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

Percentage Accurate: 99.8% → 99.9%

Time: 12.6s

Alternatives: 18

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: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+144} \lor \neg \left(t\_1 \leq 6 \cdot 10^{+116}\right):\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -4e+144) (not (<= t_1 6e+116)))
     (+ x (+ y (* (+ a -0.5) b)))
     (+ (* z (- 1.0 (log t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -4e+144) || !(t_1 <= 6e+116)) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (z * (1.0 - log(t))) + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-4d+144)) .or. (.not. (t_1 <= 6d+116))) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -4e+144) || !(t_1 <= 6e+116)) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -4e+144) or not (t_1 <= 6e+116):
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -4e+144) || !(t_1 <= 6e+116))
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -4e+144) || ~((t_1 <= 6e+116)))
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+144], N[Not[LessEqual[t$95$1, 6e+116]], $MachinePrecision]], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $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) < -4.00000000000000009e144 or 5.9999999999999997e116 < (*.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 a around 0 99.9%

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

   4. Taylor expanded in z around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. distribute-rgt-in 94.0%

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

   6. Simplified 94.0%

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

   if -4.00000000000000009e144 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.9999999999999997e116

   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 b around 0 91.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+144} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 6 \cdot 10^{+116}\right):\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ t_2 := z \cdot \log t\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{-27}:\\ \;\;\;\;\left(\left(z + x\right) + t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 + \left(z + y\right)\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)) (t_2 (* z (log t))))
   (if (<= (+ x y) -5e-27) (- (+ (+ z x) t_1) t_2) (- (+ t_1 (+ z y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double t_2 = z * log(t);
	double tmp;
	if ((x + y) <= -5e-27) {
		tmp = ((z + x) + t_1) - t_2;
	} else {
		tmp = (t_1 + (z + y)) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a + (-0.5d0)) * b
    t_2 = z * log(t)
    if ((x + y) <= (-5d-27)) then
        tmp = ((z + x) + t_1) - t_2
    else
        tmp = (t_1 + (z + y)) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double t_2 = z * Math.log(t);
	double tmp;
	if ((x + y) <= -5e-27) {
		tmp = ((z + x) + t_1) - t_2;
	} else {
		tmp = (t_1 + (z + y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	t_2 = z * math.log(t)
	tmp = 0
	if (x + y) <= -5e-27:
		tmp = ((z + x) + t_1) - t_2
	else:
		tmp = (t_1 + (z + y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + -0.5) * b)
	t_2 = Float64(z * log(t))
	tmp = 0.0
	if (Float64(x + y) <= -5e-27)
		tmp = Float64(Float64(Float64(z + x) + t_1) - t_2);
	else
		tmp = Float64(Float64(t_1 + Float64(z + y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + -0.5) * b;
	t_2 = z * log(t);
	tmp = 0.0;
	if ((x + y) <= -5e-27)
		tmp = ((z + x) + t_1) - t_2;
	else
		tmp = (t_1 + (z + y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e-27], N[(N[(N[(z + x), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(t$95$1 + N[(z + y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000002e-27

   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 68.8%

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

      1. associate-+r+ 68.8%

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

      2. +-commutative 68.8%

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

      3. sub-neg 68.8%

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

      4. metadata-eval 68.8%

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

      5. +-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -5.0000000000000002e-27 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 87.7%

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

      1. associate-+r+ 87.7%

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

      2. +-commutative 87.7%

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

      3. sub-neg 87.7%

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

      4. metadata-eval 87.7%

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

      5. +-commutative 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-27}:\\ \;\;\;\;\left(\left(z + x\right) + \left(a + -0.5\right) \cdot b\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot b + \left(z + y\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+102}:\\ \;\;\;\;\left(\left(z + x\right) + \left(a + -0.5\right) \cdot b\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 5e+102)
   (- (+ (+ z x) (* (+ a -0.5) b)) (* z (log t)))
   (+ x (+ y (+ (* -0.5 b) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 5e+102) {
		tmp = ((z + x) + ((a + -0.5) * b)) - (z * log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (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 ((x + y) <= 5d+102) then
        tmp = ((z + x) + ((a + (-0.5d0)) * b)) - (z * log(t))
    else
        tmp = x + (y + (((-0.5d0) * b) + (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 ((x + y) <= 5e+102) {
		tmp = ((z + x) + ((a + -0.5) * b)) - (z * Math.log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 5e+102:
		tmp = ((z + x) + ((a + -0.5) * b)) - (z * math.log(t))
	else:
		tmp = x + (y + ((-0.5 * b) + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 5e+102)
		tmp = Float64(Float64(Float64(z + x) + Float64(Float64(a + -0.5) * b)) - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 5e+102)
		tmp = ((z + x) + ((a + -0.5) * b)) - (z * log(t));
	else
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+102], N[(N[(N[(z + x), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5e102

