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

Percentage Accurate: 99.8% → 99.8%

Time: 16.0s

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

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma y i (fma (+ b -0.5) (log c) (+ (fma x (log y) z) (+ t a)))))

C

assert(z < t && t < a);
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), z) + (t + a))));
}

Julia

z, t, a = sort([z, t, a])
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), z) + Float64(t + a))))
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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] + z), $MachinePrecision] + N[(t + a), $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. fma-def 99.9%

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

   3. +-commutative 99.9%

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

   4. fma-def 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

   7. associate-+l+ 99.9%

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

   8. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := a + \left(z + t\right)\\ t_3 := y \cdot i + t_2\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{elif}\;t_1 \leq 157:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 220:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;t_1 \leq 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ a (+ z t))) (t_3 (+ (* y i) t_2)))
   (if (<= t_1 -2e+93)
     (+ (* y i) (+ a (* b (log c))))
     (if (<= t_1 157.0)
       t_3
       (if (<= t_1 220.0)
         (+ (* y i) (* x (log y)))
         (if (<= t_1 1e+71) t_3 (+ t_1 t_2)))))))

C

assert(z < t && t < a);
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 t_2 = a + (z + t);
	double t_3 = (y * i) + t_2;
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = (y * i) + (a + (b * log(c)));
	} else if (t_1 <= 157.0) {
		tmp = t_3;
	} else if (t_1 <= 220.0) {
		tmp = (y * i) + (x * log(y));
	} else if (t_1 <= 1e+71) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = a + (z + t)
    t_3 = (y * i) + t_2
    if (t_1 <= (-2d+93)) then
        tmp = (y * i) + (a + (b * log(c)))
    else if (t_1 <= 157.0d0) then
        tmp = t_3
    else if (t_1 <= 220.0d0) then
        tmp = (y * i) + (x * log(y))
    else if (t_1 <= 1d+71) then
        tmp = t_3
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

assert z < t && t < a;
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 t_2 = a + (z + t);
	double t_3 = (y * i) + t_2;
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else if (t_1 <= 157.0) {
		tmp = t_3;
	} else if (t_1 <= 220.0) {
		tmp = (y * i) + (x * Math.log(y));
	} else if (t_1 <= 1e+71) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = a + (z + t)
	t_3 = (y * i) + t_2
	tmp = 0
	if t_1 <= -2e+93:
		tmp = (y * i) + (a + (b * math.log(c)))
	elif t_1 <= 157.0:
		tmp = t_3
	elif t_1 <= 220.0:
		tmp = (y * i) + (x * math.log(y))
	elif t_1 <= 1e+71:
		tmp = t_3
	else:
		tmp = t_1 + t_2
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(a + Float64(z + t))
	t_3 = Float64(Float64(y * i) + t_2)
	tmp = 0.0
	if (t_1 <= -2e+93)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	elseif (t_1 <= 157.0)
		tmp = t_3;
	elseif (t_1 <= 220.0)
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	elseif (t_1 <= 1e+71)
		tmp = t_3;
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = a + (z + t);
	t_3 = (y * i) + t_2;
	tmp = 0.0;
	if (t_1 <= -2e+93)
		tmp = (y * i) + (a + (b * log(c)));
	elseif (t_1 <= 157.0)
		tmp = t_3;
	elseif (t_1 <= 220.0)
		tmp = (y * i) + (x * log(y));
	elseif (t_1 <= 1e+71)
		tmp = t_3;
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * i), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+93], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 157.0], t$95$3, If[LessEqual[t$95$1, 220.0], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+71], t$95$3, N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (-.f64 b 1/2) (log.f64 c)) < -2.00000000000000009e93

   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 88.4%

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

   3. Taylor expanded in b around inf 88.4%

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

   4. Taylor expanded in z around 0 86.3%

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

   5. Taylor expanded in t around 0 76.3%

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

      1. +-commutative 76.3%

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

   7. Simplified 76.3%

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

   if -2.00000000000000009e93 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 157 or 220 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 1e71

