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

Percentage Accurate: 99.8% → 99.9%

Time: 12.8s

Alternatives: 15

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. *-commutative 99.9%

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

   6. *-lft-identity 99.9%

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

   7. metadata-eval 99.9%

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

   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-def 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. Final simplification 99.9%

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

Alternative 2: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+131} \lor \neg \left(t_1 \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;t_1 + \left(\left(z + y\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -2e+131) (not (<= t_1 5e+111)))
     (+ t_1 (- (+ z y) (* z (log t))))
     (+ 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 <= -2e+131) || !(t_1 <= 5e+111)) {
		tmp = t_1 + ((z + y) - (z * log(t)));
	} 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 <= (-2d+131)) .or. (.not. (t_1 <= 5d+111))) then
        tmp = t_1 + ((z + y) - (z * log(t)))
    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 <= -2e+131) || !(t_1 <= 5e+111)) {
		tmp = t_1 + ((z + y) - (z * Math.log(t)));
	} 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 <= -2e+131) or not (t_1 <= 5e+111):
		tmp = t_1 + ((z + y) - (z * math.log(t)))
	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 <= -2e+131) || !(t_1 <= 5e+111))
		tmp = Float64(t_1 + Float64(Float64(z + y) - Float64(z * log(t))));
	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 <= -2e+131) || ~((t_1 <= 5e+111)))
		tmp = t_1 + ((z + y) - (z * log(t)));
	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, -2e+131], N[Not[LessEqual[t$95$1, 5e+111]], $MachinePrecision]], N[(t$95$1 + N[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $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 1/2) b) < -1.9999999999999998e131 or 4.9999999999999997e111 < (*.f64 (-.f64 a 1/2) 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. Taylor expanded in x around 0 93.2%

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

   if -1.9999999999999998e131 < (*.f64 (-.f64 a 1/2) b) < 4.9999999999999997e111

   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. *-commutative 99.8%

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

      6. *-lft-identity 99.8%

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

      7. metadata-eval 99.8%

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

      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-def 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. Taylor expanded in b around 0 94.5%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+131} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \]

Alternative 3: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+186}:\\ \;\;\;\;\left(x + y\right) + t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+44}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -4e+186)
     (+ (+ x y) t_1)
     (if (<= t_1 5e+44)
       (+ x (+ (* z (- 1.0 (log t))) y))
       (+ (+ z (+ x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -4e+186) {
		tmp = (x + y) + t_1;
	} else if (t_1 <= 5e+44) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = (z + (x + y)) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-4d+186)) then
        tmp = (x + y) + t_1
    else if (t_1 <= 5d+44) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = (z + (x + y)) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -4e+186) {
		tmp = (x + y) + t_1;
	} else if (t_1 <= 5e+44) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = (z + (x + y)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -4e+186:
		tmp = (x + y) + t_1
	elif t_1 <= 5e+44:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = (z + (x + y)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -4e+186)
		tmp = Float64(Float64(x + y) + t_1);
	elseif (t_1 <= 5e+44)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = Float64(Float64(z + Float64(x + y)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -4e+186)
		tmp = (x + y) + t_1;
	elseif (t_1 <= 5e+44)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = (z + (x + y)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+186], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e+44], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -3.99999999999999992e186

   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. Taylor expanded in z around 0 95.7%

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

   if -3.99999999999999992e186 < (*.f64 (-.f64 a 1/2) b) < 4.9999999999999996e44

   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. *-commutative 99.8%

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

      6. *-lft-identity 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-def 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 96.1%

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

   if 4.9999999999999996e44 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 55.5%

