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

Percentage Accurate: 99.8% → 99.9%

Time: 12.9s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+148} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+92}\right):\\ \;\;\;\;t\_1 + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+148) (not (<= t_1 5e+92)))
     (+ t_1 (+ x y))
     (+ x (+ (* z (- 1.0 (log t))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+148) || !(t_1 <= 5e+92)) {
		tmp = t_1 + (x + y);
	} else {
		tmp = x + ((z * (1.0 - log(t))) + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+148)) .or. (.not. (t_1 <= 5d+92))) then
        tmp = t_1 + (x + y)
    else
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+148) || !(t_1 <= 5e+92)) {
		tmp = t_1 + (x + y);
	} else {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+148) or not (t_1 <= 5e+92):
		tmp = t_1 + (x + y)
	else:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+148) || !(t_1 <= 5e+92))
		tmp = Float64(t_1 + Float64(x + y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+148) || ~((t_1 <= 5e+92)))
		tmp = t_1 + (x + y);
	else
		tmp = x + ((z * (1.0 - log(t))) + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+148], N[Not[LessEqual[t$95$1, 5e+92]], $MachinePrecision]], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e148 or 5.00000000000000022e92 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

      1. add-exp-log 44.0%

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

   4. Applied egg-rr 44.0%

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

   5. Taylor expanded in z around 0 94.3%

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

   if -1e148 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000022e92

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 89.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+148} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.68 \cdot 10^{+41} \lor \neg \left(z \leq 8 \cdot 10^{-34}\right):\\ \;\;\;\;\left(x + \left(y + \left(z + a \cdot b\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.68e+41) (not (<= z 8e-34)))
   (- (+ x (+ y (+ z (* a b)))) (* z (log t)))
   (+ x (+ y (+ (* -0.5 b) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.68e+41) || !(z <= 8e-34)) {
		tmp = (x + (y + (z + (a * b)))) - (z * log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.68d+41)) .or. (.not. (z <= 8d-34))) then
        tmp = (x + (y + (z + (a * b)))) - (z * log(t))
    else
        tmp = x + (y + (((-0.5d0) * b) + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.68e+41) || !(z <= 8e-34)) {
		tmp = (x + (y + (z + (a * b)))) - (z * Math.log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.68e+41) or not (z <= 8e-34):
		tmp = (x + (y + (z + (a * b)))) - (z * math.log(t))
	else:
		tmp = x + (y + ((-0.5 * b) + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.68e+41) || !(z <= 8e-34))
		tmp = Float64(Float64(x + Float64(y + Float64(z + Float64(a * b)))) - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.68e+41) || ~((z <= 8e-34)))
		tmp = (x + (y + (z + (a * b)))) - (z * log(t));
	else
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.68e+41], N[Not[LessEqual[z, 8e-34]], $MachinePrecision]], N[(N[(x + N[(y + N[(z + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.68000000000000008e41 or 7.99999999999999942e-34 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.7%

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

   6. Taylor expanded in a around inf 97.9%

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

      1. *-commutative 97.9%

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

   8. Simplified 97.9%

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

   if -1.68000000000000008e41 < z < 7.99999999999999942e-34

   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. fma-define 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate--l+ 100.0%

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

      6. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in z around 0 97.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.68 \cdot 10^{+41} \lor \neg \left(z \leq 8 \cdot 10^{-34}\right):\\ \;\;\;\;\left(x + \left(y + \left(z + a \cdot b\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+48} \lor \neg \left(z \leq 3.1 \cdot 10^{+143}\right):\\ \;\;\;\;\left(x + \left(z + a \cdot b\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.28e+48) (not (<= z 3.1e+143)))
   (- (+ x (+ z (* a b))) (* z (log t)))
   (+ x (+ y (+ (* -0.5 b) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.28e+48) || !(z <= 3.1e+143)) {
		tmp = (x + (z + (a * b))) - (z * log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.28d+48)) .or. (.not. (z <= 3.1d+143))) then
        tmp = (x + (z + (a * b))) - (z * log(t))
    else
        tmp = x + (y + (((-0.5d0) * b) + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.28e+48) || !(z <= 3.1e+143)) {
		tmp = (x + (z + (a * b))) - (z * Math.log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.28e+48) or not (z <= 3.1e+143):
		tmp = (x + (z + (a * b))) - (z * math.log(t))
	else:
		tmp = x + (y + ((-0.5 * b) + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.28e+48) || !(z <= 3.1e+143))
		tmp = Float64(Float64(x + Float64(z + Float64(a * b))) - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.28e+48) || ~((z <= 3.1e+143)))
		tmp = (x + (z + (a * b))) - (z * log(t));
	else
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.28e+48], N[Not[LessEqual[z, 3.1e+143]], $MachinePrecision]], N[(N[(x + N[(z + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e48 or 3.0999999999999999e143 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. associate--l+ 99.7%

