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

Percentage Accurate: 99.8% → 99.8%

Time: 12.9s

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+140} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+154}\right):\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -2e+140) (not (<= t_1 5e+154)))
     (+ x (+ y t_1))
     (+ (* z (- 1.0 (log t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -2e+140) || !(t_1 <= 5e+154)) {
		tmp = x + (y + t_1);
	} else {
		tmp = (z * (1.0 - log(t))) + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if ((t_1 <= (-2d+140)) .or. (.not. (t_1 <= 5d+154))) then
        tmp = x + (y + t_1)
    else
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -2e+140) || !(t_1 <= 5e+154)) {
		tmp = x + (y + t_1);
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -2e+140) or not (t_1 <= 5e+154):
		tmp = x + (y + t_1)
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -2e+140) || !(t_1 <= 5e+154))
		tmp = Float64(x + Float64(y + t_1));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((t_1 <= -2e+140) || ~((t_1 <= 5e+154)))
		tmp = x + (y + t_1);
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+140], N[Not[LessEqual[t$95$1, 5e+154]], $MachinePrecision]], N[(x + N[(y + t$95$1), $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) < -2.00000000000000012e140 or 5.00000000000000004e154 < (*.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. 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+ 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 z around 0 92.9%

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

   if -2.00000000000000012e140 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000004e154

   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+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 91.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{+140} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{+154}\right):\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+191}:\\ \;\;\;\;t\_1 + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -4e+191)
     (+ t_1 (- z (* z (log t))))
     (if (<= t_1 5e+154) (+ (* z (- 1.0 (log t))) (+ x y)) (+ x (+ y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -4e+191) {
		tmp = t_1 + (z - (z * log(t)));
	} else if (t_1 <= 5e+154) {
		tmp = (z * (1.0 - log(t))) + (x + y);
	} else {
		tmp = x + (y + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-4d+191)) then
        tmp = t_1 + (z - (z * log(t)))
    else if (t_1 <= 5d+154) then
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    else
        tmp = x + (y + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -4e+191) {
		tmp = t_1 + (z - (z * Math.log(t)));
	} else if (t_1 <= 5e+154) {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	} else {
		tmp = x + (y + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -4e+191:
		tmp = t_1 + (z - (z * math.log(t)))
	elif t_1 <= 5e+154:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	else:
		tmp = x + (y + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -4e+191)
		tmp = Float64(t_1 + Float64(z - Float64(z * log(t))));
	elseif (t_1 <= 5e+154)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(x + Float64(y + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -4e+191)
		tmp = t_1 + (z - (z * log(t)));
	elseif (t_1 <= 5e+154)
		tmp = (z * (1.0 - log(t))) + (x + y);
	else
		tmp = x + (y + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+191], N[(t$95$1 + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+154], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.00000000000000029e191

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.8%

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

   if -4.00000000000000029e191 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000004e154

   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+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 90.7%

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

   if 5.00000000000000004e154 < (*.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. 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+ 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 z around 0 94.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -4 \cdot 10^{+191}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{-14}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + t\_1\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= (+ x y) -5e-14) (+ x (+ y t_1)) (- (+ y (+ z t_1)) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((x + y) <= -5e-14) {
		tmp = x + (y + t_1);
	} else {
		tmp = (y + (z + t_1)) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if ((x + y) <= (-5d-14)) then
        tmp = x + (y + t_1)
    else
        tmp = (y + (z + t_1)) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((x + y) <= -5e-14) {
		tmp = x + (y + t_1);
	} else {
		tmp = (y + (z + t_1)) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (x + y) <= -5e-14:
		tmp = x + (y + t_1)
	else:
		tmp = (y + (z + t_1)) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (Float64(x + y) <= -5e-14)
		tmp = Float64(x + Float64(y + t_1));
	else
		tmp = Float64(Float64(y + Float64(z + t_1)) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((x + y) <= -5e-14)
		tmp = x + (y + t_1);
	else
		tmp = (y + (z + t_1)) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e-14], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000002e-14

