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

Percentage Accurate: 99.9% → 99.9%

Time: 14.8s

Alternatives: 23

Speedup: 1.0×

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: 99.9% 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 99.4%

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

   1. +-commutative 99.4%

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

   2. associate--l+ 99.4%

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

   3. associate-+r+ 99.4%

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

   4. +-commutative 99.4%

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

   5. *-lft-identity 99.4%

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

   6. metadata-eval 99.4%

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

   7. *-commutative 99.4%

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

   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-def 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. Final simplification 99.5%

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

Alternative 2: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{+110}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)))
   (if (<= (+ x y) -5e+110)
     (+ (+ y (+ z x)) t_1)
     (+ t_1 (- (+ z y) (* z (log t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if ((x + y) <= -5e+110) {
		tmp = (y + (z + x)) + t_1;
	} else {
		tmp = t_1 + ((z + y) - (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 = (a + (-0.5d0)) * b
    if ((x + y) <= (-5d+110)) then
        tmp = (y + (z + x)) + t_1
    else
        tmp = t_1 + ((z + y) - (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 = (a + -0.5) * b;
	double tmp;
	if ((x + y) <= -5e+110) {
		tmp = (y + (z + x)) + t_1;
	} else {
		tmp = t_1 + ((z + y) - (z * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	tmp = 0
	if (x + y) <= -5e+110:
		tmp = (y + (z + x)) + t_1
	else:
		tmp = t_1 + ((z + y) - (z * math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + -0.5) * b)
	tmp = 0.0
	if (Float64(x + y) <= -5e+110)
		tmp = Float64(Float64(y + Float64(z + x)) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(z + y) - Float64(z * log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + -0.5) * b;
	tmp = 0.0;
	if ((x + y) <= -5e+110)
		tmp = (y + (z + x)) + t_1;
	else
		tmp = t_1 + ((z + y) - (z * log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e+110], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.99999999999999978e110

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 52.8%

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

      2. pow2 52.8%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 52.8%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-+r+ 88.1%

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

   8. Simplified 88.1%

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

   if -4.99999999999999978e110 < (+.f64 x y)

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l- 99.3%

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

      4. associate-+l+ 99.3%

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

      5. sub-neg 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 81.9%

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

      1. +-commutative 81.9%

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

   6. Simplified 81.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+110}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-+l- 99.4%

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

   2. +-commutative 99.4%

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

   3. associate-+l- 99.4%

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

   4. associate-+l+ 99.4%

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

   5. sub-neg 99.4%

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

   6. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Final simplification 99.4%

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

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+180} \lor \neg \left(z \leq 9 \cdot 10^{+187}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -2.25e+249)
     t_1
     (if (<= z -6.5e+193)
       (+ x (+ y (* b (- a 0.5))))
       (if (or (<= z -3.7e+180) (not (<= z 9e+187)))
         t_1
         (+ (+ y (+ z x)) (* (+ a -0.5) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -2.25e+249) {
		tmp = t_1;
	} else if (z <= -6.5e+193) {
		tmp = x + (y + (b * (a - 0.5)));
	} else if ((z <= -3.7e+180) || !(z <= 9e+187)) {
		tmp = t_1;
	} else {
		tmp = (y + (z + x)) + ((a + -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) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-2.25d+249)) then
        tmp = t_1
    else if (z <= (-6.5d+193)) then
        tmp = x + (y + (b * (a - 0.5d0)))
    else if ((z <= (-3.7d+180)) .or. (.not. (z <= 9d+187))) then
        tmp = t_1
    else
        tmp = (y + (z + x)) + ((a + (-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 t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -2.25e+249) {
		tmp = t_1;
	} else if (z <= -6.5e+193) {
		tmp = x + (y + (b * (a - 0.5)));
	} else if ((z <= -3.7e+180) || !(z <= 9e+187)) {
		tmp = t_1;
	} else {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -2.25e+249:
		tmp = t_1
	elif z <= -6.5e+193:
		tmp = x + (y + (b * (a - 0.5)))
	elif (z <= -3.7e+180) or not (z <= 9e+187):
		tmp = t_1
	else:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -2.25e+249)
		tmp = t_1;
	elseif (z <= -6.5e+193)
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	elseif ((z <= -3.7e+180) || !(z <= 9e+187))
		tmp = t_1;
	else
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -2.25e+249)
		tmp = t_1;
	elseif (z <= -6.5e+193)
		tmp = x + (y + (b * (a - 0.5)));
	elseif ((z <= -3.7e+180) || ~((z <= 9e+187)))
		tmp = t_1;
	else
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	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]}, If[LessEqual[z, -2.25e+249], t$95$1, If[LessEqual[z, -6.5e+193], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.7e+180], N[Not[LessEqual[z, 9e+187]], $MachinePrecision]], t$95$1, N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999998e249 or -6.4999999999999997e193 < z < -3.7000000000000002e180 or 9.00000000000000052e187 < z

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. +-commutative 97.5%

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

      3. associate-+l- 97.5%

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

      4. associate-+l+ 97.5%

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

      5. sub-neg 97.5%

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

      6. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around 0 97.5%

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

   5. Taylor expanded in z around inf 69.6%

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

   if -2.2499999999999998e249 < z < -6.4999999999999997e193

   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-def 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. Taylor expanded in z around 0 70.2%