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

      2. pow2 55.5%

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

   3. Applied egg-rr 55.5%

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

   4. Taylor expanded in z around 0 89.7%

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

      1. associate-+r+ 89.7%

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

      2. +-commutative 89.7%

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

      3. +-commutative 89.7%

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

   6. Simplified 89.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+186}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+44}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ z (+ x y)) (* z (log (/ 1.0 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((1.0 / 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((1.0d0 / 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((1.0 / t)))) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return ((z + (x + y)) + (z * math.log((1.0 / 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(Float64(1.0 / t)))) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((z + (x + y)) + (z * log((1.0 / 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[N[(1.0 / t), $MachinePrecision]], $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. Taylor expanded in t around inf 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 6: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+140} \lor \neg \left(z \leq 6.2 \cdot 10^{+225}\right):\\ \;\;\;\;z + \left(y - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e+140) (not (<= z 6.2e+225)))
   (+ z (- y (* z (log t))))
   (+ (+ z (+ x y)) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+140) || !(z <= 6.2e+225)) {
		tmp = z + (y - (z * log(t)));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.6d+140)) .or. (.not. (z <= 6.2d+225))) then
        tmp = z + (y - (z * log(t)))
    else
        tmp = (z + (x + y)) + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+140) || !(z <= 6.2e+225)) {
		tmp = z + (y - (z * Math.log(t)));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.6e+140) or not (z <= 6.2e+225):
		tmp = z + (y - (z * math.log(t)))
	else:
		tmp = (z + (x + y)) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e+140) || !(z <= 6.2e+225))
		tmp = Float64(z + Float64(y - Float64(z * log(t))));
	else
		tmp = Float64(Float64(z + Float64(x + y)) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.6e+140) || ~((z <= 6.2e+225)))
		tmp = z + (y - (z * log(t)));
	else
		tmp = (z + (x + y)) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e+140], N[Not[LessEqual[z, 6.2e+225]], $MachinePrecision]], N[(z + N[(y - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000002e140 or 6.1999999999999995e225 < 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. Taylor expanded in t around inf 99.6%

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

   3. Taylor expanded in x around 0 90.6%

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

   4. Taylor expanded in b around 0 72.8%

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

   5. Taylor expanded in t around 0 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-+r- 72.8%

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

   7. Simplified 72.8%

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

   if -7.6000000000000002e140 < z < 6.1999999999999995e225

   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. add-sqr-sqrt 45.2%

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

      2. pow2 45.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. associate-+r+ 87.4%

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

      2. +-commutative 87.4%

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

      3. +-commutative 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+140} \lor \neg \left(z \leq 6.2 \cdot 10^{+225}\right):\\ \;\;\;\;z + \left(y - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 7: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+142} \lor \neg \left(z \leq 9.5 \cdot 10^{+248}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e+142) (not (<= z 9.5e+248)))
   (* z (- 1.0 (log t)))
   (+ (+ z (+ x y)) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+142) || !(z <= 9.5e+248)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.5d+142)) .or. (.not. (z <= 9.5d+248))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (z + (x + y)) + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+142) || !(z <= 9.5e+248)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e+142) or not (z <= 9.5e+248):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (z + (x + y)) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e+142) || !(z <= 9.5e+248))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(z + Float64(x + y)) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.5e+142) || ~((z <= 9.5e+248)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (z + (x + y)) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e+142], N[Not[LessEqual[z, 9.5e+248]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999997e142 or 9.4999999999999993e248 < 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. Taylor expanded in t around inf 99.6%

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

   3. Taylor expanded in x around 0 89.3%

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

   4. Taylor expanded in b around 0 74.8%

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

   5. Taylor expanded in z around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. log-rec 70.1%

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

      3. cancel-sign-sub 70.1%

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

      4. metadata-eval 70.1%

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

      5. distribute-rgt-in 70.1%

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

      6. +-commutative 70.1%

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

      7. neg-mul-1 70.1%

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

      8. neg-sub0 70.1%

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(\log t + -1\right)\right)} \]

      9. +-commutative 70.1%

         \[\leadsto z \cdot \left(0 - \color{blue}{\left(-1 + \log t\right)}\right) \]

