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

Percentage Accurate: 99.9% → 99.9%

Time: 11.2s

Alternatives: 16

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: 99.9% 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 99.8%

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

Alternative 2: 90.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+29}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+29)
     (+ x (+ y (+ (* -0.5 b) (* a b))))
     (if (<= t_1 2e+78)
       (+ (* z (- 1.0 (log t))) (+ x y))
       (+ x (+ y (* (+ a -0.5) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+29) {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	} else if (t_1 <= 2e+78) {
		tmp = (z * (1.0 - log(t))) + (x + y);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-5d+29)) then
        tmp = x + (y + (((-0.5d0) * b) + (a * b)))
    else if (t_1 <= 2d+78) then
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+29) {
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	} else if (t_1 <= 2e+78) {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+29:
		tmp = x + (y + ((-0.5 * b) + (a * b)))
	elif t_1 <= 2e+78:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+29)
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(a * b))));
	elseif (t_1 <= 2e+78)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -5e+29)
		tmp = x + (y + ((-0.5 * b) + (a * b)));
	elseif (t_1 <= 2e+78)
		tmp = (z * (1.0 - log(t))) + (x + y);
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+29], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+78], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000001e29

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. *-commutative 99.8%

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

      4. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 89.0%

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

   if -5.0000000000000001e29 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.00000000000000002e78

   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-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 95.5%

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

   if 2.00000000000000002e78 < (*.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. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-lft-in 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 96.9%

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

      1. +-commutative 96.9%

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

      2. distribute-rgt-in 96.9%

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

   7. Simplified 96.9%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+29}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;t\_2 + \left(\left(z + x\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(\left(z + y\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* b (- a 0.5))))
   (if (<= (+ x y) -5e-85) (+ t_2 (- (+ z x) t_1)) (+ t_2 (- (+ z y) 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 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e-85) {
		tmp = t_2 + ((z + x) - t_1);
	} else {
		tmp = t_2 + ((z + 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) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = b * (a - 0.5d0)
    if ((x + y) <= (-5d-85)) then
        tmp = t_2 + ((z + x) - t_1)
    else
        tmp = t_2 + ((z + 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 = z * Math.log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e-85) {
		tmp = t_2 + ((z + x) - t_1);
	} else {
		tmp = t_2 + ((z + y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -5e-85:
		tmp = t_2 + ((z + x) - t_1)
	else:
		tmp = t_2 + ((z + y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -5e-85)
		tmp = Float64(t_2 + Float64(Float64(z + x) - t_1));
	else
		tmp = Float64(t_2 + Float64(Float64(z + y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -5e-85)
		tmp = t_2 + ((z + x) - t_1);
	else
		tmp = t_2 + ((z + y) - 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[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e-85], N[(t$95$2 + N[(N[(z + x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(z + y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000002e-85

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 78.3%

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

      1. +-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -5.0000000000000002e-85 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 5e+140)
   (+ (* b (- a 0.5)) (- (+ z x) (* z (log t))))
   (+ x (+ y (* (+ a -0.5) b)))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= 5d+140) then
        tmp = (b * (a - 0.5d0)) + ((z + x) - (z * log(t)))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 5e+140:
		tmp = (b * (a - 0.5)) + ((z + x) - (z * math.log(t)))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+140], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5.00000000000000008e140

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if 5.00000000000000008e140 < (+.f64 x y)

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. distribute-rgt-in 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 86.3%

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

Alternative 5: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+201} \lor \neg \left(z \leq 2.25 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e+201) (not (<= z 2.25e+153)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e+201) || !(z <= 2.25e+153)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.8d+201)) .or. (.not. (z <= 2.25d+153))) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e+201) || !(z <= 2.25e+153)) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e+201) or not (z <= 2.25e+153):
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e+201) || !(z <= 2.25e+153))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.8e+201) || ~((z <= 2.25e+153)))
		tmp = (z * (1.0 - log(t))) + (a * b);
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e+201], N[Not[LessEqual[z, 2.25e+153]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999985e201 or 2.25e153 < z