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

   if -3.7000000000000002e180 < z < 9.00000000000000052e187

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 46.8%

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

      2. pow2 46.8%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 46.8%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-+r+ 92.9%

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

   8. Simplified 92.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+180} \lor \neg \left(z \leq 9 \cdot 10^{+187}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \]

Alternative 5: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+248}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{+201}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+180} \lor \neg \left(z \leq 6.5 \cdot 10^{+186}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.8e+248)
   (- z (* z (log t)))
   (if (<= z -8.3e+201)
     (+ x (+ y (* b (- a 0.5))))
     (if (or (<= z -3.7e+180) (not (<= z 6.5e+186)))
       (* z (- 1.0 (log t)))
       (+ (+ y (+ z x)) (* (+ a -0.5) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+248) {
		tmp = z - (z * log(t));
	} else if (z <= -8.3e+201) {
		tmp = x + (y + (b * (a - 0.5)));
	} else if ((z <= -3.7e+180) || !(z <= 6.5e+186)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (y + (z + x)) + ((a + -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 (z <= (-1.8d+248)) then
        tmp = z - (z * log(t))
    else if (z <= (-8.3d+201)) then
        tmp = x + (y + (b * (a - 0.5d0)))
    else if ((z <= (-3.7d+180)) .or. (.not. (z <= 6.5d+186))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (y + (z + x)) + ((a + (-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 (z <= -1.8e+248) {
		tmp = z - (z * Math.log(t));
	} else if (z <= -8.3e+201) {
		tmp = x + (y + (b * (a - 0.5)));
	} else if ((z <= -3.7e+180) || !(z <= 6.5e+186)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.8e+248:
		tmp = z - (z * math.log(t))
	elif z <= -8.3e+201:
		tmp = x + (y + (b * (a - 0.5)))
	elif (z <= -3.7e+180) or not (z <= 6.5e+186):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.8e+248)
		tmp = Float64(z - Float64(z * log(t)));
	elseif (z <= -8.3e+201)
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	elseif ((z <= -3.7e+180) || !(z <= 6.5e+186))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.8e+248)
		tmp = z - (z * log(t));
	elseif (z <= -8.3e+201)
		tmp = x + (y + (b * (a - 0.5)));
	elseif ((z <= -3.7e+180) || ~((z <= 6.5e+186)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.8e+248], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.3e+201], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.7e+180], N[Not[LessEqual[z, 6.5e+186]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.80000000000000001e248

   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. Step-by-step derivation

      1. associate-+l- 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l- 99.6%

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

      4. associate-+l+ 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around -inf 74.7%

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

      1. distribute-rgt-in 74.8%

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

      2. *-un-lft-identity 74.8%

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

      3. mul-1-neg 74.8%

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

   6. Applied egg-rr 74.8%

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

   if -1.80000000000000001e248 < z < -8.30000000000000005e201

   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-def 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. Taylor expanded in z around 0 70.2%

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

   if -8.30000000000000005e201 < z < -3.7000000000000002e180 or 6.4999999999999997e186 < z

   1. Initial program 96.5%

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

      1. associate-+l- 96.5%

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

      2. +-commutative 96.5%

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

      3. associate-+l- 96.5%

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

      4. associate-+l+ 96.5%

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

      5. sub-neg 96.5%

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

      6. metadata-eval 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in a around 0 96.4%

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

   5. Taylor expanded in z around inf 67.0%

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

   if -3.7000000000000002e180 < z < 6.4999999999999997e186

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 46.8%

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

      2. pow2 46.8%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 46.8%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-+r+ 92.9%

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

   8. Simplified 92.9%

      \[\leadsto \color{blue}{\left(y + \left(z + x\right)\right)} + \left(a + -0.5\right) \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+248}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{+201}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+180} \lor \neg \left(z \leq 6.5 \cdot 10^{+186}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \]

Alternative 6: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+117} \lor \neg \left(z \leq 3.6 \cdot 10^{+186}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e+117) (not (<= z 3.6e+186)))
   (+ (* z (- 1.0 (log t))) (+ x y))
   (+ (+ y (+ z x)) (* (+ a -0.5) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e+117) || !(z <= 3.6e+186)) {
		tmp = (z * (1.0 - log(t))) + (x + y);
	} else {
		tmp = (y + (z + x)) + ((a + -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 ((z <= (-4.4d+117)) .or. (.not. (z <= 3.6d+186))) then
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    else
        tmp = (y + (z + x)) + ((a + (-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 ((z <= -4.4e+117) || !(z <= 3.6e+186)) {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	} else {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.4e+117) or not (z <= 3.6e+186):
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	else:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.4e+117) || !(z <= 3.6e+186))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.4e+117) || ~((z <= 3.6e+186)))
		tmp = (z * (1.0 - log(t))) + (x + y);
	else
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.4e+117], N[Not[LessEqual[z, 3.6e+186]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000028e117 or 3.6000000000000002e186 < z

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate--l+ 98.2%

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

      3. associate-+r+ 98.2%

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

      4. +-commutative 98.2%

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

      5. *-lft-identity 98.2%

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

      6. metadata-eval 98.2%

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

      7. *-commutative 98.2%

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

      8. distribute-rgt-out-- 98.3%

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

      9. metadata-eval 98.3%

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

      10. fma-def 98.3%

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

      11. sub-neg 98.3%

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

      12. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in b around 0 78.5%

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

   if -4.40000000000000028e117 < z < 3.6000000000000002e186

   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. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. associate-+l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-sqr-sqrt 46.3%

