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

Percentage Accurate: 99.8% → 99.9%

Time: 10.9s

Alternatives: 17

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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -500 \lor \neg \left(t\_1 \leq 5\right):\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -500.0) (not (<= t_1 5.0)))
     (+ (+ 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 <= -500.0) || !(t_1 <= 5.0)) {
		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 <= (-500.0d0)) .or. (.not. (t_1 <= 5.0d0))) 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 <= -500.0) || !(t_1 <= 5.0)) {
		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 <= -500.0) or not (t_1 <= 5.0):
		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 <= -500.0) || !(t_1 <= 5.0))
		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 <= -500.0) || ~((t_1 <= 5.0)))
		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, -500.0], N[Not[LessEqual[t$95$1, 5.0]], $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) < -500 or 5 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) 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. Add Preprocessing

   3. Taylor expanded in z around -inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. neg-mul-1 83.4%

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

      3. mul-1-neg 83.4%

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

      4. neg-mul-1 83.4%

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

      5. sub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in z around 0 88.1%

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

      1. +-commutative 88.1%

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

   8. Simplified 88.1%

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

   if -500 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5

   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-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 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 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -500 \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5\right):\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := z + b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -1 \cdot 10^{-66}:\\ \;\;\;\;\left(x + t\_2\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (+ z (* b (- a 0.5)))))
   (if (<= (+ x y) -1e-66) (- (+ x t_2) t_1) (- (+ y t_2) 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 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -1e-66) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - 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 = z + (b * (a - 0.5d0))
    if ((x + y) <= (-1d-66)) then
        tmp = (x + t_2) - t_1
    else
        tmp = (y + t_2) - 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 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -1e-66) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = z + (b * (a - 0.5))
	tmp = 0
	if (x + y) <= -1e-66:
		tmp = (x + t_2) - t_1
	else:
		tmp = (y + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(z + Float64(b * Float64(a - 0.5)))
	tmp = 0.0
	if (Float64(x + y) <= -1e-66)
		tmp = Float64(Float64(x + t_2) - t_1);
	else
		tmp = Float64(Float64(y + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = z + (b * (a - 0.5));
	tmp = 0.0;
	if ((x + y) <= -1e-66)
		tmp = (x + t_2) - t_1;
	else
		tmp = (y + t_2) - 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[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -1e-66], N[(N[(x + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(y + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.9999999999999998e-67

   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 72.1%

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

   if -9.9999999999999998e-67 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.6%

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

Alternative 4: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;\left(x + \left(z + t\_1\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) 5e+49) (- (+ x (+ z t_1)) (* z (log t))) (+ (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 5e+49) {
		tmp = (x + (z + t_1)) - (z * log(t));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= 5d+49) then
        tmp = (x + (z + t_1)) - (z * log(t))
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 5e+49) {
		tmp = (x + (z + t_1)) - (z * Math.log(t));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= 5e+49:
		tmp = (x + (z + t_1)) - (z * math.log(t))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= 5e+49)
		tmp = Float64(Float64(x + Float64(z + t_1)) - Float64(z * log(t)));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= 5e+49)
		tmp = (x + (z + t_1)) - (z * log(t));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 5e+49], N[(N[(x + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5.0000000000000004e49

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 82.8%

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

   if 5.0000000000000004e49 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. neg-mul-1 69.1%

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

      3. mul-1-neg 69.1%

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

      4. neg-mul-1 69.1%

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

      5. sub-neg 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around 0 89.0%

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

      1. +-commutative 89.0%

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

   8. Simplified 89.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+153} \lor \neg \left(z \leq 8.5 \cdot 10^{+92}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e+153) (not (<= z 8.5e+92)))
   (+ (* 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 <= -2.8e+153) || !(z <= 8.5e+92)) {
		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 <= (-2.8d+153)) .or. (.not. (z <= 8.5d+92))) 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 <= -2.8e+153) || !(z <= 8.5e+92)) {
		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 <= -2.8e+153) or not (z <= 8.5e+92):
		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 <= -2.8e+153) || !(z <= 8.5e+92))
		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 <= -2.8e+153) || ~((z <= 8.5e+92)))
		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, -2.8e+153], N[Not[LessEqual[z, 8.5e+92]], $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 < -2.79999999999999985e153 or 8.5000000000000001e92 < 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 76.1%

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

      1. *-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -2.79999999999999985e153 < z < 8.5000000000000001e92

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 74.1%

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

      1. associate-*r* 74.1%

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

      2. neg-mul-1 74.1%

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

      3. mul-1-neg 74.1%

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

      4. neg-mul-1 74.1%

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

      5. sub-neg 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in z around 0 92.3%