   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 80.5%

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

      1. associate-+r+ 80.5%

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

      2. +-commutative 80.5%

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

      3. sub-neg 80.5%

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

      4. metadata-eval 80.5%

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

      5. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   if 5e102 < (+.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 a around 0 99.9%

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

   4. Taylor expanded in z around 0 89.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+102}:\\ \;\;\;\;\left(\left(z + x\right) + \left(a + -0.5\right) \cdot b\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+225} \lor \neg \left(z \leq 6 \cdot 10^{+166}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e+225) (not (<= z 6e+166)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+225) || !(z <= 6e+166)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.1d+225)) .or. (.not. (z <= 6d+166))) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+225) || !(z <= 6e+166)) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e+225) or not (z <= 6e+166):
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e+225) || !(z <= 6e+166))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e+225) || ~((z <= 6e+166)))
		tmp = (z * (1.0 - log(t))) + (a * b);
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e+225], N[Not[LessEqual[z, 6e+166]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e225 or 5.99999999999999997e166 < z

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. *-lft-identity 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. distribute-rgt-out-- 99.7%

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

      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 86.8%

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

      1. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   if -2.1e225 < z < 5.99999999999999997e166

   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 a around 0 99.9%

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

   4. Taylor expanded in z around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. distribute-rgt-in 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+225} \lor \neg \left(z \leq 6 \cdot 10^{+166}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+241} \lor \neg \left(z \leq 3.7 \cdot 10^{+209}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.35e+241) (not (<= z 3.7e+209)))
   (+ (* z (- 1.0 (log t))) x)
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.35e+241) || !(z <= 3.7e+209)) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.35d+241)) .or. (.not. (z <= 3.7d+209))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.35e+241) || !(z <= 3.7e+209)) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.35e+241) or not (z <= 3.7e+209):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.35e+241) || !(z <= 3.7e+209))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.35e+241) || ~((z <= 3.7e+209)))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.35e+241], N[Not[LessEqual[z, 3.7e+209]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999986e241 or 3.7e209 < z

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. *-lft-identity 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. distribute-rgt-out-- 99.6%

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

      9. metadata-eval 99.6%

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

      10. fma-define 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 76.1%

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

   if -1.34999999999999986e241 < z < 3.7e209

   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 a around 0 99.9%

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

   4. Taylor expanded in z around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. distribute-rgt-in 88.4%

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

   6. Simplified 88.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+241} \lor \neg \left(z \leq 3.7 \cdot 10^{+209}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+240}:\\ \;\;\;\;t\_1 + y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+207}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -6.8e+240)
     (+ t_1 y)
     (if (<= z 3.6e+207) (+ x (+ y (* (+ a -0.5) b))) (+ t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -6.8e+240) {
		tmp = t_1 + y;
	} else if (z <= 3.6e+207) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-6.8d+240)) then
        tmp = t_1 + y
    else if (z <= 3.6d+207) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -6.8e+240) {
		tmp = t_1 + y;
	} else if (z <= 3.6e+207) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -6.8e+240:
		tmp = t_1 + y
	elif z <= 3.6e+207:
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -6.8e+240)
		tmp = Float64(t_1 + y);
	elseif (z <= 3.6e+207)
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -6.8e+240)
		tmp = t_1 + y;
	elseif (z <= 3.6e+207)
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+240], N[(t$95$1 + y), $MachinePrecision], If[LessEqual[z, 3.6e+207], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.80000000000000017e240

   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-- 99.4%

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

      9. metadata-eval 99.4%

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

      10. fma-define 99.4%

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

      11. sub-neg 99.4%

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

      12. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 92.1%

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

   if -6.80000000000000017e240 < z < 3.60000000000000014e207

   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 a around 0 99.9%

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

   4. Taylor expanded in z around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. distribute-rgt-in 88.4%

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

   6. Simplified 88.4%

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

   if 3.60000000000000014e207 < z

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate--l+ 99.3%

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

      3. associate-+r+ 99.3%

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

      4. +-commutative 99.3%

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

      5. *-lft-identity 99.3%

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

      6. metadata-eval 99.3%

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

      7. *-commutative 99.3%

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

      8. distribute-rgt-out-- 99.7%

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

      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 70.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+207}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+240} \lor \neg \left(z \leq 3.3 \cdot 10^{+219}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.8e+240) (not (<= z 3.3e+219)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e+240) || !(z <= 3.3e+219)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.8d+240)) .or. (.not. (z <= 3.3d+219))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e+240) || !(z <= 3.3e+219)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.8e+240) or not (z <= 3.3e+219):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.8e+240) || !(z <= 3.3e+219))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.8e+240) || ~((z <= 3.3e+219)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.8e+240], N[Not[LessEqual[z, 3.3e+219]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000017e240 or 3.3000000000000002e219 < z