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

      2. pow2 46.3%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 46.3%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-+r+ 94.9%

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

   8. Simplified 94.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+117} \lor \neg \left(z \leq 3.6 \cdot 10^{+186}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \]

Alternative 7: 88.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+117}:\\ \;\;\;\;\left(x + \left(z + y\right)\right) - z \cdot \log t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+186}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.35e+117)
   (- (+ x (+ z y)) (* z (log t)))
   (if (<= z 3.3e+186)
     (+ (+ y (+ z x)) (* (+ a -0.5) b))
     (+ (* z (- 1.0 (log t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e+117) {
		tmp = (x + (z + y)) - (z * log(t));
	} else if (z <= 3.3e+186) {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	} else {
		tmp = (z * (1.0 - log(t))) + (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 (z <= (-2.35d+117)) then
        tmp = (x + (z + y)) - (z * log(t))
    else if (z <= 3.3d+186) then
        tmp = (y + (z + x)) + ((a + (-0.5d0)) * b)
    else
        tmp = (z * (1.0d0 - log(t))) + (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 (z <= -2.35e+117) {
		tmp = (x + (z + y)) - (z * Math.log(t));
	} else if (z <= 3.3e+186) {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.35e+117:
		tmp = (x + (z + y)) - (z * math.log(t))
	elif z <= 3.3e+186:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.35e+117)
		tmp = Float64(Float64(x + Float64(z + y)) - Float64(z * log(t)));
	elseif (z <= 3.3e+186)
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.35e+117)
		tmp = (x + (z + y)) - (z * log(t));
	elseif (z <= 3.3e+186)
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.35e+117], N[(N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+186], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35000000000000003e117

   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. Step-by-step derivation

      1. associate-+l- 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l- 99.6%

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

      4. associate-+l+ 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 76.0%

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

   if -2.35000000000000003e117 < z < 3.30000000000000023e186

   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. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. associate-+l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-sqr-sqrt 46.3%

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

      2. pow2 46.3%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 46.3%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-+r+ 94.9%

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

   8. Simplified 94.9%

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

   if 3.30000000000000023e186 < z

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate--l+ 95.9%

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

      3. associate-+r+ 95.9%

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

      4. +-commutative 95.9%

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

      5. *-lft-identity 95.9%

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

      6. metadata-eval 95.9%

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

      7. *-commutative 95.9%

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

      8. distribute-rgt-out-- 96.1%

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

      9. metadata-eval 96.1%

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

      10. fma-def 96.1%

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

      11. sub-neg 96.1%

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

      12. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in b around 0 82.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+117}:\\ \;\;\;\;\left(x + \left(z + y\right)\right) - z \cdot \log t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+186}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]

Alternative 8: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+171}:\\ \;\;\;\;t_1 + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+186}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)))
   (if (<= z -1.45e+171)
     (+ t_1 (- z (* z (log t))))
     (if (<= z 4.5e+186)
       (+ (+ y (+ z x)) t_1)
       (+ (* z (- 1.0 (log t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if (z <= -1.45e+171) {
		tmp = t_1 + (z - (z * log(t)));
	} else if (z <= 4.5e+186) {
		tmp = (y + (z + x)) + t_1;
	} else {
		tmp = (z * (1.0 - log(t))) + (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) :: t_1
    real(8) :: tmp
    t_1 = (a + (-0.5d0)) * b
    if (z <= (-1.45d+171)) then
        tmp = t_1 + (z - (z * log(t)))
    else if (z <= 4.5d+186) then
        tmp = (y + (z + x)) + t_1
    else
        tmp = (z * (1.0d0 - log(t))) + (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 t_1 = (a + -0.5) * b;
	double tmp;
	if (z <= -1.45e+171) {
		tmp = t_1 + (z - (z * Math.log(t)));
	} else if (z <= 4.5e+186) {
		tmp = (y + (z + x)) + t_1;
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	tmp = 0
	if z <= -1.45e+171:
		tmp = t_1 + (z - (z * math.log(t)))
	elif z <= 4.5e+186:
		tmp = (y + (z + x)) + t_1
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + -0.5) * b)
	tmp = 0.0
	if (z <= -1.45e+171)
		tmp = Float64(t_1 + Float64(z - Float64(z * log(t))));
	elseif (z <= 4.5e+186)
		tmp = Float64(Float64(y + Float64(z + x)) + t_1);
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + -0.5) * b;
	tmp = 0.0;
	if (z <= -1.45e+171)
		tmp = t_1 + (z - (z * log(t)));
	elseif (z <= 4.5e+186)
		tmp = (y + (z + x)) + t_1;
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[z, -1.45e+171], N[(t$95$1 + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+186], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999992e171

   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. associate-+l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l- 99.7%

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

      4. associate-+l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 93.6%

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

      1. +-commutative 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in y around 0 88.4%

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

   if -1.44999999999999992e171 < z < 4.50000000000000045e186

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 47.6%

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

      2. pow2 47.6%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 47.6%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+r+ 93.3%