   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 z around 0 86.7%

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

   if -5.0000000000000002e-14 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-14}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + \left(a - 0.5\right) \cdot b\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+191}:\\ \;\;\;\;y + t\_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+209}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -8.6e+191)
     (+ y t_1)
     (if (<= z 2.75e+209) (+ x (+ y (* (- a 0.5) b))) (+ t_1 (* b -0.5))))))

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 <= -8.6e+191) {
		tmp = y + t_1;
	} else if (z <= 2.75e+209) {
		tmp = x + (y + ((a - 0.5) * b));
	} else {
		tmp = t_1 + (b * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-8.6d+191)) then
        tmp = y + t_1
    else if (z <= 2.75d+209) then
        tmp = x + (y + ((a - 0.5d0) * b))
    else
        tmp = t_1 + (b * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -8.6e+191) {
		tmp = y + t_1;
	} else if (z <= 2.75e+209) {
		tmp = x + (y + ((a - 0.5) * b));
	} else {
		tmp = t_1 + (b * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -8.6e+191:
		tmp = y + t_1
	elif z <= 2.75e+209:
		tmp = x + (y + ((a - 0.5) * b))
	else:
		tmp = t_1 + (b * -0.5)
	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 <= -8.6e+191)
		tmp = Float64(y + t_1);
	elseif (z <= 2.75e+209)
		tmp = Float64(x + Float64(y + Float64(Float64(a - 0.5) * b)));
	else
		tmp = Float64(t_1 + Float64(b * -0.5));
	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 <= -8.6e+191)
		tmp = y + t_1;
	elseif (z <= 2.75e+209)
		tmp = x + (y + ((a - 0.5) * b));
	else
		tmp = t_1 + (b * -0.5);
	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, -8.6e+191], N[(y + t$95$1), $MachinePrecision], If[LessEqual[z, 2.75e+209], N[(x + N[(y + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999995e191

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 96.1%

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

   4. Taylor expanded in b around 0 73.2%

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

      1. associate--l+ 73.2%

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

      2. *-rgt-identity 73.2%

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

      3. unsub-neg 73.2%

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

      4. distribute-rgt-neg-in 73.2%

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

      5. log-rec 73.2%

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

      6. distribute-lft-in 73.2%

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

      7. log-rec 73.2%

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

      8. sub-neg 73.2%

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

   6. Simplified 73.2%

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

   if -8.5999999999999995e191 < z < 2.74999999999999984e209

   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 z around 0 88.2%

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

   if 2.74999999999999984e209 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 62.0%

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

      1. associate-/l* 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in z around inf 65.6%

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

      1. div-sub 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in a around 0 87.2%

      \[\leadsto \color{blue}{-0.5 \cdot b + z \cdot \left(1 - \log t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+191}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+209}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + b \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+188} \lor \neg \left(z \leq 5.5 \cdot 10^{+143}\right):\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.35e+188) (not (<= z 5.5e+143)))
   (+ y (* 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 <= -2.35e+188) || !(z <= 5.5e+143)) {
		tmp = y + (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 <= (-2.35d+188)) .or. (.not. (z <= 5.5d+143))) then
        tmp = y + (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 <= -2.35e+188) || !(z <= 5.5e+143)) {
		tmp = y + (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 <= -2.35e+188) or not (z <= 5.5e+143):
		tmp = y + (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 <= -2.35e+188) || !(z <= 5.5e+143))
		tmp = Float64(y + 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 <= -2.35e+188) || ~((z <= 5.5e+143)))
		tmp = y + (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, -2.35e+188], N[Not[LessEqual[z, 5.5e+143]], $MachinePrecision]], N[(y + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $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 < -2.3499999999999999e188 or 5.4999999999999997e143 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in b around 0 67.7%