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. *-lft-identity 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. distribute-rgt-out-- 99.5%

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

      9. metadata-eval 99.5%

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

      10. fma-define 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

   if -4.79999999999999985e201 < z < 2.25e153

   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. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 92.2%

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

      1. +-commutative 92.2%

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

      2. distribute-rgt-in 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+201} \lor \neg \left(z \leq 2.25 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+198} \lor \neg \left(z \leq 3.8 \cdot 10^{+212}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5e+198) (not (<= z 3.8e+212)))
   (+ (* z (- 1.0 (log t))) x)
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5e+198) || !(z <= 3.8e+212)) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5d+198)) .or. (.not. (z <= 3.8d+212))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5e+198) || !(z <= 3.8e+212)) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5e+198) or not (z <= 3.8e+212):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5e+198) || !(z <= 3.8e+212))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5e+198) || ~((z <= 3.8e+212)))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5e+198], N[Not[LessEqual[z, 3.8e+212]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000049e198 or 3.79999999999999988e212 < z

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. *-lft-identity 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. distribute-rgt-out-- 99.5%

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

      9. metadata-eval 99.5%

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

      10. fma-define 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 81.2%

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

   if -5.00000000000000049e198 < z < 3.79999999999999988e212

   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. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. distribute-rgt-in 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+198} \lor \neg \left(z \leq 3.8 \cdot 10^{+212}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+205} \lor \neg \left(z \leq 4.2 \cdot 10^{+225}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e+205) (not (<= z 4.2e+225)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e+205) || !(z <= 4.2e+225)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7d+205)) .or. (.not. (z <= 4.2d+225))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e+205) || !(z <= 4.2e+225)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7e+205) or not (z <= 4.2e+225):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e+205) || !(z <= 4.2e+225))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7e+205) || ~((z <= 4.2e+225)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e+205], N[Not[LessEqual[z, 4.2e+225]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999996e205 or 4.2e225 < z

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. *-lft-identity 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. distribute-rgt-out-- 99.5%

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

      9. metadata-eval 99.5%

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

      10. fma-define 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 80.7%

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

   6. Taylor expanded in z around inf 73.0%

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

   if -6.9999999999999996e205 < z < 4.2e225

   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. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 89.7%

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

      1. +-commutative 89.7%

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

      2. distribute-rgt-in 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+205} \lor \neg \left(z \leq 4.2 \cdot 10^{+225}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 9: 57.6% accurate, 7.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.5) || !(a <= 0.5)) {
		tmp = x + (a * b);
	} else {
		tmp = x + (-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)) .or. (.not. (a <= 0.5d0))) then
        tmp = x + (a * b)
    else
        tmp = x + ((-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) || !(a <= 0.5)) {
		tmp = x + (a * b);
	} else {
		tmp = x + (-0.5 * b);
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -0.5 or 0.5 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.7%

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

      1. associate-/l* 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in x around inf 74.7%

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

   7. Taylor expanded in a around inf 74.2%

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

   if -0.5 < a < 0.5

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in x around inf 49.5%

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

   7. Taylor expanded in a around 0 48.2%

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

4. Final simplification 60.6%

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

Alternative 10: 50.1% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-7} \lor \neg \left(a \leq 2.3\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.8e-7) (not (<= a 2.3))) (* b (- a 0.5)) (+ x (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.8e-7) || !(a <= 2.3)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + (-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 <= (-1.8d-7)) .or. (.not. (a <= 2.3d0))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + ((-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 <= -1.8e-7) || !(a <= 2.3)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.8e-7) or not (a <= 2.3):
		tmp = b * (a - 0.5)
	else:
		tmp = x + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.8e-7) || !(a <= 2.3))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.8e-7) || ~((a <= 2.3)))
		tmp = b * (a - 0.5);
	else
		tmp = x + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.8e-7], N[Not[LessEqual[a, 2.3]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999997e-7 or 2.2999999999999998 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 80.3%