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

   8. Simplified 93.3%

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

   if 4.50000000000000045e186 < z

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate--l+ 95.9%

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

      3. associate-+r+ 95.9%

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

      4. +-commutative 95.9%

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

      5. *-lft-identity 95.9%

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

      6. metadata-eval 95.9%

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

      7. *-commutative 95.9%

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

      8. distribute-rgt-out-- 96.1%

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

      9. metadata-eval 96.1%

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

      10. fma-def 96.1%

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

      11. sub-neg 96.1%

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

      12. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in b around 0 82.7%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+171}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+186}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]

Alternative 9: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+145} \lor \neg \left(z \leq 5.6 \cdot 10^{+187}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.9e+145) (not (<= z 5.6e+187)))
   (+ (* z (- 1.0 (log t))) y)
   (+ (+ y (+ z x)) (* (+ a -0.5) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e+145) || !(z <= 5.6e+187)) {
		tmp = (z * (1.0 - log(t))) + y;
	} else {
		tmp = (y + (z + x)) + ((a + -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 ((z <= (-3.9d+145)) .or. (.not. (z <= 5.6d+187))) then
        tmp = (z * (1.0d0 - log(t))) + y
    else
        tmp = (y + (z + x)) + ((a + (-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 ((z <= -3.9e+145) || !(z <= 5.6e+187)) {
		tmp = (z * (1.0 - Math.log(t))) + y;
	} else {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.9e+145) or not (z <= 5.6e+187):
		tmp = (z * (1.0 - math.log(t))) + y
	else:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.9e+145) || !(z <= 5.6e+187))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + y);
	else
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.9e+145) || ~((z <= 5.6e+187)))
		tmp = (z * (1.0 - log(t))) + y;
	else
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.9e+145], N[Not[LessEqual[z, 5.6e+187]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999998e145 or 5.59999999999999979e187 < z

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate--l+ 98.1%

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

      3. associate-+r+ 98.1%

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

      4. +-commutative 98.1%

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

      5. *-lft-identity 98.1%

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

      6. metadata-eval 98.1%

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

      7. *-commutative 98.1%

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

      8. distribute-rgt-out-- 98.2%

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

      9. metadata-eval 98.2%

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

      10. fma-def 98.2%

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

      11. sub-neg 98.2%

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

      12. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in b around 0 76.7%

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

   5. Taylor expanded in x around 0 68.3%

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

   if -3.8999999999999998e145 < z < 5.59999999999999979e187

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 47.0%

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

      2. pow2 47.0%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 47.0%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-+r+ 94.1%

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

   8. Simplified 94.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+145} \lor \neg \left(z \leq 5.6 \cdot 10^{+187}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \end{array} \]

Alternative 10: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+187}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.9e+145)
   (+ (* z (- 1.0 (log t))) y)
   (if (<= z 1.55e+187)
     (+ (+ y (+ z x)) (* (+ a -0.5) b))
     (- (+ z x) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e+145) {
		tmp = (z * (1.0 - log(t))) + y;
	} else if (z <= 1.55e+187) {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	} else {
		tmp = (z + x) - (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 <= (-3.9d+145)) then
        tmp = (z * (1.0d0 - log(t))) + y
    else if (z <= 1.55d+187) then
        tmp = (y + (z + x)) + ((a + (-0.5d0)) * b)
    else
        tmp = (z + x) - (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 <= -3.9e+145) {
		tmp = (z * (1.0 - Math.log(t))) + y;
	} else if (z <= 1.55e+187) {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	} else {
		tmp = (z + x) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.9e+145:
		tmp = (z * (1.0 - math.log(t))) + y
	elif z <= 1.55e+187:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	else:
		tmp = (z + x) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.9e+145)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + y);
	elseif (z <= 1.55e+187)
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(Float64(z + x) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.9e+145)
		tmp = (z * (1.0 - log(t))) + y;
	elseif (z <= 1.55e+187)
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	else
		tmp = (z + x) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.9e+145], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[z, 1.55e+187], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999998e145

   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-- 99.6%

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

      9. metadata-eval 99.6%

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

      10. fma-def 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 72.6%

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

   5. Taylor expanded in x around 0 62.5%

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

   if -3.8999999999999998e145 < z < 1.55000000000000006e187

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 47.0%

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

      2. pow2 47.0%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 47.0%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-+r+ 94.1%

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

   8. Simplified 94.1%

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

   if 1.55000000000000006e187 < z

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. +-commutative 95.9%

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

      3. associate-+l- 95.9%

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

      4. associate-+l+ 95.9%

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

      5. sub-neg 95.9%

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

      6. metadata-eval 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in b around 0 82.5%

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

      1. add-sqr-sqrt 58.2%

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

      2. pow2 58.2%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Applied egg-rr 48.2%

      \[\leadsto \left(x + \left(y + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}} \]

   7. Taylor expanded in y around 0 66.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+187}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \end{array} \]