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

      1. +-commutative 92.3%

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

   8. Simplified 92.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+153} \lor \neg \left(z \leq 8.5 \cdot 10^{+92}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 7: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+93}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.1e+93) (+ (+ x y) (* b (- a 0.5))) (+ (* z (- 1.0 (log t))) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.1e+93) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = (z * (1.0 - log(t))) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 2.1d+93) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = (z * (1.0d0 - log(t))) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.1e+93) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = (z * (1.0 - Math.log(t))) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2.1e+93:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = (z * (1.0 - math.log(t))) + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.1e+93)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2.1e+93)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = (z * (1.0 - log(t))) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2.1e+93], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.0999999999999998e93

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 77.3%

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

      1. associate-*r* 77.3%

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

      2. neg-mul-1 77.3%

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

      3. mul-1-neg 77.3%

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

      4. neg-mul-1 77.3%

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

      5. sub-neg 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in z around 0 86.9%

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

      1. +-commutative 86.9%

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

   8. Simplified 86.9%

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

   if 2.0999999999999998e93 < 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 71.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+93}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+168}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.1e+168) (+ (+ x y) (* b (- a 0.5))) (* z (- 1.0 (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.1e+168) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = z * (1.0 - log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 2.1d+168) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = z * (1.0d0 - log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.1e+168) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2.1e+168:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.1e+168)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2.1e+168)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2.1e+168], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.10000000000000003e168

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 78.6%

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

      1. associate-*r* 78.6%

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

      2. neg-mul-1 78.6%

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

      3. mul-1-neg 78.6%

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

      4. neg-mul-1 78.6%

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

      5. sub-neg 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

   8. Simplified 85.1%

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

   if 2.10000000000000003e168 < 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 77.8%

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

   6. Taylor expanded in z around inf 69.7%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+168}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+64} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;y + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -2e+64) (not (<= t_1 2e+149)))
     (+ y t_1)
     (+ (+ x y) (* -0.5 b)))))

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 <= -2e+64) || !(t_1 <= 2e+149)) {
		tmp = y + t_1;
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-2d+64)) .or. (.not. (t_1 <= 2d+149))) then
        tmp = y + t_1
    else
        tmp = (x + y) + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+64) || !(t_1 <= 2e+149)) {
		tmp = y + t_1;
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -2e+64) or not (t_1 <= 2e+149):
		tmp = y + t_1
	else:
		tmp = (x + y) + (-0.5 * b)
	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 <= -2e+64) || !(t_1 <= 2e+149))
		tmp = Float64(y + t_1);
	else
		tmp = Float64(Float64(x + y) + Float64(-0.5 * b));
	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 <= -2e+64) || ~((t_1 <= 2e+149)))
		tmp = y + t_1;
	else
		tmp = (x + y) + (-0.5 * b);
	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, -2e+64], N[Not[LessEqual[t$95$1, 2e+149]], $MachinePrecision]], N[(y + t$95$1), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.00000000000000004e64 or 2.0000000000000001e149 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) 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. Add Preprocessing

   3. Taylor expanded in z around -inf 83.3%

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

      1. associate-*r* 83.3%

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

      2. neg-mul-1 83.3%

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

      3. mul-1-neg 83.3%

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

      4. neg-mul-1 83.3%

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

      5. sub-neg 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around inf 85.2%

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

   if -2.00000000000000004e64 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.0000000000000001e149

   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 z around -inf 80.3%

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

      1. associate-*r* 80.3%

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

      2. neg-mul-1 80.3%

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

      3. mul-1-neg 80.3%

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

      4. neg-mul-1 80.3%

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

      5. sub-neg 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in z around 0 65.5%

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

      1. +-commutative 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in a around 0 60.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+64} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.5% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;\left(x + y\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- a 0.5) -50000.0) (not (<= (- a 0.5) -0.4)))
   (+ (+ x y) (* a b))
   (+ (+ x y) (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -50000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (x + y) + (a * b);
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a - 0.5d0) <= (-50000.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = (x + y) + (a * b)
    else
        tmp = (x + y) + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -50000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (x + y) + (a * b);
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a - 0.5) <= -50000.0) or not ((a - 0.5) <= -0.4):
		tmp = (x + y) + (a * b)
	else:
		tmp = (x + y) + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -50000.0) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(Float64(x + y) + Float64(a * b));
	else
		tmp = Float64(Float64(x + y) + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a - 0.5) <= -50000.0) || ~(((a - 0.5) <= -0.4)))
		tmp = (x + y) + (a * b);
	else
		tmp = (x + y) + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -50000.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -5e4 or -0.40000000000000002 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 82.6%

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

      1. associate-*r* 82.6%

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

      2. neg-mul-1 82.6%

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

      3. mul-1-neg 82.6%

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

      4. neg-mul-1 82.6%

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

      5. sub-neg 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around 0 83.6%

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

      1. +-commutative 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in a around inf 82.5%