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

      6. associate-+l+ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 99.7%

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

   6. Taylor expanded in a around inf 99.7%

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

      1. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around 0 90.3%

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

   if -1.28e48 < z < 3.0999999999999999e143

   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. fma-define 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate--l+ 100.0%

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

      6. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in z around 0 96.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+48} \lor \neg \left(z \leq 3.1 \cdot 10^{+143}\right):\\ \;\;\;\;\left(x + \left(z + a \cdot b\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := z + b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{-76}:\\ \;\;\;\;\left(x + t\_2\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (+ z (* b (- a 0.5)))))
   (if (<= (+ x y) -4e-76) (- (+ x t_2) t_1) (- (+ y t_2) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -4e-76) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = z + (b * (a - 0.5d0))
    if ((x + y) <= (-4d-76)) then
        tmp = (x + t_2) - t_1
    else
        tmp = (y + t_2) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double t_2 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -4e-76) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = z + (b * (a - 0.5))
	tmp = 0
	if (x + y) <= -4e-76:
		tmp = (x + t_2) - t_1
	else:
		tmp = (y + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(z + Float64(b * Float64(a - 0.5)))
	tmp = 0.0
	if (Float64(x + y) <= -4e-76)
		tmp = Float64(Float64(x + t_2) - t_1);
	else
		tmp = Float64(Float64(y + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = z + (b * (a - 0.5));
	tmp = 0.0;
	if ((x + y) <= -4e-76)
		tmp = (x + t_2) - t_1;
	else
		tmp = (y + t_2) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -4e-76], N[(N[(x + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(y + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.99999999999999971e-76

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 74.7%

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

   if -3.99999999999999971e-76 < (+.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. 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. fma-define 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 80.8%

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

Alternative 6: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+108} \lor \neg \left(z \leq 3.5 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.8e+108) (not (<= z 3.5e+153)))
   (+ (* z (- 1.0 (log t))) x)
   (+ x (+ y (+ (* -0.5 b) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.8e+108) || !(z <= 3.5e+153)) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.8d+108)) .or. (.not. (z <= 3.5d+153))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = x + (y + (((-0.5d0) * b) + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.8e+108) || !(z <= 3.5e+153)) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.8e+108) or not (z <= 3.5e+153):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = x + (y + ((-0.5 * b) + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.8e+108) || !(z <= 3.5e+153))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.8e+108) || ~((z <= 3.5e+153)))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.8e+108], N[Not[LessEqual[z, 3.5e+153]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000005e108 or 3.4999999999999999e153 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 73.7%

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

   if -8.8000000000000005e108 < z < 3.4999999999999999e153

   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. fma-define 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate--l+ 100.0%

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

      6. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in z around 0 95.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+108} \lor \neg \left(z \leq 3.5 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((-0.5d0) * b) + (a * b))))) - (z * log(t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(y + N[(z + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $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. fma-define 99.9%

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

   3. sub-neg 99.9%

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

   4. metadata-eval 99.9%

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

   5. associate--l+ 99.9%

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

   6. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in a around 0 99.9%

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

Alternative 8: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+252} \lor \neg \left(z \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e+252) (not (<= z 1.2e+181)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (+ (* -0.5 b) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e+252) || !(z <= 1.2e+181)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3d+252)) .or. (.not. (z <= 1.2d+181))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + (((-0.5d0) * b) + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e+252) || !(z <= 1.2e+181)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e+252) or not (z <= 1.2e+181):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((-0.5 * b) + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e+252) || !(z <= 1.2e+181))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e+252) || ~((z <= 1.2e+181)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e+252], N[Not[LessEqual[z, 1.2e+181]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999989e252 or 1.20000000000000001e181 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 82.2%