   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 83.3%

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

   3. Taylor expanded in b around inf 82.2%

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

   4. Taylor expanded in b around 0 81.6%

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

   if 157 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 220

   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 b around 0 99.6%

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

   3. Taylor expanded in x around inf 92.1%

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

   if 1e71 < (*.f64 (-.f64 b 1/2) (log.f64 c))

   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 92.6%

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

   3. Taylor expanded in y around 0 88.2%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 157:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 220:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 10^{+71}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := a + \left(z + t\right)\\ t_3 := y \cdot i + t_2\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + b \cdot \log c\right)\right)\\ \mathbf{elif}\;t_1 \leq 157:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 220:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;t_1 \leq 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ a (+ z t))) (t_3 (+ (* y i) t_2)))
   (if (<= t_1 -2e+93)
     (+ (* y i) (+ a (+ t (* b (log c)))))
     (if (<= t_1 157.0)
       t_3
       (if (<= t_1 220.0)
         (+ (* y i) (* x (log y)))
         (if (<= t_1 1e+71) t_3 (+ t_1 t_2)))))))

C

assert(z < t && t < a);
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 t_2 = a + (z + t);
	double t_3 = (y * i) + t_2;
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = (y * i) + (a + (t + (b * log(c))));
	} else if (t_1 <= 157.0) {
		tmp = t_3;
	} else if (t_1 <= 220.0) {
		tmp = (y * i) + (x * log(y));
	} else if (t_1 <= 1e+71) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = a + (z + t)
    t_3 = (y * i) + t_2
    if (t_1 <= (-2d+93)) then
        tmp = (y * i) + (a + (t + (b * log(c))))
    else if (t_1 <= 157.0d0) then
        tmp = t_3
    else if (t_1 <= 220.0d0) then
        tmp = (y * i) + (x * log(y))
    else if (t_1 <= 1d+71) then
        tmp = t_3
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

assert z < t && t < a;
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 t_2 = a + (z + t);
	double t_3 = (y * i) + t_2;
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = (y * i) + (a + (t + (b * Math.log(c))));
	} else if (t_1 <= 157.0) {
		tmp = t_3;
	} else if (t_1 <= 220.0) {
		tmp = (y * i) + (x * Math.log(y));
	} else if (t_1 <= 1e+71) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = a + (z + t)
	t_3 = (y * i) + t_2
	tmp = 0
	if t_1 <= -2e+93:
		tmp = (y * i) + (a + (t + (b * math.log(c))))
	elif t_1 <= 157.0:
		tmp = t_3
	elif t_1 <= 220.0:
		tmp = (y * i) + (x * math.log(y))
	elif t_1 <= 1e+71:
		tmp = t_3
	else:
		tmp = t_1 + t_2
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(a + Float64(z + t))
	t_3 = Float64(Float64(y * i) + t_2)
	tmp = 0.0
	if (t_1 <= -2e+93)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(b * log(c)))));
	elseif (t_1 <= 157.0)
		tmp = t_3;
	elseif (t_1 <= 220.0)
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	elseif (t_1 <= 1e+71)
		tmp = t_3;
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = a + (z + t);
	t_3 = (y * i) + t_2;
	tmp = 0.0;
	if (t_1 <= -2e+93)
		tmp = (y * i) + (a + (t + (b * log(c))));
	elseif (t_1 <= 157.0)
		tmp = t_3;
	elseif (t_1 <= 220.0)
		tmp = (y * i) + (x * log(y));
	elseif (t_1 <= 1e+71)
		tmp = t_3;
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * i), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+93], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 157.0], t$95$3, If[LessEqual[t$95$1, 220.0], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+71], t$95$3, N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (-.f64 b 1/2) (log.f64 c)) < -2.00000000000000009e93

   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 88.4%

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

   3. Taylor expanded in b around inf 88.4%

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

   4. Taylor expanded in z around 0 86.3%

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

   if -2.00000000000000009e93 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 157 or 220 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 1e71

   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 83.3%

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

   3. Taylor expanded in b around inf 82.2%

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

   4. Taylor expanded in b around 0 81.6%

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

   if 157 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 220

   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 b around 0 99.6%

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

   3. Taylor expanded in x around inf 92.1%

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

   if 1e71 < (*.f64 (-.f64 b 1/2) (log.f64 c))