Alternative 11: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;z \leq -5 \cdot 10^{+143}:\\ \;\;\;\;\left(z + y\right) - t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+186}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= z -5e+143)
     (- (+ z y) t_1)
     (if (<= z 2.5e+186) (+ (+ y (+ z x)) (* (+ a -0.5) b)) (- (+ z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if (z <= -5e+143) {
		tmp = (z + y) - t_1;
	} else if (z <= 2.5e+186) {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	} else {
		tmp = (z + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * log(t)
    if (z <= (-5d+143)) then
        tmp = (z + y) - t_1
    else if (z <= 2.5d+186) then
        tmp = (y + (z + x)) + ((a + (-0.5d0)) * b)
    else
        tmp = (z + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double tmp;
	if (z <= -5e+143) {
		tmp = (z + y) - t_1;
	} else if (z <= 2.5e+186) {
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	} else {
		tmp = (z + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if z <= -5e+143:
		tmp = (z + y) - t_1
	elif z <= 2.5e+186:
		tmp = (y + (z + x)) + ((a + -0.5) * b)
	else:
		tmp = (z + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (z <= -5e+143)
		tmp = Float64(Float64(z + y) - t_1);
	elseif (z <= 2.5e+186)
		tmp = Float64(Float64(y + Float64(z + x)) + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(Float64(z + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if (z <= -5e+143)
		tmp = (z + y) - t_1;
	elseif (z <= 2.5e+186)
		tmp = (y + (z + x)) + ((a + -0.5) * b);
	else
		tmp = (z + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+143], N[(N[(z + y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 2.5e+186], N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(z + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000012e143

   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. associate-+l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l- 99.7%

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

      4. associate-+l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around 0 72.6%

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

   5. Taylor expanded in x around 0 62.5%

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

   if -5.00000000000000012e143 < z < 2.49999999999999977e186

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 47.0%

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

      2. pow2 47.0%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 47.0%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-+r+ 94.1%

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

   8. Simplified 94.1%

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

   if 2.49999999999999977e186 < z

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. +-commutative 95.9%

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

      3. associate-+l- 95.9%

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

      4. associate-+l+ 95.9%

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

      5. sub-neg 95.9%

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

      6. metadata-eval 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in b around 0 82.5%

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

      1. add-sqr-sqrt 58.2%

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

      2. pow2 58.2%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Applied egg-rr 48.2%

      \[\leadsto \left(x + \left(y + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}} \]

   7. Taylor expanded in y around 0 66.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+143}:\\ \;\;\;\;\left(z + y\right) - z \cdot \log t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+186}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \end{array} \]

Alternative 12: 61.5% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+190} \lor \neg \left(b \leq -9.8 \cdot 10^{+148} \lor \neg \left(b \leq -5.7 \cdot 10^{+79}\right) \land b \leq 1.4 \cdot 10^{+111}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.8e+190)
         (not
          (or (<= b -9.8e+148) (and (not (<= b -5.7e+79)) (<= b 1.4e+111)))))
   (* b (- a 0.5))
   (+ y (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.8e+190) || !((b <= -9.8e+148) || (!(b <= -5.7e+79) && (b <= 1.4e+111)))) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (z + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.8d+190)) .or. (.not. (b <= (-9.8d+148)) .or. (.not. (b <= (-5.7d+79))) .and. (b <= 1.4d+111))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y + (z + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.8e+190) || !((b <= -9.8e+148) || (!(b <= -5.7e+79) && (b <= 1.4e+111)))) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (z + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.8e+190) or not ((b <= -9.8e+148) or (not (b <= -5.7e+79) and (b <= 1.4e+111))):
		tmp = b * (a - 0.5)
	else:
		tmp = y + (z + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.8e+190) || !((b <= -9.8e+148) || (!(b <= -5.7e+79) && (b <= 1.4e+111))))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(y + Float64(z + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.8e+190) || ~(((b <= -9.8e+148) || (~((b <= -5.7e+79)) && (b <= 1.4e+111)))))
		tmp = b * (a - 0.5);
	else
		tmp = y + (z + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.8e+190], N[Not[Or[LessEqual[b, -9.8e+148], And[N[Not[LessEqual[b, -5.7e+79]], $MachinePrecision], LessEqual[b, 1.4e+111]]]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.79999999999999997e190 or -9.8e148 < b < -5.6999999999999997e79 or 1.4e111 < b

   1. Initial program 98.9%

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

      1. +-commutative 98.9%

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

      2. associate--l+ 98.9%

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

      3. associate-+r+ 98.9%

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

      4. +-commutative 98.9%

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

      5. *-lft-identity 98.9%

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

      6. metadata-eval 98.9%

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

      7. *-commutative 98.9%

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

      8. distribute-rgt-out-- 98.9%

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

      9. metadata-eval 98.9%

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

      10. fma-def 98.9%

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

      11. sub-neg 98.9%

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

      12. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in b around inf 76.2%

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

   if -2.79999999999999997e190 < b < -9.8e148 or -5.6999999999999997e79 < b < 1.4e111

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l- 99.8%

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

      4. associate-+l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 49.5%

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

      2. pow2 49.5%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 49.5%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r+ 74.2%

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

   8. Simplified 74.2%

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

   9. Taylor expanded in b around 0 59.6%

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

       1. +-commutative 59.6%

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

       2. associate-+r+ 59.6%

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

       3. +-commutative 59.6%

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

   11. Simplified 59.6%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+190} \lor \neg \left(b \leq -9.8 \cdot 10^{+148} \lor \neg \left(b \leq -5.7 \cdot 10^{+79}\right) \land b \leq 1.4 \cdot 10^{+111}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \]

