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

Percentage Accurate: 99.8% → 99.8%

Time: 23.8s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-+r+ 99.8%

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

   3. +-commutative 99.8%

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

   4. associate-+r+ 99.8%

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

   5. +-commutative 99.8%

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

   6. associate-+r+ 99.8%

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

   7. fma-def 99.8%

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

   8. associate-+l+ 99.8%

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

   9. +-commutative 99.8%

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

   10. associate-+r+ 99.8%

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

   11. +-commutative 99.8%

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

   12. associate-+l+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. associate-+l+ 99.8%

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

   3. associate-+l+ 99.8%

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

   4. +-commutative 99.8%

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

   5. associate-+l+ 99.8%

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

   6. fma-def 99.8%

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

   7. +-commutative 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := -0.5 \cdot \log c\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;a + \left(t + \left(z + \left(t_1 + t_2\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b + -0.5\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(t_2 + \left(y \cdot i + t_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* -0.5 (log c))))
   (if (<= x -3.2e+176)
     (+ a (+ t (+ z (+ t_1 t_2))))
     (if (<= x 2.6e+188)
       (+ (* y i) (+ a (+ (* (+ b -0.5) (log c)) (+ z t))))
       (+ t (+ z (+ t_2 (+ (* y i) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = -0.5 * log(c);
	double tmp;
	if (x <= -3.2e+176) {
		tmp = a + (t + (z + (t_1 + t_2)));
	} else if (x <= 2.6e+188) {
		tmp = (y * i) + (a + (((b + -0.5) * log(c)) + (z + t)));
	} else {
		tmp = t + (z + (t_2 + ((y * i) + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (-0.5d0) * log(c)
    if (x <= (-3.2d+176)) then
        tmp = a + (t + (z + (t_1 + t_2)))
    else if (x <= 2.6d+188) then
        tmp = (y * i) + (a + (((b + (-0.5d0)) * log(c)) + (z + t)))
    else
        tmp = t + (z + (t_2 + ((y * i) + 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 c, double i) {
	double t_1 = x * Math.log(y);
	double t_2 = -0.5 * Math.log(c);
	double tmp;
	if (x <= -3.2e+176) {
		tmp = a + (t + (z + (t_1 + t_2)));
	} else if (x <= 2.6e+188) {
		tmp = (y * i) + (a + (((b + -0.5) * Math.log(c)) + (z + t)));
	} else {
		tmp = t + (z + (t_2 + ((y * i) + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = -0.5 * math.log(c)
	tmp = 0
	if x <= -3.2e+176:
		tmp = a + (t + (z + (t_1 + t_2)))
	elif x <= 2.6e+188:
		tmp = (y * i) + (a + (((b + -0.5) * math.log(c)) + (z + t)))
	else:
		tmp = t + (z + (t_2 + ((y * i) + t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(-0.5 * log(c))
	tmp = 0.0
	if (x <= -3.2e+176)
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + t_2))));
	elseif (x <= 2.6e+188)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(z + t))));
	else
		tmp = Float64(t + Float64(z + Float64(t_2 + Float64(Float64(y * i) + t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = -0.5 * log(c);
	tmp = 0.0;
	if (x <= -3.2e+176)
		tmp = a + (t + (z + (t_1 + t_2)));
	elseif (x <= 2.6e+188)
		tmp = (y * i) + (a + (((b + -0.5) * log(c)) + (z + t)));
	else
		tmp = t + (z + (t_2 + ((y * i) + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+176], N[(a + N[(t + N[(z + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+188], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z + N[(t$95$2 + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.1999999999999998e176

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 89.8%

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

   5. Taylor expanded in y around 0 86.1%

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

   if -3.1999999999999998e176 < x < 2.59999999999999987e188

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. +-commutative 96.2%

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

   4. Simplified 96.2%

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

   if 2.59999999999999987e188 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. fma-def 99.7%

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

      7. +-commutative 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around 0 90.8%

