222:
		tmp = (z * b) * ((1.0 - math.log(t)) / b)
	else:
		tmp = x + (y + (z - (z * math.log(t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.02e+201)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	elseif (z <= 1.9e+222)
		tmp = Float64(Float64(z * b) * Float64(Float64(1.0 - log(t)) / b));
	else
		tmp = Float64(x + Float64(y + Float64(z - Float64(z * log(t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.02e+201)
		tmp = (x + y) + (b * (a - 0.5));
	elseif (z <= 1.9e+222)
		tmp = (z * b) * ((1.0 - log(t)) / b);
	else
		tmp = x + (y + (z - (z * log(t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.02e+201], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+222], N[(N[(z * b), $MachinePrecision] * N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.02e201

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 1.02e201 < z < 1.90000000000000009e222

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 31.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 31.6%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 33.6%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in b around inf 71.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a + \frac{z \cdot \left(1 - \log t\right)}{b}\right) - 0.5\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 71.8%

         \[\leadsto b \cdot \color{blue}{\left(a + \left(\frac{z \cdot \left(1 - \log t\right)}{b} - 0.5\right)\right)} \]

      2. associate-/l* 71.4%

         \[\leadsto b \cdot \left(a + \left(\color{blue}{z \cdot \frac{1 - \log t}{b}} - 0.5\right)\right) \]

   9. Simplified 71.4%

      \[\leadsto \color{blue}{b \cdot \left(a + \left(z \cdot \frac{1 - \log t}{b} - 0.5\right)\right)} \]

   10. Taylor expanded in z around inf 43.0%

       \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{1}{b} - \frac{\log t}{b}\right)\right)} \]
   11. Step-by-step derivation

       1. div-sub 43.0%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\frac{1 - \log t}{b}}\right) \]

       2. associate-*r* 80.6%

          \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \frac{1 - \log t}{b}} \]

   12. Simplified 80.6%

       \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \frac{1 - \log t}{b}} \]

   if 1.90000000000000009e222 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.5%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.5%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.5%

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

      1. distribute-rgt-out-- 81.6%

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

      2. *-un-lft-identity 81.6%

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

      3. *-commutative 81.6%

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

      4. sub-neg 81.6%

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

      5. distribute-rgt-neg-in 81.6%

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

   7. Applied egg-rr 81.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.02 \cdot 10^{+201}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+222}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \frac{1 - \log t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(z - z \cdot \log t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq 4.9 \cdot 10^{+200}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+222}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \frac{t\_1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot t\_1 + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z 4.9e+200)
     (+ (+ x y) (* b (- a 0.5)))
     (if (<= z 1.9e+222) (* (* z b) (/ t_1 b)) (+ x (+ (* z t_1) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if (z <= 4.9e+200) {
		tmp = (x + y) + (b * (a - 0.5));
	} else if (z <= 1.9e+222) {
		tmp = (z * b) * (t_1 / b);
	} else {
		tmp = x + ((z * t_1) + 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) :: tmp
    t_1 = 1.0d0 - log(t)
    if (z <= 4.9d+200) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else if (z <= 1.9d+222) then
        tmp = (z * b) * (t_1 / b)
    else
        tmp = x + ((z * t_1) + 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 = 1.0 - Math.log(t);
	double tmp;
	if (z <= 4.9e+200) {
		tmp = (x + y) + (b * (a - 0.5));
	} else if (z <= 1.9e+222) {
		tmp = (z * b) * (t_1 / b);
	} else {
		tmp = x + ((z * t_1) + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 - math.log(t)
	tmp = 0
	if z <= 4.9e+200:
		tmp = (x + y) + (b * (a - 0.5))
	elif z <= 1.9e+222:
		tmp = (z * b) * (t_1 / b)
	else:
		tmp = x + ((z * t_1) + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (z <= 4.9e+200)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	elseif (z <= 1.9e+222)
		tmp = Float64(Float64(z * b) * Float64(t_1 / b));
	else
		tmp = Float64(x + Float64(Float64(z * t_1) + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 - log(t);
	tmp = 0.0;
	if (z <= 4.9e+200)
		tmp = (x + y) + (b * (a - 0.5));
	elseif (z <= 1.9e+222)
		tmp = (z * b) * (t_1 / b);
	else
		tmp = x + ((z * t_1) + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 4.9e+200], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+222], N[(N[(z * b), $MachinePrecision] * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t$95$1), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < 4.89999999999999982e200