   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 92.6%

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

   3. Taylor expanded in y around 0 88.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + b \cdot \log c\right)\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 157:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 220:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 10^{+71}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))) (* y i)))

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0))) + (y * i)
end function

Java

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

Python

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

Julia

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

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (y * i);
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(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] + N[(y * i), $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%

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

Alternative 5: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+179} \lor \neg \left(x \leq 2.2 \cdot 10^{+195}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -6.5e+179) (not (<= x 2.2e+195)))
   (+ (* y i) (* x (log y)))
   (fma y i (+ a (+ (* (log c) (- b 0.5)) (+ z t))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.5e+179) || !(x <= 2.2e+195)) {
		tmp = (y * i) + (x * log(y));
	} else {
		tmp = fma(y, i, (a + ((log(c) * (b - 0.5)) + (z + t))));
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -6.5e+179) || !(x <= 2.2e+195))
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	else
		tmp = fma(y, i, Float64(a + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + t))));
	end
	return tmp
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -6.5e+179], N[Not[LessEqual[x, 2.2e+195]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000052e179 or 2.2e195 < 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. Taylor expanded in b around 0 93.8%

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

   3. Taylor expanded in x around inf 84.1%

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

   if -6.50000000000000052e179 < x < 2.2e195

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 95.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+179} \lor \neg \left(x \leq 2.2 \cdot 10^{+195}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 6: 99.3% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z (* x (log y)))))))

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) + ((log(c) * (b - 0.5d0)) + (a + (z + (x * log(y)))))
end function

Java

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

Python

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

Julia

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

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + (x * log(y)))));
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $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 t around 0 85.6%

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

3. Final simplification 85.6%

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

Alternative 7: 97.7% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (+ a (+ z (* x (log y)))) (* b (log c)))))

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 + (z + (x * log(y)))) + (b * log(c)))
end function

Java

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

Python

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

Julia

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

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((a + (z + (x * log(y)))) + (b * log(c)));
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + N[(x * N[Log[y], $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 t around 0 85.6%

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

3. Taylor expanded in b around inf 84.8%

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

4. Final simplification 84.8%

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

Alternative 8: 90.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+179} \lor \neg \left(x \leq 2.9 \cdot 10^{+194}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.55e+179) (not (<= x 2.9e+194)))
   (+ (* y i) (* x (log y)))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.55e+179) || !(x <= 2.9e+194)) {
		tmp = (y * i) + (x * log(y));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-2.55d+179)) .or. (.not. (x <= 2.9d+194))) then
        tmp = (y * i) + (x * log(y))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.55e+179) || !(x <= 2.9e+194)) {
		tmp = (y * i) + (x * Math.log(y));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.55e+179) or not (x <= 2.9e+194):
		tmp = (y * i) + (x * math.log(y))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.55e+179) || !(x <= 2.9e+194))
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.55e+179) || ~((x <= 2.9e+194)))
		tmp = (y * i) + (x * log(y));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.55e+179], N[Not[LessEqual[x, 2.9e+194]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5500000000000001e179 or 2.9000000000000001e194 < 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. Taylor expanded in b around 0 93.8%

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

   3. Taylor expanded in x around inf 84.1%

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

   if -2.5500000000000001e179 < x < 2.9000000000000001e194

   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 95.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+179} \lor \neg \left(x \leq 2.9 \cdot 10^{+194}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 9: 89.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+179} \lor \neg \left(x \leq 7.5 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.5e+179) (not (<= x 7.5e+154)))
   (+ (* y i) (* x (log y)))
   (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.5e+179) || !(x <= 7.5e+154)) {
		tmp = (y * i) + (x * log(y));
	} else {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-8.5d+179)) .or. (.not. (x <= 7.5d+154))) then
        tmp = (y * i) + (x * log(y))
    else
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.5e+179) || !(x <= 7.5e+154)) {
		tmp = (y * i) + (x * Math.log(y));
	} else {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8.5e+179) or not (x <= 7.5e+154):
		tmp = (y * i) + (x * math.log(y))
	else:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8.5e+179) || !(x <= 7.5e+154))
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -8.5e+179) || ~((x <= 7.5e+154)))
		tmp = (y * i) + (x * log(y));
	else
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8.5e+179], N[Not[LessEqual[x, 7.5e+154]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999962e179 or 7.5000000000000004e154 < 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. Taylor expanded in b around 0 94.4%