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

   5. Taylor expanded in a around 0 90.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b + -0.5\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(-0.5 \cdot \log c + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 5: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+178} \lor \neg \left(x \leq 6.2 \cdot 10^{+204}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b + -0.5\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.2e+178) (not (<= x 6.2e+204)))
   (+ a (+ t (+ z (+ (* x (log y)) (* -0.5 (log c))))))
   (+ (* y i) (+ a (+ (* (+ b -0.5) (log c)) (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.2e+178) || !(x <= 6.2e+204)) {
		tmp = a + (t + (z + ((x * log(y)) + (-0.5 * log(c)))));
	} else {
		tmp = (y * i) + (a + (((b + -0.5) * log(c)) + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3.2d+178)) .or. (.not. (x <= 6.2d+204))) then
        tmp = a + (t + (z + ((x * log(y)) + ((-0.5d0) * log(c)))))
    else
        tmp = (y * i) + (a + (((b + (-0.5d0)) * log(c)) + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.2e+178) || !(x <= 6.2e+204)) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (-0.5 * Math.log(c)))));
	} else {
		tmp = (y * i) + (a + (((b + -0.5) * Math.log(c)) + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.2e+178) or not (x <= 6.2e+204):
		tmp = a + (t + (z + ((x * math.log(y)) + (-0.5 * math.log(c)))))
	else:
		tmp = (y * i) + (a + (((b + -0.5) * math.log(c)) + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.2e+178) || !(x <= 6.2e+204))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(-0.5 * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.2e+178) || ~((x <= 6.2e+204)))
		tmp = a + (t + (z + ((x * log(y)) + (-0.5 * log(c)))));
	else
		tmp = (y * i) + (a + (((b + -0.5) * log(c)) + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.2e+178], N[Not[LessEqual[x, 6.2e+204]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2e178 or 6.2000000000000003e204 < x

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 89.8%

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

   5. Taylor expanded in y around 0 83.2%

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

   if -3.2e178 < x < 6.2000000000000003e204

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. +-commutative 96.2%

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

   4. Simplified 96.2%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+178} \lor \neg \left(x \leq 6.2 \cdot 10^{+204}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b + -0.5\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 6: 98.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* b (log c)))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 97.8%

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

   1. *-commutative 97.8%

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

4. Simplified 97.8%

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

5. Final simplification 97.8%

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

Alternative 7: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + y \cdot i\\ t_2 := t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;a \leq 4.2 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-105}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* y i))) (t_2 (+ t (+ z (* (log c) (- b 0.5))))))
   (if (<= a 4.2e-146)
     t_2
     (if (<= a 8.5e-105)
       (+ z (* y i))
       (if (<= a 7e+19)
         t_2
         (if (<= a 8.5e+61)
           t_1
           (if (<= a 9.2e+93)
             t_2
             (if (<= a 1.08e+138)
               t_1
               (if (<= a 1.8e+148) t_2 (fma y i a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (y * i);
	double t_2 = t + (z + (log(c) * (b - 0.5)));
	double tmp;
	if (a <= 4.2e-146) {
		tmp = t_2;
	} else if (a <= 8.5e-105) {
		tmp = z + (y * i);
	} else if (a <= 7e+19) {
		tmp = t_2;
	} else if (a <= 8.5e+61) {
		tmp = t_1;
	} else if (a <= 9.2e+93) {
		tmp = t_2;
	} else if (a <= 1.08e+138) {
		tmp = t_1;
	} else if (a <= 1.8e+148) {
		tmp = t_2;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(y * i))
	t_2 = Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))
	tmp = 0.0
	if (a <= 4.2e-146)
		tmp = t_2;
	elseif (a <= 8.5e-105)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 7e+19)
		tmp = t_2;
	elseif (a <= 8.5e+61)
		tmp = t_1;
	elseif (a <= 9.2e+93)
		tmp = t_2;
	elseif (a <= 1.08e+138)
		tmp = t_1;
	elseif (a <= 1.8e+148)
		tmp = t_2;
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 4.2e-146], t$95$2, If[LessEqual[a, 8.5e-105], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+19], t$95$2, If[LessEqual[a, 8.5e+61], t$95$1, If[LessEqual[a, 9.2e+93], t$95$2, If[LessEqual[a, 1.08e+138], t$95$1, If[LessEqual[a, 1.8e+148], t$95$2, N[(y * i + a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 4.1999999999999998e-146 or 8.50000000000000038e-105 < a < 7e19 or 8.50000000000000035e61 < a < 9.2000000000000006e93 or 1.08000000000000007e138 < a < 1.80000000000000003e148

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. +-commutative 83.8%

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

      3. associate-+l+ 83.8%

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

      4. +-commutative 83.8%

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

      5. sub-neg 83.8%

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

      6. metadata-eval 83.8%

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

      7. fma-def 83.8%

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

      8. +-commutative 83.8%

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

      9. +-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in a around 0 74.2%

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

   6. Taylor expanded in i around 0 56.1%

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

   if 4.1999999999999998e-146 < a < 8.50000000000000038e-105

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 50.2%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 7e19 < a < 8.50000000000000035e61 or 9.2000000000000006e93 < a < 1.08000000000000007e138