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

   if 4.89999999999999982e200 < z < 1.90000000000000009e222

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) - \frac{z \cdot \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. sub-neg 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \left(\frac{x}{y} + \frac{z}{y}\right)\right) + \left(-\frac{z \cdot \log t}{y}\right)\right)} + \left(a - 0.5\right) \cdot b \]

      2. associate-+r+ 31.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(\left(1 + \frac{x}{y}\right) + \frac{z}{y}\right)} + \left(-\frac{z \cdot \log t}{y}\right)\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(1 + \frac{x}{y}\right) + \left(\frac{z}{y} + \left(-\frac{z \cdot \log t}{y}\right)\right)\right)} + \left(a - 0.5\right) \cdot b \]

      4. sub-neg 31.6%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\left(\frac{z}{y} - \frac{z \cdot \log t}{y}\right)}\right) + \left(a - 0.5\right) \cdot b \]

      5. div-sub 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{\frac{z - z \cdot \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

      6. *-rgt-identity 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot 1} - z \cdot \log t}{y}\right) + \left(a - 0.5\right) \cdot b \]

      7. distribute-lft-out-- 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \frac{\color{blue}{z \cdot \left(1 - \log t\right)}}{y}\right) + \left(a - 0.5\right) \cdot b \]

      8. associate-/l* 32.3%

         \[\leadsto y \cdot \left(\left(1 + \frac{x}{y}\right) + \color{blue}{z \cdot \frac{1 - \log t}{y}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) + z \cdot \frac{1 - \log t}{y}\right)} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in z around -inf 33.6%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot \left(1 - \log t\right)}{y}} + \left(a - 0.5\right) \cdot b \]

   7. Taylor expanded in b around inf 71.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a + \frac{z \cdot \left(1 - \log t\right)}{b}\right) - 0.5\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 71.8%

         \[\leadsto b \cdot \color{blue}{\left(a + \left(\frac{z \cdot \left(1 - \log t\right)}{b} - 0.5\right)\right)} \]

      2. associate-/l* 71.4%

         \[\leadsto b \cdot \left(a + \left(\color{blue}{z \cdot \frac{1 - \log t}{b}} - 0.5\right)\right) \]

   9. Simplified 71.4%

      \[\leadsto \color{blue}{b \cdot \left(a + \left(z \cdot \frac{1 - \log t}{b} - 0.5\right)\right)} \]

   10. Taylor expanded in z around inf 43.0%

       \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{1}{b} - \frac{\log t}{b}\right)\right)} \]
   11. Step-by-step derivation

       1. div-sub 43.0%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\frac{1 - \log t}{b}}\right) \]

       2. associate-*r* 80.6%

          \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \frac{1 - \log t}{b}} \]

   12. Simplified 80.6%

       \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \frac{1 - \log t}{b}} \]

   if 1.90000000000000009e222 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.5%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.5%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.5%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.9 \cdot 10^{+200}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+222}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \frac{1 - \log t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + b \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ z (- (+ x y) (* z (log t)))) (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (z + ((x + y) - (z * log(t)))) + (b * (a - 0.5));
}

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 = (z + ((x + y) - (z * log(t)))) + (b * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (z + ((x + y) - (z * Math.log(t)))) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return (z + ((x + y) - (z * math.log(t)))) + (b * (a - 0.5))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(z + Float64(Float64(x + y) - Float64(z * log(t)))) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (z + ((x + y) - (z * log(t)))) + (b * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(z + N[(N[(x + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. associate--l+ 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

5. Final simplification 99.9%

   \[\leadsto \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + b \cdot \left(a - 0.5\right) \]
6. Add Preprocessing