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

   3. Taylor expanded in x around inf 82.3%

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

   if -8.49999999999999962e179 < x < 7.5000000000000004e154

   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 96.1%

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

   3. Taylor expanded in t around 0 80.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+179} \lor \neg \left(x \leq 7.5 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]

Alternative 10: 71.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+168}:\\ \;\;\;\;a + \left(t + t_1\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-159}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))) (t_2 (+ (* y i) (+ a (+ z t)))))
   (if (<= b -1.42e+168)
     (+ a (+ t t_1))
     (if (<= b -2.7e-68)
       t_2
       (if (<= b -4.5e-159)
         (+ (* y i) (* x (log y)))
         (if (<= b 1.85e+197) t_2 (+ (* y i) t_1)))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double t_2 = (y * i) + (a + (z + t));
	double tmp;
	if (b <= -1.42e+168) {
		tmp = a + (t + t_1);
	} else if (b <= -2.7e-68) {
		tmp = t_2;
	} else if (b <= -4.5e-159) {
		tmp = (y * i) + (x * log(y));
	} else if (b <= 1.85e+197) {
		tmp = t_2;
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 = b * log(c)
    t_2 = (y * i) + (a + (z + t))
    if (b <= (-1.42d+168)) then
        tmp = a + (t + t_1)
    else if (b <= (-2.7d-68)) then
        tmp = t_2
    else if (b <= (-4.5d-159)) then
        tmp = (y * i) + (x * log(y))
    else if (b <= 1.85d+197) then
        tmp = t_2
    else
        tmp = (y * i) + t_1
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double t_2 = (y * i) + (a + (z + t));
	double tmp;
	if (b <= -1.42e+168) {
		tmp = a + (t + t_1);
	} else if (b <= -2.7e-68) {
		tmp = t_2;
	} else if (b <= -4.5e-159) {
		tmp = (y * i) + (x * Math.log(y));
	} else if (b <= 1.85e+197) {
		tmp = t_2;
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = (y * i) + (a + (z + t))
	tmp = 0
	if b <= -1.42e+168:
		tmp = a + (t + t_1)
	elif b <= -2.7e-68:
		tmp = t_2
	elif b <= -4.5e-159:
		tmp = (y * i) + (x * math.log(y))
	elif b <= 1.85e+197:
		tmp = t_2
	else:
		tmp = (y * i) + t_1
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(Float64(y * i) + Float64(a + Float64(z + t)))
	tmp = 0.0
	if (b <= -1.42e+168)
		tmp = Float64(a + Float64(t + t_1));
	elseif (b <= -2.7e-68)
		tmp = t_2;
	elseif (b <= -4.5e-159)
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	elseif (b <= 1.85e+197)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) + t_1);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	t_2 = (y * i) + (a + (z + t));
	tmp = 0.0;
	if (b <= -1.42e+168)
		tmp = a + (t + t_1);
	elseif (b <= -2.7e-68)
		tmp = t_2;
	elseif (b <= -4.5e-159)
		tmp = (y * i) + (x * log(y));
	elseif (b <= 1.85e+197)
		tmp = t_2;
	else
		tmp = (y * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e+168], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-68], t$95$2, If[LessEqual[b, -4.5e-159], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+197], t$95$2, N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.42e168

   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. Taylor expanded in x around 0 89.8%

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

   3. Taylor expanded in b around inf 89.8%

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

   4. Taylor expanded in z around 0 84.0%

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

   5. Taylor expanded in y around 0 80.1%

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

   if -1.42e168 < b < -2.7000000000000002e-68 or -4.49999999999999989e-159 < b < 1.8500000000000002e197