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. *-lft-identity 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. distribute-rgt-out-- 99.5%

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

      9. metadata-eval 99.5%

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

      10. fma-define 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 78.5%

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

   6. Taylor expanded in z around inf 78.3%

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

   if -6.80000000000000017e240 < z < 3.3000000000000002e219

   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 a around 0 99.9%

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

   4. Taylor expanded in z around 0 87.8%

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

      1. +-commutative 87.8%

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

      2. distribute-rgt-in 87.8%

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

   6. Simplified 87.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+240} \lor \neg \left(z \leq 3.3 \cdot 10^{+219}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 10: 47.2% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -5e+29)
   (+ x (* a b))
   (if (<= (+ x y) 2e+165) (* b (- a 0.5)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e+29) {
		tmp = x + (a * b);
	} else if ((x + y) <= 2e+165) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-5d+29)) then
        tmp = x + (a * b)
    else if ((x + y) <= 2d+165) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e+29) {
		tmp = x + (a * b);
	} else if ((x + y) <= 2e+165) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -5e+29:
		tmp = x + (a * b)
	elif (x + y) <= 2e+165:
		tmp = b * (a - 0.5)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -5e+29)
		tmp = Float64(x + Float64(a * b));
	elseif (Float64(x + y) <= 2e+165)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -5e+29)
		tmp = x + (a * b);
	elseif ((x + y) <= 2e+165)
		tmp = b * (a - 0.5);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+29], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e+165], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5.0000000000000001e29

   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 63.1%

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

      1. associate-+r+ 63.1%

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

      2. +-commutative 63.1%

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

      3. sub-neg 63.1%

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

      4. metadata-eval 63.1%

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

      5. +-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around 0 55.8%

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

   7. Taylor expanded in a around inf 52.1%

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

      1. *-commutative 52.1%

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

   9. Simplified 52.1%

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

   if -5.0000000000000001e29 < (+.f64 x y) < 1.9999999999999998e165

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 68.6%

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

      1. associate-+r+ 68.6%

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

      2. sub-neg 68.6%

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

      3. metadata-eval 68.6%

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

      4. associate-/l* 67.7%

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

      5. +-commutative 67.7%

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

      6. associate-/l* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in b around inf 47.9%

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

      1. associate-*r/ 47.9%

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

      2. metadata-eval 47.9%

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

      3. div-sub 47.9%

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

      4. sub-neg 47.9%

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

      5. metadata-eval 47.9%

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

   10. Simplified 47.9%

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

   11. Taylor expanded in y around 0 52.4%

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

   if 1.9999999999999998e165 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in y around inf 40.4%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-99} \lor \neg \left(b \leq 5.5 \cdot 10^{-56}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.1e-99) (not (<= b 5.5e-56))) (+ x (* b (- a 0.5))) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e-99) || !(b <= 5.5e-56)) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.1d-99)) .or. (.not. (b <= 5.5d-56))) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e-99) || !(b <= 5.5e-56)) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.1e-99) or not (b <= 5.5e-56):
		tmp = x + (b * (a - 0.5))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.1e-99) || !(b <= 5.5e-56))
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.1e-99) || ~((b <= 5.5e-56)))
		tmp = x + (b * (a - 0.5));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.1e-99], N[Not[LessEqual[b, 5.5e-56]], $MachinePrecision]], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.10000000000000002e-99 or 5.4999999999999999e-56 < 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 y around 0 83.5%

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

      1. associate-+r+ 83.5%

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

      2. +-commutative 83.5%

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

      3. sub-neg 83.5%

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

      4. metadata-eval 83.5%

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

      5. +-commutative 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 69.9%

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

   if -1.10000000000000002e-99 < b < 5.4999999999999999e-56

   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 b around 0 93.8%

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

   6. Taylor expanded in z around 0 63.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-99} \lor \neg \left(b \leq 5.5 \cdot 10^{-56}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.0% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{+92} \lor \neg \left(b \leq 1.1 \cdot 10^{-15}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.36e+92) (not (<= b 1.1e-15))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.36e+92) || !(b <= 1.1e-15)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.36d+92)) .or. (.not. (b <= 1.1d-15))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.36e+92) || !(b <= 1.1e-15)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.36e+92) or not (b <= 1.1e-15):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.36e+92) || !(b <= 1.1e-15))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.36e+92) || ~((b <= 1.1e-15)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.36e+92], N[Not[LessEqual[b, 1.1e-15]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.36e92 or 1.09999999999999993e-15 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 73.0%