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{a} + y \cdot i \]

   if 1.80000000000000003e148 < a

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 65.6%

      \[\leadsto \color{blue}{a} + y \cdot i \]

   3. Taylor expanded in a around 0 65.6%

      \[\leadsto \color{blue}{a + i \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative 65.6%

         \[\leadsto \color{blue}{i \cdot y + a} \]

      2. *-commutative 65.6%

         \[\leadsto \color{blue}{y \cdot i} + a \]

      3. fma-udef 65.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]

   5. Simplified 65.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{-146}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-105}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+19}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+93}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+138}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+148}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 8: 86.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+181} \lor \neg \left(x \leq 7.5 \cdot 10^{+209}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b + -0.5\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.5e+181) (not (<= x 7.5e+209)))
   (* x (log y))
   (+ (* y i) (+ a (+ (* (+ b -0.5) (log c)) (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.5e+181) || !(x <= 7.5e+209)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (a + (((b + -0.5) * log(c)) + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.5d+181)) .or. (.not. (x <= 7.5d+209))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (a + (((b + (-0.5d0)) * log(c)) + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.5e+181) || !(x <= 7.5e+209)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (a + (((b + -0.5) * Math.log(c)) + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.5e+181) or not (x <= 7.5e+209):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (a + (((b + -0.5) * math.log(c)) + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.5e+181) || !(x <= 7.5e+209))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.5e+181) || ~((x <= 7.5e+209)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (a + (((b + -0.5) * log(c)) + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.5e+181], N[Not[LessEqual[x, 7.5e+209]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e181 or 7.50000000000000055e209 < x

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 89.8%

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

   5. Taylor expanded in x around inf 71.4%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if -4.5e181 < x < 7.50000000000000055e209

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. +-commutative 96.2%

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

   4. Simplified 96.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+181} \lor \neg \left(x \leq 7.5 \cdot 10^{+209}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b + -0.5\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 9: 72.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;a \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + t_1\right)\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+169} \lor \neg \left(a \leq 2.05 \cdot 10^{+254}\right):\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= a 3.4e+123)
     (+ t (+ z (+ (* y i) t_1)))
     (if (or (<= a 1.95e+169) (not (<= a 2.05e+254)))
       (+ a (+ t (+ z t_1)))
       (+ a (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (a <= 3.4e+123) {
		tmp = t + (z + ((y * i) + t_1));
	} else if ((a <= 1.95e+169) || !(a <= 2.05e+254)) {
		tmp = a + (t + (z + t_1));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (a <= 3.4d+123) then
        tmp = t + (z + ((y * i) + t_1))
    else if ((a <= 1.95d+169) .or. (.not. (a <= 2.05d+254))) then
        tmp = a + (t + (z + t_1))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (a <= 3.4e+123) {
		tmp = t + (z + ((y * i) + t_1));
	} else if ((a <= 1.95e+169) || !(a <= 2.05e+254)) {
		tmp = a + (t + (z + t_1));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if a <= 3.4e+123:
		tmp = t + (z + ((y * i) + t_1))
	elif (a <= 1.95e+169) or not (a <= 2.05e+254):
		tmp = a + (t + (z + t_1))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (a <= 3.4e+123)
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + t_1)));
	elseif ((a <= 1.95e+169) || !(a <= 2.05e+254))
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (a <= 3.4e+123)
		tmp = t + (z + ((y * i) + t_1));
	elseif ((a <= 1.95e+169) || ~((a <= 2.05e+254)))
		tmp = a + (t + (z + t_1));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3.4e+123], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.95e+169], N[Not[LessEqual[a, 2.05e+254]], $MachinePrecision]], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 3.40000000000000001e123

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. +-commutative 84.9%

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

      3. associate-+l+ 84.9%

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

      4. +-commutative 84.9%

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

      5. sub-neg 84.9%

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

      6. metadata-eval 84.9%

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

      7. fma-def 84.9%

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

      8. +-commutative 84.9%

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

      9. +-commutative 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in a around 0 74.9%

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

   if 3.40000000000000001e123 < a < 1.94999999999999991e169 or 2.04999999999999993e254 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. +-commutative 86.9%

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

      3. associate-+l+ 86.9%

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

      4. +-commutative 86.9%

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

      5. sub-neg 86.9%

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

      6. metadata-eval 86.9%

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

      7. fma-def 86.9%

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

      8. +-commutative 86.9%

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

      9. +-commutative 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in y around 0 78.1%