      10. associate--r+ 70.1%

          \[\leadsto z \cdot \color{blue}{\left(\left(0 - -1\right) - \log t\right)} \]

      11. metadata-eval 70.1%

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

   7. Simplified 70.1%

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

   if -3.49999999999999997e142 < z < 9.4999999999999993e248

   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. add-sqr-sqrt 44.1%

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

      2. pow2 44.1%

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

   3. Applied egg-rr 44.1%

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

   4. Taylor expanded in z around 0 86.4%

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

      1. associate-+r+ 86.4%

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

      2. +-commutative 86.4%

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

      3. +-commutative 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+142} \lor \neg \left(z \leq 9.5 \cdot 10^{+248}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 8: 29.4% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-247}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e-135)
   x
   (if (<= y -4.8e-247)
     (* a b)
     (if (<= y 5.5e-128) x (if (<= y 6.4e+115) (* a b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e-135) {
		tmp = x;
	} else if (y <= -4.8e-247) {
		tmp = a * b;
	} else if (y <= 5.5e-128) {
		tmp = x;
	} else if (y <= 6.4e+115) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3d-135)) then
        tmp = x
    else if (y <= (-4.8d-247)) then
        tmp = a * b
    else if (y <= 5.5d-128) then
        tmp = x
    else if (y <= 6.4d+115) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e-135) {
		tmp = x;
	} else if (y <= -4.8e-247) {
		tmp = a * b;
	} else if (y <= 5.5e-128) {
		tmp = x;
	} else if (y <= 6.4e+115) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3e-135:
		tmp = x
	elif y <= -4.8e-247:
		tmp = a * b
	elif y <= 5.5e-128:
		tmp = x
	elif y <= 6.4e+115:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e-135)
		tmp = x;
	elseif (y <= -4.8e-247)
		tmp = Float64(a * b);
	elseif (y <= 5.5e-128)
		tmp = x;
	elseif (y <= 6.4e+115)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3e-135)
		tmp = x;
	elseif (y <= -4.8e-247)
		tmp = a * b;
	elseif (y <= 5.5e-128)
		tmp = x;
	elseif (y <= 6.4e+115)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e-135], x, If[LessEqual[y, -4.8e-247], N[(a * b), $MachinePrecision], If[LessEqual[y, 5.5e-128], x, If[LessEqual[y, 6.4e+115], N[(a * b), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000012e-135 or -4.80000000000000022e-247 < y < 5.5000000000000004e-128

   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. *-commutative 99.9%

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

      6. *-lft-identity 99.9%

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

      7. metadata-eval 99.9%

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

      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-def 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. Taylor expanded in x around inf 23.7%

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

   if -3.00000000000000012e-135 < y < -4.80000000000000022e-247 or 5.5000000000000004e-128 < y < 6.4e115

   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. *-commutative 99.8%

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

      6. *-lft-identity 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-def 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 30.8%

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

      1. *-commutative 30.8%

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

   6. Simplified 30.8%

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

   if 6.4e115 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 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. *-commutative 100.0%

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

      6. *-lft-identity 100.0%

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

      7. metadata-eval 100.0%

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

      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-def 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. Taylor expanded in y around inf 54.6%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-247}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 44.6% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= b -1.12e+73)
     t_1
     (if (<= b -7.5e-268) x (if (<= b 1.05e+38) y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (b <= -1.12e+73) {
		tmp = t_1;
	} else if (b <= -7.5e-268) {
		tmp = x;
	} else if (b <= 1.05e+38) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (b <= (-1.12d+73)) then
        tmp = t_1
    else if (b <= (-7.5d-268)) then
        tmp = x
    else if (b <= 1.05d+38) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (b <= -1.12e+73) {
		tmp = t_1;
	} else if (b <= -7.5e-268) {
		tmp = x;
	} else if (b <= 1.05e+38) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if b <= -1.12e+73:
		tmp = t_1
	elif b <= -7.5e-268:
		tmp = x
	elif b <= 1.05e+38:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (b <= -1.12e+73)
		tmp = t_1;
	elseif (b <= -7.5e-268)
		tmp = x;
	elseif (b <= 1.05e+38)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (b <= -1.12e+73)
		tmp = t_1;
	elseif (b <= -7.5e-268)
		tmp = x;
	elseif (b <= 1.05e+38)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.12e+73], t$95$1, If[LessEqual[b, -7.5e-268], x, If[LessEqual[b, 1.05e+38], y, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.12e73 or 1.05e38 < b

