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

Percentage Accurate: 99.8% → 99.9%

Time: 11.5s

Alternatives: 20

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+110} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+178}\right):\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+110) (not (<= t_1 5e+178)))
     (+ (+ x y) 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 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+110) || !(t_1 <= 5e+178)) {
		tmp = (x + y) + 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 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+110)) .or. (.not. (t_1 <= 5d+178))) then
        tmp = (x + y) + 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 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+110) || !(t_1 <= 5e+178)) {
		tmp = (x + y) + 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 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+110) or not (t_1 <= 5e+178):
		tmp = (x + y) + 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(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+110) || !(t_1 <= 5e+178))
		tmp = Float64(Float64(x + y) + 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 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+110) || ~((t_1 <= 5e+178)))
		tmp = (x + y) + 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[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+110], N[Not[LessEqual[t$95$1, 5e+178]], $MachinePrecision]], N[(N[(x + y), $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 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e110 or 4.9999999999999999e178 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 95.4%

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

   if -1e110 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999999e178

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 94.5%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+110} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+178}\right):\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+63} \lor \neg \left(z \leq 2.5 \cdot 10^{+67}\right):\\ \;\;\;\;t\_1 + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= z -1.25e+63) (not (<= z 2.5e+67)))
     (+ t_1 (- (+ z x) (* z (log t))))
     (+ (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((z <= -1.25e+63) || !(z <= 2.5e+67)) {
		tmp = t_1 + ((z + x) - (z * log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((z <= (-1.25d+63)) .or. (.not. (z <= 2.5d+67))) then
        tmp = t_1 + ((z + x) - (z * log(t)))
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((z <= -1.25e+63) || !(z <= 2.5e+67)) {
		tmp = t_1 + ((z + x) - (z * Math.log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (z <= -1.25e+63) or not (z <= 2.5e+67):
		tmp = t_1 + ((z + x) - (z * math.log(t)))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((z <= -1.25e+63) || !(z <= 2.5e+67))
		tmp = Float64(t_1 + Float64(Float64(z + x) - Float64(z * log(t))));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((z <= -1.25e+63) || ~((z <= 2.5e+67)))
		tmp = t_1 + ((z + x) - (z * log(t)));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.25e+63], N[Not[LessEqual[z, 2.5e+67]], $MachinePrecision]], N[(t$95$1 + N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000003e63 or 2.49999999999999988e67 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 88.2%

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

      1. +-commutative 88.2%

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

   5. Simplified 88.2%

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

   if -1.25000000000000003e63 < z < 2.49999999999999988e67

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 96.4%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+63} \lor \neg \left(z \leq 2.5 \cdot 10^{+67}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -2 \cdot 10^{-81}:\\ \;\;\;\;t\_2 + \left(\left(z + x\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(\left(z + y\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* b (- a 0.5))))
   (if (<= (+ x y) -2e-81) (+ t_2 (- (+ z x) t_1)) (+ t_2 (- (+ z y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -2e-81) {
		tmp = t_2 + ((z + x) - t_1);
	} else {
		tmp = t_2 + ((z + 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) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = b * (a - 0.5d0)
    if ((x + y) <= (-2d-81)) then
        tmp = t_2 + ((z + x) - t_1)
    else
        tmp = t_2 + ((z + 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 = z * Math.log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -2e-81) {
		tmp = t_2 + ((z + x) - t_1);
	} else {
		tmp = t_2 + ((z + y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -2e-81:
		tmp = t_2 + ((z + x) - t_1)
	else:
		tmp = t_2 + ((z + y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -2e-81)
		tmp = Float64(t_2 + Float64(Float64(z + x) - t_1));
	else
		tmp = Float64(t_2 + Float64(Float64(z + y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -2e-81)
		tmp = t_2 + ((z + x) - t_1);
	else
		tmp = t_2 + ((z + y) - 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]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -2e-81], N[(t$95$2 + N[(N[(z + x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(z + y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.9999999999999999e-81

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   if -1.9999999999999999e-81 < (+.f64 x 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. Add Preprocessing

   3. Taylor expanded in x around 0 77.5%

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

      1. +-commutative 77.5%

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

   5. Simplified 77.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+156} \lor \neg \left(z \leq 1.05 \cdot 10^{+134}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+156) (not (<= z 1.05e+134)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (+ (+ x y) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+156) || !(z <= 1.05e+134)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	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 <= (-4.2d+156)) .or. (.not. (z <= 1.05d+134))) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else
        tmp = (x + y) + (b * (a - 0.5d0))
    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 <= -4.2e+156) || !(z <= 1.05e+134)) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+156) or not (z <= 1.05e+134):
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	else:
		tmp = (x + y) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+156) || !(z <= 1.05e+134))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+156) || ~((z <= 1.05e+134)))
		tmp = (z * (1.0 - log(t))) + (a * b);
	else
		tmp = (x + y) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+156], N[Not[LessEqual[z, 1.05e+134]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999963e156 or 1.05e134 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 87.0%