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

   if 1.94999999999999991e169 < a < 2.04999999999999993e254

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 67.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+169} \lor \neg \left(a \leq 2.05 \cdot 10^{+254}\right):\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 10: 66.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;i \leq -1.6 \cdot 10^{+195}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+207}:\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= i -1.6e+195)
     (+ (* y i) t_1)
     (if (<= i 2.1e+207) (+ a (+ t (+ z t_1))) (+ a (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (i <= -1.6e+195) {
		tmp = (y * i) + t_1;
	} else if (i <= 2.1e+207) {
		tmp = a + (t + (z + t_1));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (i <= (-1.6d+195)) then
        tmp = (y * i) + t_1
    else if (i <= 2.1d+207) then
        tmp = a + (t + (z + t_1))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (i <= -1.6e+195) {
		tmp = (y * i) + t_1;
	} else if (i <= 2.1e+207) {
		tmp = a + (t + (z + t_1));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if i <= -1.6e+195:
		tmp = (y * i) + t_1
	elif i <= 2.1e+207:
		tmp = a + (t + (z + t_1))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (i <= -1.6e+195)
		tmp = Float64(Float64(y * i) + t_1);
	elseif (i <= 2.1e+207)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (i <= -1.6e+195)
		tmp = (y * i) + t_1;
	elseif (i <= 2.1e+207)
		tmp = a + (t + (z + t_1));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.6e+195], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[i, 2.1e+207], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.59999999999999991e195

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. +-commutative 92.0%

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

      3. associate-+l+ 92.0%

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

      4. +-commutative 92.0%

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

      5. sub-neg 92.0%

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

      6. metadata-eval 92.0%

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

      7. fma-def 92.0%

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

      8. +-commutative 92.0%

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

      9. +-commutative 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in a around 0 92.0%

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

   6. Taylor expanded in z around 0 86.7%

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

   7. Taylor expanded in t around 0 82.2%

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

   if -1.59999999999999991e195 < i < 2.0999999999999999e207

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. +-commutative 83.9%

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

      3. associate-+l+ 83.9%

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

      4. +-commutative 83.9%

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

      5. sub-neg 83.9%

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

      6. metadata-eval 83.9%

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

      7. fma-def 83.9%

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

      8. +-commutative 83.9%

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

      9. +-commutative 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around 0 73.6%

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

   if 2.0999999999999999e207 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 71.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.6 \cdot 10^{+195}:\\ \;\;\;\;y \cdot i + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+207}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 11: 67.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;i \leq -9.6 \cdot 10^{+194}:\\ \;\;\;\;t + \left(y \cdot i + t_1\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+207}:\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= i -9.6e+194)
     (+ t (+ (* y i) t_1))
     (if (<= i 1.7e+207) (+ a (+ t (+ z t_1))) (+ a (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (i <= -9.6e+194) {
		tmp = t + ((y * i) + t_1);
	} else if (i <= 1.7e+207) {
		tmp = a + (t + (z + t_1));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (i <= (-9.6d+194)) then
        tmp = t + ((y * i) + t_1)
    else if (i <= 1.7d+207) then
        tmp = a + (t + (z + t_1))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (i <= -9.6e+194) {
		tmp = t + ((y * i) + t_1);
	} else if (i <= 1.7e+207) {
		tmp = a + (t + (z + t_1));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if i <= -9.6e+194:
		tmp = t + ((y * i) + t_1)
	elif i <= 1.7e+207:
		tmp = a + (t + (z + t_1))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (i <= -9.6e+194)
		tmp = Float64(t + Float64(Float64(y * i) + t_1));
	elseif (i <= 1.7e+207)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (i <= -9.6e+194)
		tmp = t + ((y * i) + t_1);
	elseif (i <= 1.7e+207)
		tmp = a + (t + (z + t_1));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.6e+194], N[(t + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e+207], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.6e194

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. +-commutative 92.0%

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

      3. associate-+l+ 92.0%

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

      4. +-commutative 92.0%

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

      5. sub-neg 92.0%

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

      6. metadata-eval 92.0%

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

      7. fma-def 92.0%

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

      8. +-commutative 92.0%

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

      9. +-commutative 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in a around 0 92.0%

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

   6. Taylor expanded in z around 0 86.7%

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

   if -9.6e194 < i < 1.6999999999999999e207

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. +-commutative 83.9%

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

      3. associate-+l+ 83.9%

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

      4. +-commutative 83.9%

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

      5. sub-neg 83.9%

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

      6. metadata-eval 83.9%

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

      7. fma-def 83.9%

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

      8. +-commutative 83.9%

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

      9. +-commutative 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around 0 73.6%