Alternative 13: 51.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 2.32 \cdot 10^{+64}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 10^{+241}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+247}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+279}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e+249)
   (* -0.5 b)
   (if (<= b -1.32e+127)
     (* a b)
     (if (<= b 2.32e+64)
       (+ x y)
       (if (<= b 1e+241)
         (* a b)
         (if (<= b 3e+247) x (if (<= b 2.9e+279) (* -0.5 b) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+249) {
		tmp = -0.5 * b;
	} else if (b <= -1.32e+127) {
		tmp = a * b;
	} else if (b <= 2.32e+64) {
		tmp = x + y;
	} else if (b <= 1e+241) {
		tmp = a * b;
	} else if (b <= 3e+247) {
		tmp = x;
	} else if (b <= 2.9e+279) {
		tmp = -0.5 * b;
	} else {
		tmp = a * 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 <= (-2.3d+249)) then
        tmp = (-0.5d0) * b
    else if (b <= (-1.32d+127)) then
        tmp = a * b
    else if (b <= 2.32d+64) then
        tmp = x + y
    else if (b <= 1d+241) then
        tmp = a * b
    else if (b <= 3d+247) then
        tmp = x
    else if (b <= 2.9d+279) then
        tmp = (-0.5d0) * b
    else
        tmp = a * 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 <= -2.3e+249) {
		tmp = -0.5 * b;
	} else if (b <= -1.32e+127) {
		tmp = a * b;
	} else if (b <= 2.32e+64) {
		tmp = x + y;
	} else if (b <= 1e+241) {
		tmp = a * b;
	} else if (b <= 3e+247) {
		tmp = x;
	} else if (b <= 2.9e+279) {
		tmp = -0.5 * b;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e+249:
		tmp = -0.5 * b
	elif b <= -1.32e+127:
		tmp = a * b
	elif b <= 2.32e+64:
		tmp = x + y
	elif b <= 1e+241:
		tmp = a * b
	elif b <= 3e+247:
		tmp = x
	elif b <= 2.9e+279:
		tmp = -0.5 * b
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e+249)
		tmp = Float64(-0.5 * b);
	elseif (b <= -1.32e+127)
		tmp = Float64(a * b);
	elseif (b <= 2.32e+64)
		tmp = Float64(x + y);
	elseif (b <= 1e+241)
		tmp = Float64(a * b);
	elseif (b <= 3e+247)
		tmp = x;
	elseif (b <= 2.9e+279)
		tmp = Float64(-0.5 * b);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.3e+249)
		tmp = -0.5 * b;
	elseif (b <= -1.32e+127)
		tmp = a * b;
	elseif (b <= 2.32e+64)
		tmp = x + y;
	elseif (b <= 1e+241)
		tmp = a * b;
	elseif (b <= 3e+247)
		tmp = x;
	elseif (b <= 2.9e+279)
		tmp = -0.5 * b;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e+249], N[(-0.5 * b), $MachinePrecision], If[LessEqual[b, -1.32e+127], N[(a * b), $MachinePrecision], If[LessEqual[b, 2.32e+64], N[(x + y), $MachinePrecision], If[LessEqual[b, 1e+241], N[(a * b), $MachinePrecision], If[LessEqual[b, 3e+247], x, If[LessEqual[b, 2.9e+279], N[(-0.5 * b), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.2999999999999998e249 or 3e247 < b < 2.89999999999999975e279

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 100.0%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 89.0%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around 0 63.4%

      \[\leadsto \color{blue}{-0.5 \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{b \cdot -0.5} \]

   8. Simplified 63.4%

      \[\leadsto \color{blue}{b \cdot -0.5} \]

   if -2.2999999999999998e249 < b < -1.32000000000000005e127 or 2.3199999999999999e64 < b < 1.0000000000000001e241 or 2.89999999999999975e279 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 50.9%

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

      1. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -1.32000000000000005e127 < b < 2.3199999999999999e64