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

   if -5e4 < (-.f64 a #s(literal 1/2 binary64)) < -0.40000000000000002

   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 z around -inf 80.5%

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

      1. associate-*r* 80.5%

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

      2. neg-mul-1 80.5%

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

      3. mul-1-neg 80.5%

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

      4. neg-mul-1 80.5%

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

      5. sub-neg 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in z around 0 70.9%

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

      1. +-commutative 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in a around 0 69.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;\left(x + y\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.0% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -24000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.5:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -24000000000.0)
   (* a b)
   (if (<= a -1.4e-37) x (if (<= a 0.5) (* -0.5 b) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -24000000000.0) {
		tmp = a * b;
	} else if (a <= -1.4e-37) {
		tmp = x;
	} else if (a <= 0.5) {
		tmp = -0.5 * b;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-24000000000.0d0)) then
        tmp = a * b
    else if (a <= (-1.4d-37)) then
        tmp = x
    else if (a <= 0.5d0) then
        tmp = (-0.5d0) * b
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -24000000000.0) {
		tmp = a * b;
	} else if (a <= -1.4e-37) {
		tmp = x;
	} else if (a <= 0.5) {
		tmp = -0.5 * b;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -24000000000.0:
		tmp = a * b
	elif a <= -1.4e-37:
		tmp = x
	elif a <= 0.5:
		tmp = -0.5 * b
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -24000000000.0)
		tmp = Float64(a * b);
	elseif (a <= -1.4e-37)
		tmp = x;
	elseif (a <= 0.5)
		tmp = Float64(-0.5 * b);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -24000000000.0)
		tmp = a * b;
	elseif (a <= -1.4e-37)
		tmp = x;
	elseif (a <= 0.5)
		tmp = -0.5 * b;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -24000000000.0], N[(a * b), $MachinePrecision], If[LessEqual[a, -1.4e-37], x, If[LessEqual[a, 0.5], N[(-0.5 * b), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4e10 or 0.5 < a

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 80.4%

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

      1. sub-neg 80.4%

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

      2. metadata-eval 80.4%

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

      3. +-commutative 80.4%

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

      4. associate-/l* 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in b around inf 49.8%

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

      1. associate-*r* 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-*r/ 47.4%

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

      4. metadata-eval 47.4%

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

      5. div-sub 47.4%

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

      6. sub-neg 47.4%

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

      7. metadata-eval 47.4%

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

      8. +-commutative 47.4%

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

   10. Simplified 47.4%

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

   11. Taylor expanded in a around inf 54.1%

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

       1. *-commutative 54.1%

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

   13. Simplified 54.1%

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

   if -2.4e10 < a < -1.4000000000000001e-37

   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-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 59.0%

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

   6. Taylor expanded in z around 0 34.7%

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

   if -1.4000000000000001e-37 < a < 0.5

   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. Taylor expanded in x around inf 76.8%

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

      1. sub-neg 76.8%

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

      2. metadata-eval 76.8%

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

      3. +-commutative 76.8%

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

      4. associate-/l* 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in b around inf 28.1%

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

      1. associate-*r* 19.1%

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

      2. *-commutative 19.1%

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

      3. associate-*r/ 19.1%

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

      4. metadata-eval 19.1%

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

      5. div-sub 19.1%

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

      6. sub-neg 19.1%

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

      7. metadata-eval 19.1%

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

      8. +-commutative 19.1%

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

   10. Simplified 19.1%

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

   11. Taylor expanded in a around 0 27.2%

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

       1. *-commutative 27.2%

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

   13. Simplified 27.2%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -24000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.5:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.4% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.09 \lor \neg \left(b \leq 1.32 \cdot 10^{-5}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.09) (not (<= b 1.32e-5)))
   (* b (- a 0.5))
   (* x (+ 1.0 (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.09) || !(b <= 1.32e-5)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x * (1.0 + (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.09d0)) .or. (.not. (b <= 1.32d-5))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x * (1.0d0 + (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.09) || !(b <= 1.32e-5)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x * (1.0 + (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.09) or not (b <= 1.32e-5):
		tmp = b * (a - 0.5)
	else:
		tmp = x * (1.0 + (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.09) || !(b <= 1.32e-5))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.09) || ~((b <= 1.32e-5)))
		tmp = b * (a - 0.5);
	else
		tmp = x * (1.0 + (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.09], N[Not[LessEqual[b, 1.32e-5]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.089999999999999997 or 1.32000000000000007e-5 < 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-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 78.3%

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

      1. sub-neg 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

      4. associate-/l* 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in b around inf 68.6%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*r/ 58.3%