Alternative 13: 29.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2050000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-28}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-181}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+88)
   x
   (if (<= x -2050000.0)
     (* a b)
     (if (<= x -5.8e-28) (* -0.5 b) (if (<= x 1.95e-181) (* a b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+88) {
		tmp = x;
	} else if (x <= -2050000.0) {
		tmp = a * b;
	} else if (x <= -5.8e-28) {
		tmp = -0.5 * b;
	} else if (x <= 1.95e-181) {
		tmp = a * 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+88)) then
        tmp = x
    else if (x <= (-2050000.0d0)) then
        tmp = a * b
    else if (x <= (-5.8d-28)) then
        tmp = (-0.5d0) * b
    else if (x <= 1.95d-181) then
        tmp = a * 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+88) {
		tmp = x;
	} else if (x <= -2050000.0) {
		tmp = a * b;
	} else if (x <= -5.8e-28) {
		tmp = -0.5 * b;
	} else if (x <= 1.95e-181) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+88:
		tmp = x
	elif x <= -2050000.0:
		tmp = a * b
	elif x <= -5.8e-28:
		tmp = -0.5 * b
	elif x <= 1.95e-181:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+88)
		tmp = x;
	elseif (x <= -2050000.0)
		tmp = Float64(a * b);
	elseif (x <= -5.8e-28)
		tmp = Float64(-0.5 * b);
	elseif (x <= 1.95e-181)
		tmp = Float64(a * 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+88)
		tmp = x;
	elseif (x <= -2050000.0)
		tmp = a * b;
	elseif (x <= -5.8e-28)
		tmp = -0.5 * b;
	elseif (x <= 1.95e-181)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+88], x, If[LessEqual[x, -2050000.0], N[(a * b), $MachinePrecision], If[LessEqual[x, -5.8e-28], N[(-0.5 * b), $MachinePrecision], If[LessEqual[x, 1.95e-181], N[(a * b), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.49999999999999999e88

   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-def 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. Taylor expanded in x around inf 49.2%

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

   if -2.49999999999999999e88 < x < -2.05e6 or -5.80000000000000026e-28 < x < 1.95e-181

   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-- 99.8%

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

      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-def 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. Taylor expanded in a around inf 30.8%

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

      1. *-commutative 30.8%

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

   6. Simplified 30.8%

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

   if -2.05e6 < x < -5.80000000000000026e-28

   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-def 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. Taylor expanded in b around inf 71.9%

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

   5. Taylor expanded in a around 0 45.0%

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

   if 1.95e-181 < x

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate--l+ 99.0%

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

      3. associate-+r+ 99.0%

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

      4. +-commutative 99.0%

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

      5. *-lft-identity 99.0%

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

      6. metadata-eval 99.0%

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

      7. *-commutative 99.0%

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

      8. distribute-rgt-out-- 99.0%

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

      9. metadata-eval 99.0%

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

      10. fma-def 99.0%

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

      11. sub-neg 99.0%

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

      12. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around inf 21.3%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2050000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-28}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-181}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 29.1% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+89}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -80000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-27}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-182}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.12e+89)
   (+ z x)
   (if (<= x -80000.0)
     (* a b)
     (if (<= x -2.2e-27) (* -0.5 b) (if (<= x 2.4e-182) (* a b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.12e+89) {
		tmp = z + x;
	} else if (x <= -80000.0) {
		tmp = a * b;
	} else if (x <= -2.2e-27) {
		tmp = -0.5 * b;
	} else if (x <= 2.4e-182) {
		tmp = a * 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 <= (-1.12d+89)) then
        tmp = z + x
    else if (x <= (-80000.0d0)) then
        tmp = a * b
    else if (x <= (-2.2d-27)) then
        tmp = (-0.5d0) * b
    else if (x <= 2.4d-182) then
        tmp = a * 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 <= -1.12e+89) {
		tmp = z + x;
	} else if (x <= -80000.0) {
		tmp = a * b;
	} else if (x <= -2.2e-27) {
		tmp = -0.5 * b;
	} else if (x <= 2.4e-182) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.12e+89:
		tmp = z + x
	elif x <= -80000.0:
		tmp = a * b
	elif x <= -2.2e-27:
		tmp = -0.5 * b
	elif x <= 2.4e-182:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.12e+89)
		tmp = Float64(z + x);
	elseif (x <= -80000.0)
		tmp = Float64(a * b);
	elseif (x <= -2.2e-27)
		tmp = Float64(-0.5 * b);
	elseif (x <= 2.4e-182)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.12e+89)
		tmp = z + x;
	elseif (x <= -80000.0)
		tmp = a * b;
	elseif (x <= -2.2e-27)
		tmp = -0.5 * b;
	elseif (x <= 2.4e-182)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.12e+89], N[(z + x), $MachinePrecision], If[LessEqual[x, -80000.0], N[(a * b), $MachinePrecision], If[LessEqual[x, -2.2e-27], N[(-0.5 * b), $MachinePrecision], If[LessEqual[x, 2.4e-182], N[(a * b), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.11999999999999995e89

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 49.9%

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

      2. pow2 49.9%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 49.9%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-+r+ 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in y around 0 69.3%