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 76.9%

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

   6. Taylor expanded in y around inf 54.0%

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

   if 1.0000000000000001e241 < b < 3e247

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.7%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 33.7%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 2.32 \cdot 10^{+64}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 10^{+241}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+247}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+279}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+40}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-47}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-197}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.06e+40)
   (* a b)
   (if (<= a -1e-47)
     (* -0.5 b)
     (if (<= a -7.2e-102)
       x
       (if (<= a 1.25e-197)
         (* -0.5 b)
         (if (<= a 1.02e-95) y (if (<= a 2.5e-39) x (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.06e+40) {
		tmp = a * b;
	} else if (a <= -1e-47) {
		tmp = -0.5 * b;
	} else if (a <= -7.2e-102) {
		tmp = x;
	} else if (a <= 1.25e-197) {
		tmp = -0.5 * b;
	} else if (a <= 1.02e-95) {
		tmp = y;
	} else if (a <= 2.5e-39) {
		tmp = x;
	} else {
		tmp = a * 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 (a <= (-1.06d+40)) then
        tmp = a * b
    else if (a <= (-1d-47)) then
        tmp = (-0.5d0) * b
    else if (a <= (-7.2d-102)) then
        tmp = x
    else if (a <= 1.25d-197) then
        tmp = (-0.5d0) * b
    else if (a <= 1.02d-95) then
        tmp = y
    else if (a <= 2.5d-39) then
        tmp = x
    else
        tmp = a * 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 (a <= -1.06e+40) {
		tmp = a * b;
	} else if (a <= -1e-47) {
		tmp = -0.5 * b;
	} else if (a <= -7.2e-102) {
		tmp = x;
	} else if (a <= 1.25e-197) {
		tmp = -0.5 * b;
	} else if (a <= 1.02e-95) {
		tmp = y;
	} else if (a <= 2.5e-39) {
		tmp = x;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.06e+40:
		tmp = a * b
	elif a <= -1e-47:
		tmp = -0.5 * b
	elif a <= -7.2e-102:
		tmp = x
	elif a <= 1.25e-197:
		tmp = -0.5 * b
	elif a <= 1.02e-95:
		tmp = y
	elif a <= 2.5e-39:
		tmp = x
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.06e+40)
		tmp = Float64(a * b);
	elseif (a <= -1e-47)
		tmp = Float64(-0.5 * b);
	elseif (a <= -7.2e-102)
		tmp = x;
	elseif (a <= 1.25e-197)
		tmp = Float64(-0.5 * b);
	elseif (a <= 1.02e-95)
		tmp = y;
	elseif (a <= 2.5e-39)
		tmp = x;
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.06e+40)
		tmp = a * b;
	elseif (a <= -1e-47)
		tmp = -0.5 * b;
	elseif (a <= -7.2e-102)
		tmp = x;
	elseif (a <= 1.25e-197)
		tmp = -0.5 * b;
	elseif (a <= 1.02e-95)
		tmp = y;
	elseif (a <= 2.5e-39)
		tmp = x;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.06e+40], N[(a * b), $MachinePrecision], If[LessEqual[a, -1e-47], N[(-0.5 * b), $MachinePrecision], If[LessEqual[a, -7.2e-102], x, If[LessEqual[a, 1.25e-197], N[(-0.5 * b), $MachinePrecision], If[LessEqual[a, 1.02e-95], y, If[LessEqual[a, 2.5e-39], x, N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.05999999999999996e40 or 2.4999999999999999e-39 < a

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -1.05999999999999996e40 < a < -9.9999999999999997e-48 or -7.2e-102 < a < 1.2500000000000001e-197

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 46.7%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around 0 43.5%

      \[\leadsto \color{blue}{-0.5 \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto \color{blue}{b \cdot -0.5} \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{b \cdot -0.5} \]

   if -9.9999999999999997e-48 < a < -7.2e-102 or 1.01999999999999995e-95 < a < 2.4999999999999999e-39

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.8%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.7%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 19.1%

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

   if 1.2500000000000001e-197 < a < 1.01999999999999995e-95

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 20.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+40}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-47}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-197}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.5% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot b\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a b))) (t_2 (* b (- a 0.5))))
   (if (<= b -7.8e+64)
     t_2
     (if (<= b -3.5e-12)
       t_1
       (if (<= b 4.1e-96) (+ x y) (if (<= b 4.1e+98) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * b);
	double t_2 = b * (a - 0.5);
	double tmp;
	if (b <= -7.8e+64) {
		tmp = t_2;
	} else if (b <= -3.5e-12) {
		tmp = t_1;
	} else if (b <= 4.1e-96) {
		tmp = x + y;
	} else if (b <= 4.1e+98) {
		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 * b)
    t_2 = b * (a - 0.5d0)
    if (b <= (-7.8d+64)) then
        tmp = t_2
    else if (b <= (-3.5d-12)) then
        tmp = t_1
    else if (b <= 4.1d-96) then
        tmp = x + y
    else if (b <= 4.1d+98) 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 * b);
	double t_2 = b * (a - 0.5);
	double tmp;
	if (b <= -7.8e+64) {
		tmp = t_2;
	} else if (b <= -3.5e-12) {
		tmp = t_1;
	} else if (b <= 4.1e-96) {
		tmp = x + y;
	} else if (b <= 4.1e+98) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * b)
	t_2 = b * (a - 0.5)
	tmp = 0
	if b <= -7.8e+64:
		tmp = t_2
	elif b <= -3.5e-12:
		tmp = t_1
	elif b <= 4.1e-96:
		tmp = x + y
	elif b <= 4.1e+98:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * b))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (b <= -7.8e+64)
		tmp = t_2;
	elseif (b <= -3.5e-12)
		tmp = t_1;
	elseif (b <= 4.1e-96)
		tmp = Float64(x + y);
	elseif (b <= 4.1e+98)
		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 * b);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if (b <= -7.8e+64)
		tmp = t_2;
	elseif (b <= -3.5e-12)
		tmp = t_1;
	elseif (b <= 4.1e-96)
		tmp = x + y;
	elseif (b <= 4.1e+98)
		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 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+64], t$95$2, If[LessEqual[b, -3.5e-12], t$95$1, If[LessEqual[b, 4.1e-96], N[(x + y), $MachinePrecision], If[LessEqual[b, 4.1e+98], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.7999999999999996e64 or 4.1e98 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 74.8%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   if -7.7999999999999996e64 < b < -3.5e-12 or 4.10000000000000024e-96 < b < 4.1e98