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

      1. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   if -4.19999999999999963e156 < z < 1.05e134

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 92.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+156} \lor \neg \left(z \leq 1.05 \cdot 10^{+134}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+152} \lor \neg \left(z \leq 1.1 \cdot 10^{+150}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.85e+152) (not (<= z 1.1e+150)))
   (+ (* z (- 1.0 (log t))) x)
   (+ (+ x y) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.85e+152) || !(z <= 1.1e+150)) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	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 <= (-2.85d+152)) .or. (.not. (z <= 1.1d+150))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = (x + y) + (b * (a - 0.5d0))
    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 <= -2.85e+152) || !(z <= 1.1e+150)) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.85e+152) or not (z <= 1.1e+150):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = (x + y) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.85e+152) || !(z <= 1.1e+150))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.85e+152) || ~((z <= 1.1e+150)))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = (x + y) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.85e+152], N[Not[LessEqual[z, 1.1e+150]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85000000000000003e152 or 1.1e150 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.9%

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

   if -2.85000000000000003e152 < z < 1.1e150

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 92.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+152} \lor \neg \left(z \leq 1.1 \cdot 10^{+150}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t\_1 + y\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+146}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -1.35e+154)
     (+ t_1 y)
     (if (<= z 3.1e+146) (+ (+ x y) (* b (- a 0.5))) (+ t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -1.35e+154) {
		tmp = t_1 + y;
	} else if (z <= 3.1e+146) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-1.35d+154)) then
        tmp = t_1 + y
    else if (z <= 3.1d+146) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -1.35e+154) {
		tmp = t_1 + y;
	} else if (z <= 3.1e+146) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -1.35e+154:
		tmp = t_1 + y
	elif z <= 3.1e+146:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -1.35e+154)
		tmp = Float64(t_1 + y);
	elseif (z <= 3.1e+146)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -1.35e+154)
		tmp = t_1 + y;
	elseif (z <= 3.1e+146)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+154], N[(t$95$1 + y), $MachinePrecision], If[LessEqual[z, 3.1e+146], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000003e154

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. *-lft-identity 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. distribute-rgt-out-- 99.5%

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

      9. metadata-eval 99.5%

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

      10. fma-define 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 77.6%

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

   if -1.35000000000000003e154 < z < 3.1000000000000002e146

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 92.0%

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

   if 3.1000000000000002e146 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 78.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+146}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. sub-neg 99.8%

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

   2. metadata-eval 99.8%

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

   3. *-commutative 99.8%

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

   4. distribute-lft-in 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 9: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+156} \lor \neg \left(z \leq 1.25 \cdot 10^{+150}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e+156) (not (<= z 1.25e+150)))
   (* z (- 1.0 (log t)))
   (+ (+ x y) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e+156) || !(z <= 1.25e+150)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	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 <= (-1.2d+156)) .or. (.not. (z <= 1.25d+150))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (x + y) + (b * (a - 0.5d0))
    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 <= -1.2e+156) || !(z <= 1.25e+150)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e+156) or not (z <= 1.25e+150):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (x + y) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e+156) || !(z <= 1.25e+150))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e+156) || ~((z <= 1.25e+150)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (x + y) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e+156], N[Not[LessEqual[z, 1.25e+150]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2000000000000001e156 or 1.25000000000000002e150 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.9%

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

   6. Taylor expanded in z around inf 68.2%

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

   if -1.2000000000000001e156 < z < 1.25000000000000002e150

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 92.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+156} \lor \neg \left(z \leq 1.25 \cdot 10^{+150}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 11: 68.0% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+110} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+182}\right):\\ \;\;\;\;y + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+110) (not (<= t_1 2e+182))) (+ y t_1) (+ x y))))

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 ((t_1 <= -1e+110) || !(t_1 <= 2e+182)) {
		tmp = y + t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+110)) .or. (.not. (t_1 <= 2d+182))) then
        tmp = y + t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+110) || !(t_1 <= 2e+182)) {
		tmp = y + t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+110) or not (t_1 <= 2e+182):
		tmp = y + t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+110) || !(t_1 <= 2e+182))
		tmp = Float64(y + t_1);
	else
		tmp = Float64(x + y);
	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 ((t_1 <= -1e+110) || ~((t_1 <= 2e+182)))
		tmp = y + t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+110], N[Not[LessEqual[t$95$1, 2e+182]], $MachinePrecision]], N[(y + t$95$1), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e110 or 2.0000000000000001e182 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. add-sqr-sqrt 100.0%

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

      2. log-prod 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. count-2 100.0%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   7. Simplified 100.0%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   8. Taylor expanded in y around inf 86.8%

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

   if -1e110 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.0000000000000001e182