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

      1. associate--l+ 67.7%

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

      2. *-rgt-identity 67.7%

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

      3. unsub-neg 67.7%

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

      4. distribute-rgt-neg-in 67.7%

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

      5. log-rec 67.7%

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

      6. distribute-lft-in 67.7%

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

      7. log-rec 67.7%

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

      8. sub-neg 67.7%

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

   6. Simplified 67.7%

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

   if -2.3499999999999999e188 < z < 5.4999999999999997e143

   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 z around 0 91.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+188} \lor \neg \left(z \leq 5.5 \cdot 10^{+143}\right):\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+244} \lor \neg \left(z \leq 2.4 \cdot 10^{+209}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e+244) (not (<= z 2.4e+209)))
   (* 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 <= -5.4e+244) || !(z <= 2.4e+209)) {
		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 <= (-5.4d+244)) .or. (.not. (z <= 2.4d+209))) 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 <= -5.4e+244) || !(z <= 2.4e+209)) {
		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 <= -5.4e+244) or not (z <= 2.4e+209):
		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 <= -5.4e+244) || !(z <= 2.4e+209))
		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 <= -5.4e+244) || ~((z <= 2.4e+209)))
		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, -5.4e+244], N[Not[LessEqual[z, 2.4e+209]], $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 < -5.39999999999999995e244 or 2.39999999999999996e209 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

   4. Taylor expanded in z around inf 68.1%

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

   if -5.39999999999999995e244 < z < 2.39999999999999996e209

   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 z around 0 86.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+244} \lor \neg \left(z \leq 2.4 \cdot 10^{+209}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+244}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+209}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.2e+244)
   (* z (- 1.0 (log t)))
   (if (<= z 3.05e+209) (+ x (+ y (* (- a 0.5) b))) (- z (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e+244) {
		tmp = z * (1.0 - log(t));
	} else if (z <= 3.05e+209) {
		tmp = x + (y + ((a - 0.5) * b));
	} else {
		tmp = z - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.2d+244)) then
        tmp = z * (1.0d0 - log(t))
    else if (z <= 3.05d+209) then
        tmp = x + (y + ((a - 0.5d0) * b))
    else
        tmp = z - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e+244) {
		tmp = z * (1.0 - Math.log(t));
	} else if (z <= 3.05e+209) {
		tmp = x + (y + ((a - 0.5) * b));
	} else {
		tmp = z - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.2e+244:
		tmp = z * (1.0 - math.log(t))
	elif z <= 3.05e+209:
		tmp = x + (y + ((a - 0.5) * b))
	else:
		tmp = z - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.2e+244)
		tmp = Float64(z * Float64(1.0 - log(t)));
	elseif (z <= 3.05e+209)
		tmp = Float64(x + Float64(y + Float64(Float64(a - 0.5) * b)));
	else
		tmp = Float64(z - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.2e+244)
		tmp = z * (1.0 - log(t));
	elseif (z <= 3.05e+209)
		tmp = x + (y + ((a - 0.5) * b));
	else
		tmp = z - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.2e+244], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+209], N[(x + N[(y + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000001e244

   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. Add Preprocessing

   3. Taylor expanded in x around 0 99.4%

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

   4. Taylor expanded in z around inf 66.7%

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

   if -6.20000000000000001e244 < z < 3.05000000000000015e209

   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 z around 0 86.4%

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

   if 3.05000000000000015e209 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in z around inf 68.9%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+244}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+209}:\\ \;\;\;\;x + \left(y + \left(a - 0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.2% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+191} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+167}\right):\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -4e+191) (not (<= t_1 5e+167)))
     (+ x t_1)
     (+ x (+ y (* b -0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -4e+191) || !(t_1 <= 5e+167)) {
		tmp = x + t_1;
	} else {
		tmp = x + (y + (b * -0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if ((t_1 <= (-4d+191)) .or. (.not. (t_1 <= 5d+167))) then
        tmp = x + t_1
    else
        tmp = x + (y + (b * (-0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -4e+191) || !(t_1 <= 5e+167)) {
		tmp = x + t_1;
	} else {
		tmp = x + (y + (b * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -4e+191) or not (t_1 <= 5e+167):
		tmp = x + t_1
	else:
		tmp = x + (y + (b * -0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -4e+191) || !(t_1 <= 5e+167))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(y + Float64(b * -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((t_1 <= -4e+191) || ~((t_1 <= 5e+167)))
		tmp = x + t_1;
	else
		tmp = x + (y + (b * -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+191], N[Not[LessEqual[t$95$1, 5e+167]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(x + N[(y + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.00000000000000029e191 or 4.9999999999999997e167 < (*.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. 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+ 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 z around 0 92.5%