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-commutative 100.0%

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

      6. *-lft-identity 100.0%

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

      7. metadata-eval 100.0%

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

      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-def 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. Taylor expanded in b around inf 71.5%

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

   if -1.12e73 < b < -7.4999999999999999e-268

   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. *-commutative 99.8%

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

      6. *-lft-identity 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-def 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 32.8%

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

   if -7.4999999999999999e-268 < b < 1.05e38

   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. *-commutative 99.8%

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

      6. *-lft-identity 99.8%

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

      7. metadata-eval 99.8%

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

      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-def 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. Taylor expanded in y around inf 31.9%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 10: 79.3% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. add-sqr-sqrt 45.6%

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

   2. pow2 45.6%

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

3. Applied egg-rr 45.6%

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

4. Taylor expanded in z around 0 75.7%

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

   1. associate-+r+ 75.7%

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

   2. +-commutative 75.7%

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

   3. +-commutative 75.7%

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

6. Simplified 75.7%

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

7. Final simplification 75.7%

   \[\leadsto \left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right) \]

Alternative 11: 61.4% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+184}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 4.1e+184) (+ x (* b (- a 0.5))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 4.1e+184) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 4.1d+184) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 4.1e+184) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 4.1e+184:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 4.1e+184)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 4.1e+184)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 4.1e+184], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if y < 4.0999999999999997e184

   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. Taylor expanded in t around inf 99.9%

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

   3. Taylor expanded in x around inf 58.8%

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

   if 4.0999999999999997e184 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. *-lft-identity 99.9%

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

      7. metadata-eval 99.9%

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

      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-def 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. Taylor expanded in y around inf 64.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+184}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12: 64.5% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= x -1.5e+47) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (x <= -1.5e+47) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (x <= (-1.5d+47)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (x <= -1.5e+47) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if x <= -1.5e+47:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (x <= -1.5e+47)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (x <= -1.5e+47)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+47], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5000000000000001e47

   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. Taylor expanded in t around inf 99.9%

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

   3. Taylor expanded in x around inf 76.0%

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

   if -1.5000000000000001e47 < 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. Taylor expanded in t around inf 99.9%

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

   3. Taylor expanded in y around inf 61.3%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 13: 78.6% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0 75.1%

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

3. Final simplification 75.1%

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

Alternative 14: 29.2% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -8.5e+56) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+56) {
		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 <= (-8.5d+56)) 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 <= -8.5e+56) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.5e+56:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.5e+56)
		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 <= -8.5e+56)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.5e+56], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999998e56

   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. *-commutative 99.9%

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

      6. *-lft-identity 99.9%

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

      7. metadata-eval 99.9%

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

      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-def 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. Taylor expanded in x around inf 52.5%

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

   if -8.4999999999999998e56 < 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. *-commutative 99.9%

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

      6. *-lft-identity 99.9%

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

      7. metadata-eval 99.9%

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

      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-def 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. Taylor expanded in y around inf 23.1%

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

4. Final simplification 29.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 22.5% 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. *-commutative 99.9%

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

   6. *-lft-identity 99.9%

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

   7. metadata-eval 99.9%

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

   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-def 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. Taylor expanded in x around inf 20.1%

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

5. Final simplification 20.1%

   \[\leadsto x \]

Developer target: 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 2023301 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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