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

       1. associate-+r+ 69.3%

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

       2. sub-neg 69.3%

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

       3. metadata-eval 69.3%

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

       4. +-commutative 69.3%

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

   11. Simplified 69.3%

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

   12. Taylor expanded in b around 0 50.3%

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

   if -1.11999999999999995e89 < x < -8e4 or -2.19999999999999987e-27 < x < 2.3999999999999998e-182

   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-- 99.8%

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

      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-def 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. Taylor expanded in a around inf 30.8%

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

      1. *-commutative 30.8%

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

   6. Simplified 30.8%

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

   if -8e4 < x < -2.19999999999999987e-27

   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-def 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. Taylor expanded in b around inf 71.9%

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

   5. Taylor expanded in a around 0 45.0%

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

   if 2.3999999999999998e-182 < x

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate--l+ 99.0%

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

      3. associate-+r+ 99.0%

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

      4. +-commutative 99.0%

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

      5. *-lft-identity 99.0%

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

      6. metadata-eval 99.0%

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

      7. *-commutative 99.0%

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

      8. distribute-rgt-out-- 99.0%

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

      9. metadata-eval 99.0%

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

      10. fma-def 99.0%

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

      11. sub-neg 99.0%

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

      12. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around inf 21.3%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+89}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -80000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-27}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-182}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 79.3% accurate, 10.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (y + ((-0.5 * b) + (a * 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 + (((-0.5d0) * b) + (a * b)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-+l- 99.4%

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

   2. +-commutative 99.4%

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

   3. associate-+l- 99.4%

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

   4. associate-+l+ 99.4%

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

   5. sub-neg 99.4%

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

   6. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Taylor expanded in a around 0 99.4%

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

5. Taylor expanded in z around 0 78.2%

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

6. Final simplification 78.2%

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

Alternative 16: 80.1% accurate, 10.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (y + (z + x)) + ((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 = (y + (z + x)) + ((a + (-0.5d0)) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-+l- 99.4%

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

   2. +-commutative 99.4%

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

   3. associate-+l- 99.4%

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

   4. associate-+l+ 99.4%

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

   5. sub-neg 99.4%

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

   6. metadata-eval 99.4%

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

3. Simplified 99.4%

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

   1. add-sqr-sqrt 48.7%

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

   2. pow2 48.7%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

5. Applied egg-rr 48.7%

   \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

6. Taylor expanded in z around 0 78.9%

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

   1. +-commutative 78.9%

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

   2. associate-+r+ 78.9%

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

8. Simplified 78.9%

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

9. Final simplification 78.9%

   \[\leadsto \left(y + \left(z + x\right)\right) + \left(a + -0.5\right) \cdot b \]

Alternative 17: 39.6% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+136}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.5e+136) (+ z x) (if (<= x 3.5e+77) (* b (- a 0.5)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.5e+136) {
		tmp = z + x;
	} else if (x <= 3.5e+77) {
		tmp = b * (a - 0.5);
	} 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 <= (-1.5d+136)) then
        tmp = z + x
    else if (x <= 3.5d+77) then
        tmp = b * (a - 0.5d0)
    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 <= -1.5e+136) {
		tmp = z + x;
	} else if (x <= 3.5e+77) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.5e+136:
		tmp = z + x
	elif x <= 3.5e+77:
		tmp = b * (a - 0.5)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.5e+136)
		tmp = Float64(z + x);
	elseif (x <= 3.5e+77)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.5e+136)
		tmp = z + x;
	elseif (x <= 3.5e+77)
		tmp = b * (a - 0.5);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.5e+136], N[(z + x), $MachinePrecision], If[LessEqual[x, 3.5e+77], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -1.49999999999999989e136

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 48.4%

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

      2. pow2 48.4%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 48.4%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 79.3%

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

      1. +-commutative 79.3%

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

      2. associate-+r+ 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in y around 0 73.2%

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

       1. associate-+r+ 73.2%

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

       2. sub-neg 73.2%

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

       3. metadata-eval 73.2%

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

       4. +-commutative 73.2%

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

   11. Simplified 73.2%

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

   12. Taylor expanded in b around 0 54.4%

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

   if -1.49999999999999989e136 < x < 3.5000000000000001e77

   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-- 99.9%

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

      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-def 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. Taylor expanded in b around inf 47.3%

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

   if 3.5000000000000001e77 < x

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate--l+ 98.1%

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

      3. associate-+r+ 98.1%

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

      4. +-commutative 98.1%

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

      5. *-lft-identity 98.1%

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

      6. metadata-eval 98.1%

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

      7. *-commutative 98.1%

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

      8. distribute-rgt-out-- 98.1%

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

      9. metadata-eval 98.1%

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

      10. fma-def 98.1%

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

      11. sub-neg 98.1%

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

      12. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around inf 21.3%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+136}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 63.2% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+162}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.15e+162) (+ x (* b (- a 0.5))) (+ y (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.15e+162) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (z + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.15d+162) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + (z + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.15e+162) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (z + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.15e+162:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (z + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.15e+162)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(z + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.15e+162)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (z + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.15e+162], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.14999999999999997e162

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+l- 99.4%

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

      4. associate-+l+ 99.4%

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

      5. sub-neg 99.4%

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

      6. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

      1. add-sqr-sqrt 48.5%

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

      2. pow2 48.5%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 48.5%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-+r+ 77.7%