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

   if 1.6999999999999999e207 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 71.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.6 \cdot 10^{+194}:\\ \;\;\;\;t + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+207}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 12: 74.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;a \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + t\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= a 7.5e+79)
     (+ t (+ z (+ (* y i) t_1)))
     (+ (* y i) (+ (+ a t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (a <= 7.5e+79) {
		tmp = t + (z + ((y * i) + t_1));
	} else {
		tmp = (y * i) + ((a + t) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (a <= 7.5d+79) then
        tmp = t + (z + ((y * i) + t_1))
    else
        tmp = (y * i) + ((a + t) + 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 c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (a <= 7.5e+79) {
		tmp = t + (z + ((y * i) + t_1));
	} else {
		tmp = (y * i) + ((a + t) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if a <= 7.5e+79:
		tmp = t + (z + ((y * i) + t_1))
	else:
		tmp = (y * i) + ((a + t) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (a <= 7.5e+79)
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + t_1)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + t) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (a <= 7.5e+79)
		tmp = t + (z + ((y * i) + t_1));
	else
		tmp = (y * i) + ((a + t) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 7.5e+79], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 7.49999999999999967e79

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. +-commutative 84.5%

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

      3. associate-+l+ 84.5%

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

      4. +-commutative 84.5%

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

      5. sub-neg 84.5%

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

      6. metadata-eval 84.5%

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

      7. fma-def 84.5%

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

      8. +-commutative 84.5%

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

      9. +-commutative 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in a around 0 74.7%

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

   if 7.49999999999999967e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 90.4%

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

      1. +-commutative 90.4%

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

      2. +-commutative 90.4%

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

      3. associate-+l+ 90.4%

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

      4. +-commutative 90.4%

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

      5. sub-neg 90.4%

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

      6. metadata-eval 90.4%

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

      7. fma-def 90.4%

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

      8. +-commutative 90.4%

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

      9. +-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in z around 0 79.5%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + t\right) + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]

Alternative 13: 41.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 1.65 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= a 1.65e-273)
     t_1
     (if (<= a 8.5e-219)
       (* b (log c))
       (if (<= a 3.8e-182)
         t_1
         (if (<= a 3.6e-147)
           (* x (log y))
           (if (<= a 2.7e+79) t_1 (fma y i a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 1.65e-273) {
		tmp = t_1;
	} else if (a <= 8.5e-219) {
		tmp = b * log(c);
	} else if (a <= 3.8e-182) {
		tmp = t_1;
	} else if (a <= 3.6e-147) {
		tmp = x * log(y);
	} else if (a <= 2.7e+79) {
		tmp = t_1;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 1.65e-273)
		tmp = t_1;
	elseif (a <= 8.5e-219)
		tmp = Float64(b * log(c));
	elseif (a <= 3.8e-182)
		tmp = t_1;
	elseif (a <= 3.6e-147)
		tmp = Float64(x * log(y));
	elseif (a <= 2.7e+79)
		tmp = t_1;
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.65e-273], t$95$1, If[LessEqual[a, 8.5e-219], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-182], t$95$1, If[LessEqual[a, 3.6e-147], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+79], t$95$1, N[(y * i + a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1.64999999999999995e-273 or 8.49999999999999964e-219 < a < 3.8000000000000003e-182 or 3.60000000000000012e-147 < a < 2.7e79

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 37.1%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 1.64999999999999995e-273 < a < 8.49999999999999964e-219

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. +-commutative 76.7%

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

      3. associate-+l+ 76.7%

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

      4. +-commutative 76.7%

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

      5. sub-neg 76.7%

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

      6. metadata-eval 76.7%

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

      7. fma-def 76.7%

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

      8. +-commutative 76.7%

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

      9. +-commutative 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in b around inf 27.9%

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

      1. *-commutative 27.9%

         \[\leadsto \color{blue}{\log c \cdot b} \]

   7. Simplified 27.9%

      \[\leadsto \color{blue}{\log c \cdot b} \]

   if 3.8000000000000003e-182 < a < 3.60000000000000012e-147

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 75.8%

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

   5. Taylor expanded in x around inf 33.1%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if 2.7e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 58.4%

      \[\leadsto \color{blue}{a} + y \cdot i \]

   3. Taylor expanded in a around 0 58.4%

      \[\leadsto \color{blue}{a + i \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto \color{blue}{i \cdot y + a} \]

      2. *-commutative 58.4%

         \[\leadsto \color{blue}{y \cdot i} + a \]