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

   6. Taylor expanded in y around 0 90.3%

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

   if -4.00000000000000029e191 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999997e167

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 70.9%

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

   6. Taylor expanded in a around 0 66.6%

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

      1. *-commutative 66.6%

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

   8. Simplified 66.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -4 \cdot 10^{+191} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{+167}\right):\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.1% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;b \leq -2.16 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+195}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= b -2.16e+15)
     t_1
     (if (<= b 2.8e-36) (+ x y) (if (<= b 3e+195) (+ x (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (b <= -2.16e+15) {
		tmp = t_1;
	} else if (b <= 2.8e-36) {
		tmp = x + y;
	} else if (b <= 3e+195) {
		tmp = x + (a * b);
	} else {
		tmp = 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 = (a - 0.5d0) * b
    if (b <= (-2.16d+15)) then
        tmp = t_1
    else if (b <= 2.8d-36) then
        tmp = x + y
    else if (b <= 3d+195) then
        tmp = x + (a * b)
    else
        tmp = 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 = (a - 0.5) * b;
	double tmp;
	if (b <= -2.16e+15) {
		tmp = t_1;
	} else if (b <= 2.8e-36) {
		tmp = x + y;
	} else if (b <= 3e+195) {
		tmp = x + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if b <= -2.16e+15:
		tmp = t_1
	elif b <= 2.8e-36:
		tmp = x + y
	elif b <= 3e+195:
		tmp = x + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (b <= -2.16e+15)
		tmp = t_1;
	elseif (b <= 2.8e-36)
		tmp = Float64(x + y);
	elseif (b <= 3e+195)
		tmp = Float64(x + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (b <= -2.16e+15)
		tmp = t_1;
	elseif (b <= 2.8e-36)
		tmp = x + y;
	elseif (b <= 3e+195)
		tmp = x + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.16e+15], t$95$1, If[LessEqual[b, 2.8e-36], N[(x + y), $MachinePrecision], If[LessEqual[b, 3e+195], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.16e15 or 3.0000000000000001e195 < 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 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 73.1%

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

   if -2.16e15 < b < 2.8000000000000001e-36

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 71.3%

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

   6. Taylor expanded in a around inf 69.4%

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

   7. Taylor expanded in b around inf 44.5%

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

   8. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   10. Simplified 65.1%

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

   if 2.8000000000000001e-36 < b < 3.0000000000000001e195

   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 z around 0 82.7%

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

   6. Taylor expanded in a around inf 61.0%

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

      1. *-commutative 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.16 \cdot 10^{+15}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+195}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.02 \cdot 10^{+15} \lor \neg \left(b \leq 6.2 \cdot 10^{+100}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.02e+15) (not (<= b 6.2e+100))) (* (- a 0.5) b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.02e+15) || !(b <= 6.2e+100)) {
		tmp = (a - 0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.02d+15)) .or. (.not. (b <= 6.2d+100))) then
        tmp = (a - 0.5d0) * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.02e+15) || !(b <= 6.2e+100)) {
		tmp = (a - 0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.02e+15) or not (b <= 6.2e+100):
		tmp = (a - 0.5) * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.02e+15) || !(b <= 6.2e+100))
		tmp = Float64(Float64(a - 0.5) * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.02e+15) || ~((b <= 6.2e+100)))
		tmp = (a - 0.5) * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.02e+15], N[Not[LessEqual[b, 6.2e+100]], $MachinePrecision]], N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.02e15 or 6.20000000000000014e100 < 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 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 69.4%

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

   if -2.02e15 < b < 6.20000000000000014e100

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 71.9%

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

   6. Taylor expanded in a around inf 69.0%

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

   7. Taylor expanded in b around inf 48.2%

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

   8. Taylor expanded in b around 0 61.7%

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

      1. +-commutative 61.7%

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

   10. Simplified 61.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.02 \cdot 10^{+15} \lor \neg \left(b \leq 6.2 \cdot 10^{+100}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+124} \lor \neg \left(b \leq 6.2 \cdot 10^{+100}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+124) (not (<= b 6.2e+100))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+124) || !(b <= 6.2e+100)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.5d+124)) .or. (.not. (b <= 6.2d+100))) then
        tmp = a * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+124) || !(b <= 6.2e+100)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e+124) or not (b <= 6.2e+100):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e+124) || !(b <= 6.2e+100))
		tmp = Float64(a * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e+124) || ~((b <= 6.2e+100)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e+124], N[Not[LessEqual[b, 6.2e+100]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5000000000000001e124 or 6.20000000000000014e100 < b