   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 84.3%

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

   3. Taylor expanded in b around inf 83.4%

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

   4. Taylor expanded in b around 0 78.3%

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

   if -2.7000000000000002e-68 < b < -4.49999999999999989e-159

   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 0 99.8%

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

   3. Taylor expanded in x around inf 77.9%

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

   if 1.8500000000000002e197 < b

   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 99.6%

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

   3. Taylor expanded in b around inf 99.6%

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

   4. Taylor expanded in b around inf 99.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+168}:\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-68}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-159}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+197}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]

Alternative 11: 72.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.55 \cdot 10^{+168} \lor \neg \left(b \leq 8.5 \cdot 10^{+149}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -3.55e+168) (not (<= b 8.5e+149)))
   (+ a (+ t (* b (log c))))
   (+ (* y i) (+ a (+ z t)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.55e+168) || !(b <= 8.5e+149)) {
		tmp = a + (t + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 ((b <= (-3.55d+168)) .or. (.not. (b <= 8.5d+149))) then
        tmp = a + (t + (b * log(c)))
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.55e+168) || !(b <= 8.5e+149)) {
		tmp = a + (t + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -3.55e+168) or not (b <= 8.5e+149):
		tmp = a + (t + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -3.55e+168) || !(b <= 8.5e+149))
		tmp = Float64(a + Float64(t + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -3.55e+168) || ~((b <= 8.5e+149)))
		tmp = a + (t + (b * log(c)));
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -3.55e+168], N[Not[LessEqual[b, 8.5e+149]], $MachinePrecision]], N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.55000000000000006e168 or 8.49999999999999956e149 < b

   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. Taylor expanded in x around 0 90.7%

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

   3. Taylor expanded in b around inf 90.7%

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

   4. Taylor expanded in z around 0 85.8%

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

   5. Taylor expanded in y around 0 80.2%

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

   if -3.55000000000000006e168 < b < 8.49999999999999956e149

   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 81.1%

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

   3. Taylor expanded in b around inf 80.3%

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

   4. Taylor expanded in b around 0 76.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.55 \cdot 10^{+168} \lor \neg \left(b \leq 8.5 \cdot 10^{+149}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 12: 73.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+168}:\\ \;\;\;\;a + \left(t + t_1\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+194}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= b -1.75e+168)
     (+ a (+ t t_1))
     (if (<= b 8.6e+194) (+ (* y i) (+ a (+ z t))) (+ (* y i) t_1)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (b <= -1.75e+168) {
		tmp = a + (t + t_1);
	} else if (b <= 8.6e+194) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 = b * log(c)
    if (b <= (-1.75d+168)) then
        tmp = a + (t + t_1)
    else if (b <= 8.6d+194) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = (y * i) + t_1
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (b <= -1.75e+168) {
		tmp = a + (t + t_1);
	} else if (b <= 8.6e+194) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if b <= -1.75e+168:
		tmp = a + (t + t_1)
	elif b <= 8.6e+194:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = (y * i) + t_1
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (b <= -1.75e+168)
		tmp = Float64(a + Float64(t + t_1));
	elseif (b <= 8.6e+194)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(Float64(y * i) + t_1);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (b <= -1.75e+168)
		tmp = a + (t + t_1);
	elseif (b <= 8.6e+194)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = (y * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e+168], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+194], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7500000000000001e168

   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. Taylor expanded in x around 0 89.8%

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

   3. Taylor expanded in b around inf 89.8%

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

   4. Taylor expanded in z around 0 84.0%

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

   5. Taylor expanded in y around 0 80.1%

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

   if -1.7500000000000001e168 < b < 8.59999999999999988e194

   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 80.9%

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

   3. Taylor expanded in b around inf 80.1%

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

   4. Taylor expanded in b around 0 75.5%

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

   if 8.59999999999999988e194 < b

   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 99.6%

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

   3. Taylor expanded in b around inf 99.6%

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

   4. Taylor expanded in b around inf 99.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+168}:\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+194}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]

Alternative 13: 75.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.45e+70)
   (+ (* y i) (+ a (+ z t)))
   (+ (* y i) (+ a (* b (log c))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+70) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-2.45d+70)) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+70) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.45e+70:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.45e+70)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.45e+70)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.45e+70], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000014e70