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

      1. associate-+r+ 73.0%

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

      2. sub-neg 73.0%

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

      3. metadata-eval 73.0%

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

      4. associate-/l* 72.9%

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

      5. +-commutative 72.9%

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

      6. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in b around inf 65.7%

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

      1. associate-*r/ 65.7%

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

      2. metadata-eval 65.7%

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

      3. div-sub 65.7%

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

      4. sub-neg 65.7%

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

      5. metadata-eval 65.7%

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

   10. Simplified 65.7%

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

   11. Taylor expanded in y around 0 68.0%

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

   if -1.36e92 < b < 1.09999999999999993e-15

   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 b around 0 85.8%

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

   6. Taylor expanded in z around 0 59.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{+92} \lor \neg \left(b \leq 1.1 \cdot 10^{-15}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.4% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -1 \cdot 10^{-93}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -1e-93) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -1e-93) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-1d-93)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -1e-93) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -1e-93:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -1e-93)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -1e-93)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -1e-93], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.999999999999999e-94

   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 70.7%

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

      1. associate-+r+ 70.7%

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

      2. +-commutative 70.7%

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

      3. sub-neg 70.7%

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

      4. metadata-eval 70.7%

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

      5. +-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around 0 53.6%

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

   if -9.999999999999999e-94 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in z around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. distribute-rgt-in 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in x around 0 66.0%

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

Alternative 14: 52.4% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+94} \lor \neg \left(a \leq 3.6 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.7e+94) (not (<= a 3.6e+93))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e+94) || !(a <= 3.6e+93)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.7d+94)) .or. (.not. (a <= 3.6d+93))) then
        tmp = a * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e+94) || !(a <= 3.6e+93)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.7e+94) or not (a <= 3.6e+93):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.7e+94) || !(a <= 3.6e+93))
		tmp = Float64(a * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.7e+94) || ~((a <= 3.6e+93)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.7e+94], N[Not[LessEqual[a, 3.6e+93]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7000000000000001e94 or 3.5999999999999999e93 < 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 y around inf 75.2%

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

      1. associate-+r+ 75.2%

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

      2. sub-neg 75.2%

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

      3. metadata-eval 75.2%

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

      4. associate-/l* 74.0%

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

      5. +-commutative 74.0%

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

      6. associate-/l* 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in b around inf 56.6%

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

      1. associate-*r/ 56.6%

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

      2. metadata-eval 56.6%

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

      3. div-sub 56.6%

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

      4. sub-neg 56.6%

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

      5. metadata-eval 56.6%

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

   10. Simplified 56.6%

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

   11. Taylor expanded in a around inf 63.6%

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

   if -2.7000000000000001e94 < a < 3.5999999999999999e93

   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 b around 0 78.1%

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

   6. Taylor expanded in z around 0 51.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+94} \lor \neg \left(a \leq 3.6 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.7% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-295}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8e+181) x (if (<= x 4e-295) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+181) {
		tmp = x;
	} else if (x <= 4e-295) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8d+181)) then
        tmp = x
    else if (x <= 4d-295) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+181) {
		tmp = x;
	} else if (x <= 4e-295) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8e+181:
		tmp = x
	elif x <= 4e-295:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8e+181)
		tmp = x;
	elseif (x <= 4e-295)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8e+181)
		tmp = x;
	elseif (x <= 4e-295)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8e+181], x, If[LessEqual[x, 4e-295], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -7.9999999999999993e181

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 78.9%

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

   6. Taylor expanded in z around 0 79.2%

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

   if -7.9999999999999993e181 < x < 4.00000000000000024e-295

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.8%

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

      1. associate-+r+ 80.8%

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

      2. sub-neg 80.8%

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

      3. metadata-eval 80.8%

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

      4. associate-/l* 80.7%

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

      5. +-commutative 80.7%

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

      6. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in b around inf 43.6%

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

      1. associate-*r/ 43.6%

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

      2. metadata-eval 43.6%

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

      3. div-sub 43.5%

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

      4. sub-neg 43.5%

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

      5. metadata-eval 43.5%

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

   10. Simplified 43.5%

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

   11. Taylor expanded in a around inf 34.6%

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

   if 4.00000000000000024e-295 < x

   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 a around 0 99.8%

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

   4. Taylor expanded in y around inf 27.1%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-295}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 78.8% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $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 a around 0 99.9%

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

4. Taylor expanded in z around 0 79.7%

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

   1. +-commutative 79.7%

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

   2. distribute-rgt-in 79.7%

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

6. Simplified 79.7%

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

7. Final simplification 79.7%

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

Alternative 17: 29.1% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1.75e+54) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.75e+54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.75d+54)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.75e+54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.75e+54:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.75e+54)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.75e+54)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.75e+54], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e54

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 56.1%

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

   6. Taylor expanded in z around 0 48.8%

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

   if -1.7500000000000001e54 < x

   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 a around 0 99.8%

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

   4. Taylor expanded in y around inf 26.6%

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

Alternative 18: 22.1% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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 38.6%

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

6. Taylor expanded in z around 0 19.4%

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

Developer Target 1: 99.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024157 
(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)))