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 54.6%

      \[\leadsto \color{blue}{x} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in x around inf 49.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{b \cdot \left(a - 0.5\right)}{x}\right)} \]

   7. Taylor expanded in a around inf 46.7%

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

   8. Taylor expanded in x around 0 50.2%

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

      1. *-commutative 50.2%

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

   10. Simplified 50.2%

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

   if -3.5e-12 < b < 4.10000000000000024e-96

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 87.4%

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

   6. Taylor expanded in y around inf 63.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+98}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.1% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1 \cdot 10^{+79} \lor \neg \left(a - 0.5 \leq -0.5\right):\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- a 0.5) -1e+79) (not (<= (- a 0.5) -0.5)))
   (+ x (* a b))
   (+ y (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -1e+79) || !((a - 0.5) <= -0.5)) {
		tmp = x + (a * b);
	} else {
		tmp = y + (-0.5 * 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 (((a - 0.5d0) <= (-1d+79)) .or. (.not. ((a - 0.5d0) <= (-0.5d0)))) then
        tmp = x + (a * b)
    else
        tmp = y + ((-0.5d0) * 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 (((a - 0.5) <= -1e+79) || !((a - 0.5) <= -0.5)) {
		tmp = x + (a * b);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a - 0.5) <= -1e+79) or not ((a - 0.5) <= -0.5):
		tmp = x + (a * b)
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -1e+79) || !(Float64(a - 0.5) <= -0.5))
		tmp = Float64(x + Float64(a * b));
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a - 0.5) <= -1e+79) || ~(((a - 0.5) <= -0.5)))
		tmp = x + (a * b);
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -1e+79], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.5]], $MachinePrecision]], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -9.99999999999999967e78 or -0.5 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 70.3%

      \[\leadsto \color{blue}{x} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in x around inf 62.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{b \cdot \left(a - 0.5\right)}{x}\right)} \]

   7. Taylor expanded in a around inf 63.0%

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

   8. Taylor expanded in x around 0 70.4%

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

      1. *-commutative 70.4%

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

   10. Simplified 70.4%

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

   if -9.99999999999999967e78 < (-.f64 a #s(literal 1/2 binary64)) < -0.5

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 62.6%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in a around 0 60.0%

      \[\leadsto y + \color{blue}{-0.5 \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 97.2%

         \[\leadsto \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + \color{blue}{b \cdot -0.5} \]

   8. Simplified 60.0%

      \[\leadsto y + \color{blue}{b \cdot -0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1 \cdot 10^{+79} \lor \neg \left(a - 0.5 \leq -0.5\right):\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.4% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+38} \lor \neg \left(b \leq 5.5 \cdot 10^{-25}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.1e+38) (not (<= b 5.5e-25))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.1e+38) || !(b <= 5.5e-25)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + 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) :: tmp
    if ((b <= (-4.1d+38)) .or. (.not. (b <= 5.5d-25))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + 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 tmp;
	if ((b <= -4.1e+38) || !(b <= 5.5e-25)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.1e+38) or not (b <= 5.5e-25):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.1e+38) || !(b <= 5.5e-25))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.1e+38) || ~((b <= 5.5e-25)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.1e+38], N[Not[LessEqual[b, 5.5e-25]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.1000000000000003e38 or 5.50000000000000004e-25 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 67.8%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   if -4.1000000000000003e38 < b < 5.50000000000000004e-25