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

      4. metadata-eval 58.3%

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

      5. div-sub 58.3%

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

      6. sub-neg 58.3%

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

      7. metadata-eval 58.3%

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

      8. +-commutative 58.3%

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

   10. Simplified 58.3%

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

   11. Taylor expanded in x around 0 71.0%

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

   if -0.089999999999999997 < b < 1.32000000000000007e-5

   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. Taylor expanded in x around inf 79.4%

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

      1. sub-neg 79.4%

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

      2. metadata-eval 79.4%

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

      3. +-commutative 79.4%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in y around inf 48.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.09 \lor \neg \left(b \leq 1.32 \cdot 10^{-5}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.8% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.5e+144) (* x (+ 1.0 (/ y x))) (+ y (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.5e+144) {
		tmp = x * (1.0 + (y / x));
	} 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 <= (-5.5d+144)) then
        tmp = x * (1.0d0 + (y / x))
    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 <= -5.5e+144) {
		tmp = x * (1.0 + (y / x));
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.5e+144:
		tmp = x * (1.0 + (y / x))
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.5e+144)
		tmp = Float64(x * Float64(1.0 + Float64(y / x)));
	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 <= -5.5e+144)
		tmp = x * (1.0 + (y / x));
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.5e+144], N[(x * N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000022e144

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 64.0%

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

   if -5.50000000000000022e144 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 84.4%

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

      1. associate-*r* 84.4%

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

      2. neg-mul-1 84.4%

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

      3. mul-1-neg 84.4%

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

      4. neg-mul-1 84.4%

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

      5. sub-neg 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in y around inf 61.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.5% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+144) x (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+144) {
		tmp = x;
	} else {
		tmp = 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 <= (-6d+144)) then
        tmp = x
    else
        tmp = 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 <= -6e+144) {
		tmp = x;
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+144:
		tmp = x
	else:
		tmp = b * (a - 0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+144)
		tmp = x;
	else
		tmp = 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 <= -6e+144)
		tmp = x;
	else
		tmp = b * (a - 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+144], x, N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999998e144

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 57.5%

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

   6. Taylor expanded in z around 0 51.4%

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

   if -5.9999999999999998e144 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 76.0%

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

      1. sub-neg 76.0%

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

      2. metadata-eval 76.0%

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

      3. +-commutative 76.0%

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

      4. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in b around inf 39.4%

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

      1. associate-*r* 34.7%

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

      2. *-commutative 34.7%

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

      3. associate-*r/ 34.7%

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

      4. metadata-eval 34.7%

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

      5. div-sub 34.7%

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

      6. sub-neg 34.7%

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

      7. metadata-eval 34.7%

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

      8. +-commutative 34.7%

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

   10. Simplified 34.7%

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

   11. Taylor expanded in x around 0 42.1%

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

Alternative 15: 78.0% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around -inf 81.6%

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

   1. associate-*r* 81.6%

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

   2. neg-mul-1 81.6%

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

   3. mul-1-neg 81.6%

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

   4. neg-mul-1 81.6%

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

   5. sub-neg 81.6%

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

5. Simplified 81.6%

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

6. Taylor expanded in z around 0 77.1%

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

   1. +-commutative 77.1%

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

8. Simplified 77.1%

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

9. Final simplification 77.1%

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

Alternative 16: 20.6% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -4.8e+51) x (* -0.5 b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e+51) {
		tmp = x;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.8d+51)) then
        tmp = x
    else
        tmp = (-0.5d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e+51) {
		tmp = x;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.8e+51:
		tmp = x
	else:
		tmp = -0.5 * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.8e+51)
		tmp = x;
	else
		tmp = Float64(-0.5 * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.8e+51)
		tmp = x;
	else
		tmp = -0.5 * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.8e+51], x, N[(-0.5 * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999997e51

   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 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 45.7%

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

   6. Taylor expanded in z around 0 35.7%

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

   if -4.7999999999999997e51 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. metadata-eval 73.9%

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

      3. +-commutative 73.9%

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

      4. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in b around inf 37.4%

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

      1. associate-*r* 34.1%

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

      2. *-commutative 34.1%

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

      3. associate-*r/ 34.1%

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

      4. metadata-eval 34.1%

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

      5. div-sub 34.1%

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

      6. sub-neg 34.1%

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

      7. metadata-eval 34.1%

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

      8. +-commutative 34.1%

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

   10. Simplified 34.1%

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

   11. Taylor expanded in a around 0 15.2%

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

       1. *-commutative 15.2%

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

   13. Simplified 15.2%

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

4. Final simplification 19.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.3% accurate, 115.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 40.8%

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

6. Taylor expanded in z around 0 19.5%

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

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + y) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024167 
(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)))