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

   6. Taylor expanded in z around inf 70.2%

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

   if -2.99999999999999989e252 < z < 1.20000000000000001e181

   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. fma-define 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 88.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+252} \lor \neg \left(z \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 10: 78.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1000000 \lor \neg \left(a - 0.5 \leq -0.5\right):\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- a 0.5) -1000000.0) (not (<= (- a 0.5) -0.5)))
   (+ x (+ y (* a b)))
   (+ x (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -1000000.0) || !((a - 0.5) <= -0.5)) {
		tmp = x + (y + (a * b));
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a - 0.5d0) <= (-1000000.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.5d0)))) then
        tmp = x + (y + (a * b))
    else
        tmp = x + (y + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -1000000.0) || !((a - 0.5) <= -0.5)) {
		tmp = x + (y + (a * b));
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a - 0.5) <= -1000000.0) or not ((a - 0.5) <= -0.5):
		tmp = x + (y + (a * b))
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -1000000.0) || !(Float64(a - 0.5) <= -0.5))
		tmp = Float64(x + Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a - 0.5) <= -1000000.0) || ~(((a - 0.5) <= -0.5)))
		tmp = x + (y + (a * b));
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.5]], $MachinePrecision]], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -1e6 or -0.5 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.9%

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

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 83.8%

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

   7. Taylor expanded in a around inf 83.2%

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

      1. *-commutative 99.3%

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

   9. Simplified 83.2%

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

   if -1e6 < (-.f64 a #s(literal 1/2 binary64)) < -0.5

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.8%

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

   6. Taylor expanded in z around 0 74.5%

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

   7. Taylor expanded in a around 0 74.0%

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

      1. *-commutative 74.0%

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

   9. Simplified 74.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1000000 \lor \neg \left(a - 0.5 \leq -0.5\right):\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.500005 \lor \neg \left(a - 0.5 \leq 5 \cdot 10^{+73}\right):\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- a 0.5) -0.500005) (not (<= (- a 0.5) 5e+73)))
   (+ x (* (+ a -0.5) b))
   (+ x (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -0.500005) || !((a - 0.5) <= 5e+73)) {
		tmp = x + ((a + -0.5) * b);
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a - 0.5d0) <= (-0.500005d0)) .or. (.not. ((a - 0.5d0) <= 5d+73))) then
        tmp = x + ((a + (-0.5d0)) * b)
    else
        tmp = x + (y + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -0.500005) || !((a - 0.5) <= 5e+73)) {
		tmp = x + ((a + -0.5) * b);
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a - 0.5) <= -0.500005) or not ((a - 0.5) <= 5e+73):
		tmp = x + ((a + -0.5) * b)
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -0.500005) || !(Float64(a - 0.5) <= 5e+73))
		tmp = Float64(x + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a - 0.5) <= -0.500005) || ~(((a - 0.5) <= 5e+73)))
		tmp = x + ((a + -0.5) * b);
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -0.500005], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], 5e+73]], $MachinePrecision]], N[(x + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -0.50000500000000003 or 4.99999999999999976e73 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.9%

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

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 85.6%

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

   7. Taylor expanded in y around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. distribute-rgt-in 73.1%

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

   9. Simplified 73.1%

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

   if -0.50000500000000003 < (-.f64 a #s(literal 1/2 binary64)) < 4.99999999999999976e73

   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. fma-define 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 73.9%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. *-commutative 71.6%

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

   9. Simplified 71.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.500005 \lor \neg \left(a - 0.5 \leq 5 \cdot 10^{+73}\right):\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.1% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+14} \lor \neg \left(b \leq 9 \cdot 10^{+88}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.45e+14) (not (<= b 9e+88))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.45e+14) || !(b <= 9e+88)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.45d+14)) .or. (.not. (b <= 9d+88))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.45e+14) || !(b <= 9e+88)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.45e+14) or not (b <= 9e+88):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.45e+14) || !(b <= 9e+88))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.45e+14) || ~((b <= 9e+88)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.45e+14], N[Not[LessEqual[b, 9e+88]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.45e14 or 9e88 < 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. fma-define 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 91.3%

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

   7. Taylor expanded in b around inf 73.1%

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

   if -2.45e14 < b < 9e88

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.8%

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

   6. Taylor expanded in z around 0 70.8%

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

   7. Taylor expanded in b around 0 54.9%

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

      1. +-commutative 54.9%

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

   9. Simplified 54.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+14} \lor \neg \left(b \leq 9 \cdot 10^{+88}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.9% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+66} \lor \neg \left(a \leq 8.5 \cdot 10^{+77}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.15e+66) (not (<= a 8.5e+77))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.15e+66) || !(a <= 8.5e+77)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.15d+66)) .or. (.not. (a <= 8.5d+77))) then
        tmp = a * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.15e+66) || !(a <= 8.5e+77)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.15e+66) or not (a <= 8.5e+77):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.15e+66) || !(a <= 8.5e+77))
		tmp = Float64(a * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.15e+66) || ~((a <= 8.5e+77)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.15e+66], N[Not[LessEqual[a, 8.5e+77]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e66 or 8.50000000000000018e77 < a