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -3.5000000000000001e124 < b < 6.20000000000000014e100

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 70.6%

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

   6. Taylor expanded in a around inf 67.1%

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

   7. Taylor expanded in b around inf 48.7%

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

   8. Taylor expanded in b around 0 57.6%

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

      1. +-commutative 57.6%

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

   10. Simplified 57.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+124} \lor \neg \left(b \leq 6.2 \cdot 10^{+100}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.6e-147) x (if (<= y 7.5e+76) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e-147) {
		tmp = x;
	} else if (y <= 7.5e+76) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.6d-147)) then
        tmp = x
    else if (y <= 7.5d+76) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e-147) {
		tmp = x;
	} else if (y <= 7.5e+76) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.6e-147:
		tmp = x
	elif y <= 7.5e+76:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.6e-147)
		tmp = x;
	elseif (y <= 7.5e+76)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.6e-147)
		tmp = x;
	elseif (y <= 7.5e+76)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.6e-147], x, If[LessEqual[y, 7.5e+76], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6000000000000001e-147

   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 22.2%

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

   if -5.6000000000000001e-147 < y < 7.4999999999999995e76

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf 30.1%

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

      1. *-commutative 30.1%

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

   7. Simplified 30.1%

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

   if 7.4999999999999995e76 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-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 55.7%

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

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.5e-25) (+ x (* (- a 0.5) b)) (+ x (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.5e-25) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = x + (y + (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 (y <= 1.5d-25) then
        tmp = x + ((a - 0.5d0) * b)
    else
        tmp = x + (y + (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 (y <= 1.5e-25) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = x + (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.5e-25:
		tmp = x + ((a - 0.5) * b)
	else:
		tmp = x + (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.5e-25)
		tmp = Float64(x + Float64(Float64(a - 0.5) * b));
	else
		tmp = Float64(x + Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.5e-25)
		tmp = x + ((a - 0.5) * b);
	else
		tmp = x + (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.5e-25], N[(x + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4999999999999999e-25

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 76.7%

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

   6. Taylor expanded in y around 0 60.6%

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

   if 1.4999999999999999e-25 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-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 z around 0 79.2%

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

   6. Taylor expanded in a around inf 78.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+160}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 7.2e+160) (+ x (* (- a 0.5) b)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7.2e+160) {
		tmp = x + ((a - 0.5) * 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 (y <= 7.2d+160) then
        tmp = x + ((a - 0.5d0) * 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 (y <= 7.2e+160) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 7.2e+160:
		tmp = x + ((a - 0.5) * b)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 7.2e+160)
		tmp = Float64(x + Float64(Float64(a - 0.5) * 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 (y <= 7.2e+160)
		tmp = x + ((a - 0.5) * b);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 7.2e+160], N[(x + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.20000000000000042e160

   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 z around 0 76.2%

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

   6. Taylor expanded in y around 0 59.8%

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

   if 7.20000000000000042e160 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-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 z around 0 84.8%

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

   6. Taylor expanded in a around inf 84.8%

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

   7. Taylor expanded in b around inf 35.3%

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

   8. Taylor expanded in b around 0 76.4%

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

      1. +-commutative 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+160}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 77.5% 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. 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 z around 0 77.3%

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

6. Final simplification 77.3%

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

Alternative 17: 27.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.25e+61) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.25e+61) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.25d+61) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.25e+61) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.25e+61:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.25e+61)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.25e+61)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.25e+61], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.25000000000000004e61

   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 25.4%

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

   if 1.25000000000000004e61 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-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 51.3%

      \[\leadsto \color{blue}{y} \]
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 23.6%

   \[\leadsto \color{blue}{x} \]
6. 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 2024128 
(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)))