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

   8. Simplified 77.7%

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

   9. Taylor expanded in y around 0 63.4%

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

       1. associate-+r+ 63.4%

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

       2. sub-neg 63.4%

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

       3. metadata-eval 63.4%

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

       4. +-commutative 63.4%

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

   11. Simplified 63.4%

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

   12. Taylor expanded in z around 0 62.6%

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

   if 1.14999999999999997e162 < 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. Step-by-step derivation

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 49.8%

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

      2. pow2 49.8%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 49.8%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. associate-+r+ 86.6%

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

   8. Simplified 86.6%

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

   9. Taylor expanded in b around 0 63.8%

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

       1. +-commutative 63.8%

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

       2. associate-+r+ 63.8%

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

       3. +-commutative 63.8%

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

   11. Simplified 63.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+162}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \]

Alternative 19: 64.5% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x \leq -29000000:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= x -29000000.0) (+ 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 <= -29000000.0) {
		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 <= (-29000000.0d0)) 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 <= -29000000.0) {
		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 <= -29000000.0:
		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 (x <= -29000000.0)
		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 <= -29000000.0)
		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[x, -29000000.0], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e7

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. associate-+l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 50.7%

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

      2. pow2 50.7%

         \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 50.7%

      \[\leadsto \left(\left(y + \left(x + z\right)\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. associate-+r+ 78.9%

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

   8. Simplified 78.9%

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

   9. Taylor expanded in y around 0 64.0%

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

       1. associate-+r+ 64.0%

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

       2. sub-neg 64.0%

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

       3. metadata-eval 64.0%

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

       4. +-commutative 64.0%

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

   11. Simplified 64.0%

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

   12. Taylor expanded in z around 0 63.5%

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

   if -2.9e7 < x

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l- 99.3%

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

      4. associate-+l+ 99.3%

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

      5. sub-neg 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 85.2%

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

      1. +-commutative 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in z around 0 64.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29000000:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 20: 79.3% accurate, 12.8× speedup

Math

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

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(x + Float64(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[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. associate--l+ 99.4%

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

   3. associate-+r+ 99.4%

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

   4. +-commutative 99.4%

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

   5. *-lft-identity 99.4%

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

   6. metadata-eval 99.4%

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

   7. *-commutative 99.4%

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

   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-def 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. Taylor expanded in z around 0 78.2%

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

5. Final simplification 78.2%

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

Alternative 21: 27.1% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.85 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+155}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.85e-27) x (if (<= y 4.8e+155) (* -0.5 b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.85e-27) {
		tmp = x;
	} else if (y <= 4.8e+155) {
		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 (y <= 2.85d-27) then
        tmp = x
    else if (y <= 4.8d+155) 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 (y <= 2.85e-27) {
		tmp = x;
	} else if (y <= 4.8e+155) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.85e-27:
		tmp = x
	elif y <= 4.8e+155:
		tmp = -0.5 * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.85e-27)
		tmp = x;
	elseif (y <= 4.8e+155)
		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 (y <= 2.85e-27)
		tmp = x;
	elseif (y <= 4.8e+155)
		tmp = -0.5 * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.85e-27], x, If[LessEqual[y, 4.8e+155], N[(-0.5 * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 2.8499999999999998e-27

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate--l+ 99.3%

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

      3. associate-+r+ 99.3%

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

      4. +-commutative 99.3%

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

      5. *-lft-identity 99.3%

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

      6. metadata-eval 99.3%

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

      7. *-commutative 99.3%

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

      8. distribute-rgt-out-- 99.4%

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

      9. metadata-eval 99.4%

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

      10. fma-def 99.4%

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

      11. sub-neg 99.4%

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

      12. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 22.9%

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

   if 2.8499999999999998e-27 < y < 4.80000000000000042e155

   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-def 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. Taylor expanded in b around inf 41.1%

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

   5. Taylor expanded in a around 0 24.3%

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

   if 4.80000000000000042e155 < 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. 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-def 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. Taylor expanded in y around inf 53.3%

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

4. Final simplification 27.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.85 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+155}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22: 28.3% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 3.4e+17) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.4e+17) {
		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 (y <= 3.4d+17) 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 (y <= 3.4e+17) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.4e+17:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.4e+17)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.4e+17)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.4e+17], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.4e17

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate--l+ 99.3%

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

      3. associate-+r+ 99.3%

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

      4. +-commutative 99.3%

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

      5. *-lft-identity 99.3%

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

      6. metadata-eval 99.3%

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

      7. *-commutative 99.3%

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

      8. distribute-rgt-out-- 99.4%

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

      9. metadata-eval 99.4%

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

      10. fma-def 99.4%

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

      11. sub-neg 99.4%

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

      12. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 23.2%

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

   if 3.4e17 < y

   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-def 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. Taylor expanded in y around inf 38.3%

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

4. Final simplification 26.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 22.1% 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 99.4%

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

   1. +-commutative 99.4%

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

   2. associate--l+ 99.4%

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

   3. associate-+r+ 99.4%

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

   4. +-commutative 99.4%

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

   5. *-lft-identity 99.4%

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

   6. metadata-eval 99.4%

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

   7. *-commutative 99.4%

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

   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-def 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. Taylor expanded in x around inf 21.3%

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

5. Final simplification 21.3%

   \[\leadsto x \]

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 2023320 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ 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)))