   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 81.3%

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

   3. Taylor expanded in b around inf 81.3%

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

   4. Taylor expanded in b around 0 74.6%

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

   if -2.45000000000000014e70 < 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 x around 0 83.6%

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

   3. Taylor expanded in b around inf 82.8%

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

   4. Taylor expanded in z around 0 75.7%

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

   5. Taylor expanded in t around 0 60.9%

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

      1. +-commutative 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 14: 70.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+177} \lor \neg \left(b \leq 1.25 \cdot 10^{+198}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -2.2e+177) (not (<= b 1.25e+198)))
   (* b (log c))
   (+ (* y i) (+ a (+ z t)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -2.2e+177) || !(b <= 1.25e+198)) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 ((b <= (-2.2d+177)) .or. (.not. (b <= 1.25d+198))) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -2.2e+177) || !(b <= 1.25e+198)) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -2.2e+177) or not (b <= 1.25e+198):
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -2.2e+177) || !(b <= 1.25e+198))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -2.2e+177) || ~((b <= 1.25e+198)))
		tmp = b * log(c);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -2.2e+177], N[Not[LessEqual[b, 1.25e+198]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1999999999999998e177 or 1.25000000000000012e198 < b

   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. Taylor expanded in x around 0 92.7%

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

   3. Taylor expanded in b around inf 92.7%

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

   4. Taylor expanded in z around 0 90.7%

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

   5. Taylor expanded in b around inf 74.4%

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

   if -2.1999999999999998e177 < b < 1.25000000000000012e198

   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 81.3%

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

   3. Taylor expanded in b around inf 80.4%

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

   4. Taylor expanded in b around 0 75.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+177} \lor \neg \left(b \leq 1.25 \cdot 10^{+198}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 15: 36.8% accurate, 19.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-307}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-98}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+208}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -1.3e-237)
   z
   (if (<= a -4.3e-307)
     (* y i)
     (if (<= a 9.2e-98) z (if (<= a 4e+208) (* y i) a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.3e-237) {
		tmp = z;
	} else if (a <= -4.3e-307) {
		tmp = y * i;
	} else if (a <= 9.2e-98) {
		tmp = z;
	} else if (a <= 4e+208) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-1.3d-237)) then
        tmp = z
    else if (a <= (-4.3d-307)) then
        tmp = y * i
    else if (a <= 9.2d-98) then
        tmp = z
    else if (a <= 4d+208) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.3e-237) {
		tmp = z;
	} else if (a <= -4.3e-307) {
		tmp = y * i;
	} else if (a <= 9.2e-98) {
		tmp = z;
	} else if (a <= 4e+208) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -1.3e-237:
		tmp = z
	elif a <= -4.3e-307:
		tmp = y * i
	elif a <= 9.2e-98:
		tmp = z
	elif a <= 4e+208:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -1.3e-237)
		tmp = z;
	elseif (a <= -4.3e-307)
		tmp = Float64(y * i);
	elseif (a <= 9.2e-98)
		tmp = z;
	elseif (a <= 4e+208)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -1.3e-237)
		tmp = z;
	elseif (a <= -4.3e-307)
		tmp = y * i;
	elseif (a <= 9.2e-98)
		tmp = z;
	elseif (a <= 4e+208)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -1.3e-237], z, If[LessEqual[a, -4.3e-307], N[(y * i), $MachinePrecision], If[LessEqual[a, 9.2e-98], z, If[LessEqual[a, 4e+208], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3000000000000001e-237 or -4.3000000000000001e-307 < a < 9.20000000000000002e-98

   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 78.6%

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

   3. Taylor expanded in z around inf 14.1%

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

   if -1.3000000000000001e-237 < a < -4.3000000000000001e-307 or 9.20000000000000002e-98 < a < 3.9999999999999999e208

   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 y around inf 40.3%

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

      1. *-commutative 40.3%

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

   4. Simplified 40.3%

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

   if 3.9999999999999999e208 < 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 x around 0 99.9%