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

      1. associate-/l* 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around inf 74.8%

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

   7. Taylor expanded in x around 0 59.6%

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

   if -1.79999999999999997e-7 < a < 2.2999999999999998

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 84.1%

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

      1. associate-/l* 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in x around inf 49.1%

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

   7. Taylor expanded in a around 0 48.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-7} \lor \neg \left(a \leq 2.3\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.7% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-7} \lor \neg \left(a \leq 1.2 \cdot 10^{+48}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.8e-7) (not (<= a 1.2e+48))) (* a b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.8e-7) || !(a <= 1.2e+48)) {
		tmp = a * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.8d-7)) .or. (.not. (a <= 1.2d+48))) then
        tmp = a * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.8e-7) || !(a <= 1.2e+48)) {
		tmp = a * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.8e-7) or not (a <= 1.2e+48):
		tmp = a * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.8e-7) || !(a <= 1.2e+48))
		tmp = Float64(a * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.8e-7) || ~((a <= 1.2e+48)))
		tmp = a * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.8e-7], N[Not[LessEqual[a, 1.2e+48]], $MachinePrecision]], N[(a * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999997e-7 or 1.2000000000000001e48 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 81.6%

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

      1. associate-/l* 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in x around inf 76.0%

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

   7. Taylor expanded in a around inf 60.2%

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

   if -1.79999999999999997e-7 < a < 1.2000000000000001e48

   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-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 52.9%

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

   6. Taylor expanded in z around 0 30.4%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-7} \lor \neg \left(a \leq 1.2 \cdot 10^{+48}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;y \leq 0.00012:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= y 0.00012) (+ 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 (y <= 0.00012) {
		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 (y <= 0.00012d0) 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 (y <= 0.00012) {
		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 y <= 0.00012:
		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 (y <= 0.00012)
		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 (y <= 0.00012)
		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[y, 0.00012], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.20000000000000003e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in x around inf 65.6%

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

   if 1.20000000000000003e-4 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 89.2%

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

   7. Taylor expanded in y around inf 74.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00012:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.1% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.1e+121) x (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e+121) {
		tmp = x;
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.1d+121)) then
        tmp = x
    else
        tmp = b * (a - 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e+121) {
		tmp = x;
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.1e+121:
		tmp = x
	else:
		tmp = b * (a - 0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.1e+121)
		tmp = x;
	else
		tmp = Float64(b * Float64(a - 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.1e+121)
		tmp = x;
	else
		tmp = b * (a - 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.1e+121], x, N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000001e121

   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+ 99.9%

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

      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 69.2%

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

   6. Taylor expanded in z around 0 58.0%

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

   if -1.10000000000000001e121 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 78.8%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in x around inf 58.5%

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

   7. Taylor expanded in x around 0 43.3%

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

Alternative 14: 78.4% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. sub-neg 99.8%

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

   2. metadata-eval 99.8%

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

   3. *-commutative 99.8%

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

   4. distribute-lft-in 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in z around 0 80.8%

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

   1. +-commutative 80.8%

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

   2. distribute-rgt-in 80.8%

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

7. Simplified 80.8%

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

8. Final simplification 80.8%

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

Alternative 15: 58.1% accurate, 16.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around inf 82.2%

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

   1. associate-/l* 82.2%

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

5. Simplified 82.2%

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

6. Taylor expanded in x around inf 61.5%

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

7. Final simplification 61.5%

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

Alternative 16: 21.3% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate--l+ 99.8%

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

   3. associate-+r+ 99.8%

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

   4. +-commutative 99.8%

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

   5. *-lft-identity 99.8%

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

   6. metadata-eval 99.8%

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

   7. *-commutative 99.8%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 42.7%

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

6. Taylor expanded in z around 0 24.0%

   \[\leadsto \color{blue}{x} \]
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 2024170 
(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)))