      3. fma-udef 58.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.65 \cdot 10^{-273}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-182}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 14: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 1.25 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-221}:\\ \;\;\;\;t + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= a 1.25e-273)
     t_1
     (if (<= a 1.7e-221)
       (+ t (* (log c) (- b 0.5)))
       (if (<= a 3.8e-182)
         t_1
         (if (<= a 4.5e-146)
           (* x (log y))
           (if (<= a 4.5e+79) t_1 (fma y i a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 1.25e-273) {
		tmp = t_1;
	} else if (a <= 1.7e-221) {
		tmp = t + (log(c) * (b - 0.5));
	} else if (a <= 3.8e-182) {
		tmp = t_1;
	} else if (a <= 4.5e-146) {
		tmp = x * log(y);
	} else if (a <= 4.5e+79) {
		tmp = t_1;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 1.25e-273)
		tmp = t_1;
	elseif (a <= 1.7e-221)
		tmp = Float64(t + Float64(log(c) * Float64(b - 0.5)));
	elseif (a <= 3.8e-182)
		tmp = t_1;
	elseif (a <= 4.5e-146)
		tmp = Float64(x * log(y));
	elseif (a <= 4.5e+79)
		tmp = t_1;
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.25e-273], t$95$1, If[LessEqual[a, 1.7e-221], N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-182], t$95$1, If[LessEqual[a, 4.5e-146], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+79], t$95$1, N[(y * i + a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1.24999999999999991e-273 or 1.7000000000000001e-221 < a < 3.8000000000000003e-182 or 4.5000000000000001e-146 < a < 4.49999999999999994e79

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 37.1%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 1.24999999999999991e-273 < a < 1.7000000000000001e-221

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. +-commutative 76.7%

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

      3. associate-+l+ 76.7%

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

      4. +-commutative 76.7%

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

      5. sub-neg 76.7%

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

      6. metadata-eval 76.7%

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

      7. fma-def 76.7%

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

      8. +-commutative 76.7%

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

      9. +-commutative 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in a around 0 76.7%

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

   6. Taylor expanded in z around 0 65.3%

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

   7. Taylor expanded in i around 0 62.4%

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

   if 3.8000000000000003e-182 < a < 4.5000000000000001e-146

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 75.8%

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

   5. Taylor expanded in x around inf 33.1%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if 4.49999999999999994e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 58.4%

      \[\leadsto \color{blue}{a} + y \cdot i \]

   3. Taylor expanded in a around 0 58.4%

      \[\leadsto \color{blue}{a + i \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto \color{blue}{i \cdot y + a} \]

      2. *-commutative 58.4%

         \[\leadsto \color{blue}{y \cdot i} + a \]

      3. fma-udef 58.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{-273}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-221}:\\ \;\;\;\;t + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-182}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 15: 42.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 8 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= a 8e-275)
     t_1
     (if (<= a 6e-222)
       (* b (log c))
       (if (<= a 2.6e-182)
         t_1
         (if (<= a 3.6e-147)
           (* x (log y))
           (if (<= a 7.5e+79) t_1 (+ a (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 8e-275) {
		tmp = t_1;
	} else if (a <= 6e-222) {
		tmp = b * log(c);
	} else if (a <= 2.6e-182) {
		tmp = t_1;
	} else if (a <= 3.6e-147) {
		tmp = x * log(y);
	} else if (a <= 7.5e+79) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (y * i)
    if (a <= 8d-275) then
        tmp = t_1
    else if (a <= 6d-222) then
        tmp = b * log(c)
    else if (a <= 2.6d-182) then
        tmp = t_1
    else if (a <= 3.6d-147) then
        tmp = x * log(y)
    else if (a <= 7.5d+79) then
        tmp = t_1
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 8e-275) {
		tmp = t_1;
	} else if (a <= 6e-222) {
		tmp = b * Math.log(c);
	} else if (a <= 2.6e-182) {
		tmp = t_1;
	} else if (a <= 3.6e-147) {
		tmp = x * Math.log(y);
	} else if (a <= 7.5e+79) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 8e-275:
		tmp = t_1
	elif a <= 6e-222:
		tmp = b * math.log(c)
	elif a <= 2.6e-182:
		tmp = t_1
	elif a <= 3.6e-147:
		tmp = x * math.log(y)
	elif a <= 7.5e+79:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 8e-275)
		tmp = t_1;
	elseif (a <= 6e-222)
		tmp = Float64(b * log(c));
	elseif (a <= 2.6e-182)
		tmp = t_1;
	elseif (a <= 3.6e-147)
		tmp = Float64(x * log(y));
	elseif (a <= 7.5e+79)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 8e-275)
		tmp = t_1;
	elseif (a <= 6e-222)
		tmp = b * log(c);
	elseif (a <= 2.6e-182)
		tmp = t_1;
	elseif (a <= 3.6e-147)
		tmp = x * log(y);
	elseif (a <= 7.5e+79)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 8e-275], t$95$1, If[LessEqual[a, 6e-222], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-182], t$95$1, If[LessEqual[a, 3.6e-147], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+79], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 7.99999999999999947e-275 or 6.00000000000000059e-222 < a < 2.60000000000000006e-182 or 3.60000000000000012e-147 < a < 7.49999999999999967e79