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.3%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 66.5%

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

   6. Taylor expanded in b around 0 61.1%

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

      1. +-commutative 61.1%

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

   8. Simplified 61.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+110} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+182}\right):\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+86}:\\ \;\;\;\;\left(x + y\right) + a \cdot b\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(\left(a + \frac{x}{b}\right) - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e+86)
   (+ (+ x y) (* a b))
   (if (<= (+ x y) -1e-92) (* b (- (+ a (/ x b)) 0.5)) (+ y (* b (- a 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+86) {
		tmp = (x + y) + (a * b);
	} else if ((x + y) <= -1e-92) {
		tmp = b * ((a + (x / b)) - 0.5);
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-1d+86)) then
        tmp = (x + y) + (a * b)
    else if ((x + y) <= (-1d-92)) then
        tmp = b * ((a + (x / b)) - 0.5d0)
    else
        tmp = y + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+86) {
		tmp = (x + y) + (a * b);
	} else if ((x + y) <= -1e-92) {
		tmp = b * ((a + (x / b)) - 0.5);
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e+86:
		tmp = (x + y) + (a * b)
	elif (x + y) <= -1e-92:
		tmp = b * ((a + (x / b)) - 0.5)
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e+86)
		tmp = Float64(Float64(x + y) + Float64(a * b));
	elseif (Float64(x + y) <= -1e-92)
		tmp = Float64(b * Float64(Float64(a + Float64(x / b)) - 0.5));
	else
		tmp = Float64(y + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e+86)
		tmp = (x + y) + (a * b);
	elseif ((x + y) <= -1e-92)
		tmp = b * ((a + (x / b)) - 0.5);
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+86], N[(N[(x + y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -1e-92], N[(b * N[(N[(a + N[(x / b), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1e86

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 85.2%

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

   6. Taylor expanded in a around inf 77.5%

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

   if -1e86 < (+.f64 x y) < -9.99999999999999988e-93

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf 75.7%

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

   4. Taylor expanded in x around inf 68.0%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. mul-1-neg 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in b around inf 68.0%

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

   if -9.99999999999999988e-93 < (+.f64 x 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. Add Preprocessing

   3. Taylor expanded in t around inf 99.8%

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

      1. add-sqr-sqrt 99.8%

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

      2. log-prod 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. count-2 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   7. Simplified 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   8. Taylor expanded in y around inf 50.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+86}:\\ \;\;\;\;\left(x + y\right) + a \cdot b\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(\left(a + \frac{x}{b}\right) - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;x + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e-92) (+ x (+ (* a b) (* -0.5 b))) (+ y (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e-92) {
		tmp = x + ((a * b) + (-0.5 * b));
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-1d-92)) then
        tmp = x + ((a * b) + ((-0.5d0) * b))
    else
        tmp = y + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e-92) {
		tmp = x + ((a * b) + (-0.5 * b));
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e-92:
		tmp = x + ((a * b) + (-0.5 * b))
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e-92)
		tmp = Float64(x + Float64(Float64(a * b) + Float64(-0.5 * b)));
	else
		tmp = Float64(y + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e-92)
		tmp = x + ((a * b) + (-0.5 * b));
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-92], N[(x + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999988e-93

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 76.1%

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

   4. Taylor expanded in x around inf 57.8%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. mul-1-neg 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in a around 0 57.8%

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

   if -9.99999999999999988e-93 < (+.f64 x 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. Add Preprocessing

   3. Taylor expanded in t around inf 99.8%

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

      1. add-sqr-sqrt 99.8%

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

      2. log-prod 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. count-2 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   7. Simplified 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   8. Taylor expanded in y around inf 50.0%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;x + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.7% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+168} \lor \neg \left(b \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+168) (not (<= b 3e+47))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+168) || !(b <= 3e+47)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.5d+168)) .or. (.not. (b <= 3d+47))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+168) || !(b <= 3e+47)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e+168) or not (b <= 3e+47):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e+168) || !(b <= 3e+47))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e+168) || ~((b <= 3e+47)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e+168], N[Not[LessEqual[b, 3e+47]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5000000000000002e168 or 3.0000000000000001e47 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. pow2 99.9%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in b around inf 68.1%

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

   if -3.5000000000000002e168 < b < 3.0000000000000001e47

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.4%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in b around 0 58.7%

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

      1. +-commutative 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+168} \lor \neg \left(b \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.5% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+39}:\\ \;\;\;\;\left(x + y\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -4e+39) (+ (+ x y) (* a b)) (+ y (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e+39) {
		tmp = (x + y) + (a * b);
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-4d+39)) then
        tmp = (x + y) + (a * b)
    else
        tmp = y + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e+39) {
		tmp = (x + y) + (a * b);
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -4e+39:
		tmp = (x + y) + (a * b)
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -4e+39)
		tmp = Float64(Float64(x + y) + Float64(a * b));
	else
		tmp = Float64(y + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -4e+39)
		tmp = (x + y) + (a * b);
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e+39], N[(N[(x + y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.99999999999999976e39