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 86.8%

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

   6. Taylor expanded in y around inf 61.9%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+38} \lor \neg \left(b \leq 5.5 \cdot 10^{-25}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 58.7% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -400000:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) -400000.0) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -400000.0) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-400000.0d0)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -400000.0) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -400000.0:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -400000.0)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -400000.0)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -400000.0], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4e5

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 56.8%

      \[\leadsto \color{blue}{x} + \left(a - 0.5\right) \cdot b \]

   if -4e5 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 66.8%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -400000:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+105}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e+105) (+ x (* b (- a 0.5))) (+ y (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e+105) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (-0.5 * 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 ((x + y) <= 1d+105) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + ((-0.5d0) * 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 ((x + y) <= 1e+105) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e+105:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e+105)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 1e+105)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 1e+105], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999994e104

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 62.7%

      \[\leadsto \color{blue}{x} + \left(a - 0.5\right) \cdot b \]

   if 9.9999999999999994e104 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 60.4%

      \[\leadsto \color{blue}{y} + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in a around 0 33.2%

      \[\leadsto y + \color{blue}{-0.5 \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 73.0%

         \[\leadsto \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) + \color{blue}{b \cdot -0.5} \]

   8. Simplified 33.2%

      \[\leadsto y + \color{blue}{b \cdot -0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+105}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.4% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-80}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+123) x (if (<= x -2.9e-80) (* -0.5 b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+123) {
		tmp = x;
	} else if (x <= -2.9e-80) {
		tmp = -0.5 * b;
	} else {
		tmp = 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) :: tmp
    if (x <= (-2.5d+123)) then
        tmp = x
    else if (x <= (-2.9d-80)) then
        tmp = (-0.5d0) * b
    else
        tmp = 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 tmp;
	if (x <= -2.5e+123) {
		tmp = x;
	} else if (x <= -2.9e-80) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+123:
		tmp = x
	elif x <= -2.9e-80:
		tmp = -0.5 * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+123)
		tmp = x;
	elseif (x <= -2.9e-80)
		tmp = Float64(-0.5 * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.5e+123)
		tmp = x;
	elseif (x <= -2.9e-80)
		tmp = -0.5 * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+123], x, If[LessEqual[x, -2.9e-80], N[(-0.5 * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999987e123

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 100.0%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 50.3%

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

   if -2.49999999999999987e123 < x < -2.89999999999999998e-80

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.8%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 55.4%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around 0 26.3%

      \[\leadsto \color{blue}{-0.5 \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 26.3%

         \[\leadsto \color{blue}{b \cdot -0.5} \]

   8. Simplified 26.3%

      \[\leadsto \color{blue}{b \cdot -0.5} \]

   if -2.89999999999999998e-80 < x

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 24.1%

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

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-80}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 79.0% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) + b \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (+ x y) (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + (b * (a - 0.5));
}

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) + (b * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return (x + y) + (b * (a - 0.5))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + y) + (b * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in z around 0 82.4%

   \[\leadsto \color{blue}{\left(x + y\right)} + \left(a - 0.5\right) \cdot b \]

4. Final simplification 82.4%

   \[\leadsto \left(x + y\right) + b \cdot \left(a - 0.5\right) \]
5. Add Preprocessing

Alternative 22: 27.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -3.6e+155) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+155) {
		tmp = x;
	} else {
		tmp = 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) :: tmp
    if (x <= (-3.6d+155)) then
        tmp = x
    else
        tmp = 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 tmp;
	if (x <= -3.6e+155) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.6e+155:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.6e+155)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.6e+155)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.6e+155], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -3.60000000000000007e155

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 100.0%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 51.3%

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

   if -3.60000000000000007e155 < x

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 22.9%

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

Alternative 23: 22.0% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

   2. associate--l+ 99.9%

      \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

   3. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

   4. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

   5. *-lft-identity 99.9%

      \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   7. *-commutative 99.9%

      \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   8. distribute-rgt-out-- 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   9. metadata-eval 99.9%

      \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   10. fma-define 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

   11. sub-neg 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

   12. metadata-eval 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 17.9%

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

Developer target: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * 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 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * 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 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))