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 37.1%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 7.99999999999999947e-275 < a < 6.00000000000000059e-222

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. +-commutative 76.7%

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

      3. associate-+l+ 76.7%

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

      4. +-commutative 76.7%

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

      5. sub-neg 76.7%

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

      6. metadata-eval 76.7%

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

      7. fma-def 76.7%

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

      8. +-commutative 76.7%

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

      9. +-commutative 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in b around inf 27.9%

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

      1. *-commutative 27.9%

         \[\leadsto \color{blue}{\log c \cdot b} \]

   7. Simplified 27.9%

      \[\leadsto \color{blue}{\log c \cdot b} \]

   if 2.60000000000000006e-182 < a < 3.60000000000000012e-147

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 75.8%

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

   5. Taylor expanded in x around inf 33.1%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if 7.49999999999999967e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 58.4%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8 \cdot 10^{-275}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-182}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 16: 42.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 1.9 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= a 1.9e-183)
     t_1
     (if (<= a 1.3e-146)
       (* x (log y))
       (if (<= a 1.05e+79) t_1 (+ a (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 1.9e-183) {
		tmp = t_1;
	} else if (a <= 1.3e-146) {
		tmp = x * log(y);
	} else if (a <= 1.05e+79) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (y * i)
    if (a <= 1.9d-183) then
        tmp = t_1
    else if (a <= 1.3d-146) then
        tmp = x * log(y)
    else if (a <= 1.05d+79) then
        tmp = t_1
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 1.9e-183) {
		tmp = t_1;
	} else if (a <= 1.3e-146) {
		tmp = x * Math.log(y);
	} else if (a <= 1.05e+79) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 1.9e-183:
		tmp = t_1
	elif a <= 1.3e-146:
		tmp = x * math.log(y)
	elif a <= 1.05e+79:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 1.9e-183)
		tmp = t_1;
	elseif (a <= 1.3e-146)
		tmp = Float64(x * log(y));
	elseif (a <= 1.05e+79)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 1.9e-183)
		tmp = t_1;
	elseif (a <= 1.3e-146)
		tmp = x * log(y);
	elseif (a <= 1.05e+79)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.9e-183], t$95$1, If[LessEqual[a, 1.3e-146], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+79], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.8999999999999998e-183 or 1.29999999999999993e-146 < a < 1.05000000000000004e79

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 36.2%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 1.8999999999999998e-183 < a < 1.29999999999999993e-146

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 75.8%

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

   5. Taylor expanded in x around inf 33.1%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if 1.05000000000000004e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 58.4%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.9 \cdot 10^{-183}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 17: 22.7% accurate, 19.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-207}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-138}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+123}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.6e-207)
   z
   (if (<= a 1.4e-138)
     (* y i)
     (if (<= a 1.36e-34) z (if (<= a 1.6e+123) (* y i) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.6e-207) {
		tmp = z;
	} else if (a <= 1.4e-138) {
		tmp = y * i;
	} else if (a <= 1.36e-34) {
		tmp = z;
	} else if (a <= 1.6e+123) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.6d-207) then
        tmp = z
    else if (a <= 1.4d-138) then
        tmp = y * i
    else if (a <= 1.36d-34) then
        tmp = z
    else if (a <= 1.6d+123) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.6e-207) {
		tmp = z;
	} else if (a <= 1.4e-138) {
		tmp = y * i;
	} else if (a <= 1.36e-34) {
		tmp = z;
	} else if (a <= 1.6e+123) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.6e-207:
		tmp = z
	elif a <= 1.4e-138:
		tmp = y * i
	elif a <= 1.36e-34:
		tmp = z
	elif a <= 1.6e+123:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.6e-207)
		tmp = z;
	elseif (a <= 1.4e-138)
		tmp = Float64(y * i);
	elseif (a <= 1.36e-34)
		tmp = z;
	elseif (a <= 1.6e+123)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.6e-207)
		tmp = z;
	elseif (a <= 1.4e-138)
		tmp = y * i;
	elseif (a <= 1.36e-34)
		tmp = z;
	elseif (a <= 1.6e+123)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.6e-207], z, If[LessEqual[a, 1.4e-138], N[(y * i), $MachinePrecision], If[LessEqual[a, 1.36e-34], z, If[LessEqual[a, 1.6e+123], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.6000000000000002e-207 or 1.4e-138 < a < 1.3600000000000001e-34