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

   3. Taylor expanded in a around inf 69.5%

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

4. Final simplification 25.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-307}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-98}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+208}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 47.6% accurate, 19.6× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-233}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-309}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -6.8e-233)
   z
   (if (<= a 3e-309) (* y i) (if (<= a 9e-99) z (+ a (* y i))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -6.8e-233) {
		tmp = z;
	} else if (a <= 3e-309) {
		tmp = y * i;
	} else if (a <= 9e-99) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-6.8d-233)) then
        tmp = z
    else if (a <= 3d-309) then
        tmp = y * i
    else if (a <= 9d-99) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -6.8e-233) {
		tmp = z;
	} else if (a <= 3e-309) {
		tmp = y * i;
	} else if (a <= 9e-99) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -6.8e-233:
		tmp = z
	elif a <= 3e-309:
		tmp = y * i
	elif a <= 9e-99:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -6.8e-233)
		tmp = z;
	elseif (a <= 3e-309)
		tmp = Float64(y * i);
	elseif (a <= 9e-99)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -6.8e-233)
		tmp = z;
	elseif (a <= 3e-309)
		tmp = y * i;
	elseif (a <= 9e-99)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -6.8e-233], z, If[LessEqual[a, 3e-309], N[(y * i), $MachinePrecision], If[LessEqual[a, 9e-99], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.8000000000000004e-233 or 3.000000000000001e-309 < a < 9.0000000000000006e-99

   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 78.6%

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

   3. Taylor expanded in z around inf 14.1%

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

   if -6.8000000000000004e-233 < a < 3.000000000000001e-309

   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 y around inf 31.4%

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

      1. *-commutative 31.4%

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

   4. Simplified 31.4%

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

   if 9.0000000000000006e-99 < a

   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 60.9%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-233}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-309}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 17: 60.0% accurate, 24.2× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{+48}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2e+48) (+ z (* y i)) (+ (+ t a) (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2e+48) {
		tmp = z + (y * i);
	} else {
		tmp = (t + a) + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= 2d+48) then
        tmp = z + (y * i)
    else
        tmp = (t + a) + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2e+48) {
		tmp = z + (y * i);
	} else {
		tmp = (t + a) + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2e+48:
		tmp = z + (y * i)
	else:
		tmp = (t + a) + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2e+48)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(t + a) + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2e+48)
		tmp = z + (y * i);
	else
		tmp = (t + a) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2e+48], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.00000000000000009e48

   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 39.7%

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

   if 2.00000000000000009e48 < a

   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 95.6%

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

   3. Taylor expanded in b around inf 95.6%

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

   4. Taylor expanded in z around 0 89.2%

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

   5. Taylor expanded in b around 0 74.3%

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

      1. +-commutative 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{+48}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \]

Alternative 18: 67.2% accurate, 24.3× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ y \cdot i + \left(a + \left(z + t\right)\right) \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ a (+ z t))))

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 + (z + t))
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (a + (z + t));
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	return (y * i) + (a + (z + t))

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(a + Float64(z + t)))
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (a + (z + t));
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $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 x around 0 83.2%

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

3. Taylor expanded in b around inf 82.5%

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

4. Taylor expanded in b around 0 65.6%

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

5. Final simplification 65.6%

   \[\leadsto y \cdot i + \left(a + \left(z + t\right)\right) \]

Alternative 19: 59.7% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.6e+48) (+ z (* y i)) (+ a (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.6e+48) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= 3.6d+48) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.6e+48) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.6e+48:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.6e+48)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.6e+48)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.6e+48], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.59999999999999983e48

   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 39.7%

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

   if 3.59999999999999983e48 < a

   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 68.2%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 20: 37.4% accurate, 71.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= a 4e+48) z a))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4e+48) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= 4d+48) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4e+48) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4e+48:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4e+48)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4e+48)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4e+48], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 4.00000000000000018e48

   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 80.7%

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

   3. Taylor expanded in z around inf 13.4%

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

   if 4.00000000000000018e48 < a

   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 95.6%

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

   3. Taylor expanded in a around inf 45.8%

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

4. Final simplification 19.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 21: 22.3% accurate, 219.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ a \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 a)

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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

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

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	return a

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 83.2%

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

3. Taylor expanded in a around inf 15.6%

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

4. Final simplification 15.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023228 
(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)))