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 83.6%

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

   6. Taylor expanded in a around inf 74.7%

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

   if -3.99999999999999976e39 < (+.f64 x 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. Add Preprocessing

   3. Taylor expanded in t around inf 99.8%

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

      1. add-sqr-sqrt 99.8%

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

      2. log-prod 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. count-2 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   7. Simplified 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \left(-1 \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt{\frac{1}{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b \]

   8. Taylor expanded in y around inf 53.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+39}:\\ \;\;\;\;\left(x + y\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.7% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+168} \lor \neg \left(b \leq 4.8 \cdot 10^{+162}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.25e+168) (not (<= b 4.8e+162))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+168) || !(b <= 4.8e+162)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.25d+168)) .or. (.not. (b <= 4.8d+162))) then
        tmp = a * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+168) || !(b <= 4.8e+162)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.25e+168) or not (b <= 4.8e+162):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.25e+168) || !(b <= 4.8e+162))
		tmp = Float64(a * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.25e+168) || ~((b <= 4.8e+162)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.25e+168], N[Not[LessEqual[b, 4.8e+162]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.25000000000000006e168 or 4.80000000000000018e162 < b

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. flip-- 100.0%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. pow2 99.9%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 100.0%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in a around inf 49.5%

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

       1. *-commutative 49.5%

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

   11. Simplified 49.5%

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

   if -2.25000000000000006e168 < b < 4.80000000000000018e162

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.4%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 71.9%

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

   6. Taylor expanded in b around 0 55.8%

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

      1. +-commutative 55.8%

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

   8. Simplified 55.8%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+168} \lor \neg \left(b \leq 4.8 \cdot 10^{+162}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.1% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 9e-191) x (if (<= y 1.45e-32) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 9e-191) {
		tmp = x;
	} else if (y <= 1.45e-32) {
		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 (y <= 9d-191) then
        tmp = x
    else if (y <= 1.45d-32) 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 (y <= 9e-191) {
		tmp = x;
	} else if (y <= 1.45e-32) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 9e-191:
		tmp = x
	elif y <= 1.45e-32:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 9e-191)
		tmp = x;
	elseif (y <= 1.45e-32)
		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 (y <= 9e-191)
		tmp = x;
	elseif (y <= 1.45e-32)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 9e-191], x, If[LessEqual[y, 1.45e-32], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 9.00000000000000017e-191

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. pow2 99.9%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in x around inf 27.2%

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

   if 9.00000000000000017e-191 < y < 1.44999999999999998e-32

   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-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. flip-- 99.8%

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

      2. associate-*r/ 99.7%

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

      3. metadata-eval 99.7%

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

      4. pow2 99.7%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in a around inf 27.6%

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

       1. *-commutative 27.6%

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

   11. Simplified 27.6%

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

   if 1.44999999999999998e-32 < 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-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. flip-- 100.0%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. pow2 99.9%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in y around inf 47.7%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 78.9% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. add-cube-cbrt 99.5%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right) + \left(a - 0.5\right) \cdot b \]

   2. pow3 99.5%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

4. Applied egg-rr 99.5%

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right) + \left(a - 0.5\right) \cdot b \]

5. Taylor expanded in z around 0 77.2%

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

6. Final simplification 77.2%

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

Alternative 19: 26.3% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 5.5e-139) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.5e-139) {
		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 <= 5.5d-139) 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 <= 5.5e-139) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.5e-139:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.5e-139)
		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 <= 5.5e-139)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.5e-139], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 5.4999999999999997e-139

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. pow2 99.9%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in x around inf 28.2%

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

   if 5.4999999999999997e-139 < 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-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 99.9%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. pow2 99.8%

         \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   9. Taylor expanded in y around inf 38.2%

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

Alternative 20: 22.6% 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 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. flip-- 99.9%

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

   2. associate-*r/ 99.8%

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

   3. metadata-eval 99.8%

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

   4. pow2 99.8%

      \[\leadsto \frac{z \cdot \left(1 - \color{blue}{{\log t}^{2}}\right)}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

6. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{z \cdot \left(1 - {\log t}^{2}\right)}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]
7. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \frac{\color{blue}{\left(1 - {\log t}^{2}\right) \cdot z}}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   2. associate-/l* 99.9%

      \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

8. Simplified 99.9%

   \[\leadsto \color{blue}{\left(1 - {\log t}^{2}\right) \cdot \frac{z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

9. Taylor expanded in x around inf 23.8%

   \[\leadsto \color{blue}{x} \]
10. Add Preprocessing

Developer Target 1: 99.4% 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 2024158 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 1/2) b)))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))