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. +-commutative 83.8%

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

      3. associate-+l+ 83.8%

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

      4. +-commutative 83.8%

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

      5. sub-neg 83.8%

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

      6. metadata-eval 83.8%

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

      7. fma-def 83.8%

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

      8. +-commutative 83.8%

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

      9. +-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around inf 17.9%

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

   if 1.6000000000000002e-207 < a < 1.4e-138 or 1.3600000000000001e-34 < a < 1.60000000000000002e123

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 20.6%

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

      1. *-commutative 20.6%

         \[\leadsto \color{blue}{y \cdot i} \]

   6. Simplified 20.6%

      \[\leadsto \color{blue}{y \cdot i} \]

   if 1.60000000000000002e123 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. +-commutative 89.3%

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

      3. associate-+l+ 89.3%

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

      4. +-commutative 89.3%

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

      5. sub-neg 89.3%

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

      6. metadata-eval 89.3%

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

      7. fma-def 89.3%

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

      8. +-commutative 89.3%

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

      9. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in a around inf 39.3%

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

4. Final simplification 22.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-207}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-138}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+123}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 18: 42.5% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+196}:\\ \;\;\;\;z + t\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.5e+196) (+ z t) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.5e+196) {
		tmp = z + t;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-9.5d+196)) then
        tmp = z + t
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.5e+196) {
		tmp = z + t;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9.5e+196:
		tmp = z + t
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9.5e+196)
		tmp = Float64(z + t);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -9.5e+196)
		tmp = z + t;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9.5e+196], N[(z + t), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000004e196

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. +-commutative 81.6%

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

      3. associate-+l+ 81.6%

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

      4. +-commutative 81.6%

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

      5. sub-neg 81.6%

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

      6. metadata-eval 81.6%

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

      7. fma-def 81.6%

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

      8. +-commutative 81.6%

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

      9. +-commutative 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in a around 0 81.6%

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

   6. Taylor expanded in z around inf 63.9%

      \[\leadsto t + \color{blue}{z} \]

   if -9.5000000000000004e196 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 37.5%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+196}:\\ \;\;\;\;z + t\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 19: 43.7% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.5e+79) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.5e+79) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 7.5d+79) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.5e+79) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 7.5e+79:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7.5e+79)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 7.5e+79)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7.5e+79], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.49999999999999967e79

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 36.1%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 7.49999999999999967e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 58.4%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 20: 21.2% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 4.5e+79) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.5e+79) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.5d+79) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.5e+79) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.5e+79:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.5e+79)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.5e+79)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.5e+79], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 4.49999999999999994e79

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. +-commutative 84.5%

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

      3. associate-+l+ 84.5%

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

      4. +-commutative 84.5%

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

      5. sub-neg 84.5%

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

      6. metadata-eval 84.5%

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

      7. fma-def 84.5%

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

      8. +-commutative 84.5%

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

      9. +-commutative 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in z around inf 16.9%

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

   if 4.49999999999999994e79 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 90.4%

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

      1. +-commutative 90.4%

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

      2. +-commutative 90.4%

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

      3. associate-+l+ 90.4%

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

      4. +-commutative 90.4%

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

      5. sub-neg 90.4%

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

      6. metadata-eval 90.4%

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

      7. fma-def 90.4%

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

      8. +-commutative 90.4%

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

      9. +-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in a around inf 37.6%

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

4. Final simplification 21.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 21: 16.5% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0 85.7%

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

   1. +-commutative 85.7%

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

   2. +-commutative 85.7%

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

   3. associate-+l+ 85.7%

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

   4. +-commutative 85.7%

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

   5. sub-neg 85.7%

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

   6. metadata-eval 85.7%

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

   7. fma-def 85.7%

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

   8. +-commutative 85.7%

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

   9. +-commutative 85.7%

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

4. Simplified 85.7%

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

5. Taylor expanded in a around inf 16.6%

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

6. Final simplification 16.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))