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 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 b around inf 76.9%

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

      1. associate--l+ 76.9%

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

      2. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

   9. Applied egg-rr 76.9%

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

       1. unpow-1 76.9%

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

   11. Simplified 76.9%

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

   12. Taylor expanded in a around inf 64.2%

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

       1. *-commutative 64.2%

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

   14. Simplified 64.2%

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

   if -1.15e66 < a < 8.50000000000000018e77

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 75.0%

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

   7. Taylor expanded in b around 0 51.2%

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

      1. +-commutative 51.2%

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

   9. Simplified 51.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+66} \lor \neg \left(a \leq 8.5 \cdot 10^{+77}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.6% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-206}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.6e+146) x (if (<= x 9.2e-206) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+146) {
		tmp = x;
	} else if (x <= 9.2e-206) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.6d+146)) then
        tmp = x
    else if (x <= 9.2d-206) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+146) {
		tmp = x;
	} else if (x <= 9.2e-206) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.6e+146:
		tmp = x
	elif x <= 9.2e-206:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.6e+146)
		tmp = x;
	elseif (x <= 9.2e-206)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.6e+146)
		tmp = x;
	elseif (x <= 9.2e-206)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.6e+146], x, If[LessEqual[x, 9.2e-206], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5999999999999998e146

   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 x around inf 69.5%

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

   6. Taylor expanded in z around 0 59.4%

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

   if -3.5999999999999998e146 < x < 9.2e-206

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around inf 85.0%

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

      1. associate--l+ 85.0%

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

      2. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

      1. clear-num 85.0%

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

      2. inv-pow 85.0%

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

   9. Applied egg-rr 85.0%

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

       1. unpow-1 85.0%

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

   11. Simplified 85.0%

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

   12. Taylor expanded in a around inf 39.1%

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

       1. *-commutative 39.1%

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

   14. Simplified 39.1%

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

   if 9.2e-206 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

      1. clear-num 72.2%

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

      2. inv-pow 72.2%

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

   9. Applied egg-rr 72.2%

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

       1. unpow-1 72.2%

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

   11. Simplified 72.2%

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

   12. Taylor expanded in y around inf 22.0%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-206}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.8% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+141}:\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.05e+141) (+ 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 <= 1.05e+141) {
		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 <= 1.05d+141) 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 <= 1.05e+141) {
		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 <= 1.05e+141:
		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 <= 1.05e+141)
		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 <= 1.05e+141)
		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, 1.05e+141], 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 < 1.0499999999999999e141

   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. fma-define 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 79.4%

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

   7. Taylor expanded in y around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. distribute-rgt-in 63.3%

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

   9. Simplified 63.3%

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

   if 1.0499999999999999e141 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.8%

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

   6. Taylor expanded in z around 0 81.2%

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

   7. Taylor expanded in b around 0 43.8%

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

      1. +-commutative 43.8%

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

   9. Simplified 43.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+141}:\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 78.8% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

   3. sub-neg 99.9%

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

   4. metadata-eval 99.9%

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

   5. associate--l+ 99.9%

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

   6. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in a around 0 99.9%

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

6. Taylor expanded in z around 0 79.6%

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

Alternative 17: 78.8% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

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 = (b * (a - 0.5d0)) + (x + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. add-exp-log 46.8%

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

4. Applied egg-rr 46.8%

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

5. Taylor expanded in z around 0 79.6%

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

6. Final simplification 79.6%

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

Alternative 18: 28.0% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1e-22) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1d-22)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1e-22:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1e-22)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1e-22)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1e-22], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1e-22

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 54.3%

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

   6. Taylor expanded in z around 0 42.8%

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

   if -1e-22 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

      1. clear-num 78.5%

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

      2. inv-pow 78.5%

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

   9. Applied egg-rr 78.5%

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

       1. unpow-1 78.5%

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

   11. Simplified 78.5%

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

   12. Taylor expanded in y around inf 21.2%

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

Alternative 19: 22.2% 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 43.0%

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

6. Taylor expanded in z around 0 23.2%

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

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024186 
(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)))