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

Percentage Accurate: 99.8% → 99.8%

Time: 18.8s

Alternatives: 22

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, 0.7× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. fma-def 99.9%

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

   6. sub-neg 99.9%

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

   7. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 92.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\left(y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right) + \left(t + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+145}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(b + -0.5\right) \cdot \log c + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (- b 0.5) -2e+212)
   (+ (+ (* y i) (fma (log c) (+ b -0.5) z)) (+ t a))
   (if (<= (- b 0.5) 1e+145)
     (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* -0.5 (log c))))
     (+ a (+ (* (+ b -0.5) (log c)) (fma y i z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b - 0.5) <= -2e+212) {
		tmp = ((y * i) + fma(log(c), (b + -0.5), z)) + (t + a);
	} else if ((b - 0.5) <= 1e+145) {
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (-0.5 * log(c)));
	} else {
		tmp = a + (((b + -0.5) * log(c)) + fma(y, i, z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b - 0.5) <= -2e+212)
		tmp = Float64(Float64(Float64(y * i) + fma(log(c), Float64(b + -0.5), z)) + Float64(t + a));
	elseif (Float64(b - 0.5) <= 1e+145)
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(-0.5 * log(c))));
	else
		tmp = Float64(a + Float64(Float64(Float64(b + -0.5) * log(c)) + fma(y, i, z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+212], N[(N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+145], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b 1/2) < -1.9999999999999998e212

   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. Add Preprocessing

   3. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

   5. Simplified 99.7%

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

   if -1.9999999999999998e212 < (-.f64 b 1/2) < 9.9999999999999999e144

   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. Add Preprocessing

   3. Taylor expanded in b around 0 98.2%

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

   if 9.9999999999999999e144 < (-.f64 b 1/2)

   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. Add Preprocessing

   3. Taylor expanded in x around 0 91.6%

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

   4. Taylor expanded in t around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. *-commutative 79.1%

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

      3. sub-neg 79.1%

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

      4. metadata-eval 79.1%

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

      5. +-commutative 79.1%

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

      6. +-commutative 79.1%

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

      7. fma-def 79.1%

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

   6. Simplified 79.1%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\left(y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right) + \left(t + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+145}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(b + -0.5\right) \cdot \log c + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+138} \lor \neg \left(x \leq 1.7 \cdot 10^{+240}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= x -7.2e+138) (not (<= x 1.7e+240)))
     (+ a (+ t (+ z (+ (* x (log y)) t_1))))
     (fma y i (+ a (+ t (+ z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((x <= -7.2e+138) || !(x <= 1.7e+240)) {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = fma(y, i, (a + (t + (z + t_1))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((x <= -7.2e+138) || !(x <= 1.7e+240))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -7.2e+138], N[Not[LessEqual[x, 1.7e+240]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000002e138 or 1.70000000000000004e240 < x

   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. Add Preprocessing

   3. Taylor expanded in y around 0 77.4%

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

   if -7.2000000000000002e138 < x < 1.70000000000000004e240

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 96.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+138} \lor \neg \left(x \leq 1.7 \cdot 10^{+240}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+118} \lor \neg \left(x \leq 8.5 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot i + \left(-0.5 \cdot \log c + \left(a + \left(t + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.2e+118) (not (<= x 8.5e+236)))
   (+ (* y i) (+ (* -0.5 (log c)) (+ a (+ t (* x (log y))))))
   (fma y i (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.2e+118) || !(x <= 8.5e+236)) {
		tmp = (y * i) + ((-0.5 * log(c)) + (a + (t + (x * log(y)))));
	} else {
		tmp = fma(y, i, (a + (t + (z + (log(c) * (b - 0.5))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.2e+118) || !(x <= 8.5e+236))
		tmp = Float64(Float64(y * i) + Float64(Float64(-0.5 * log(c)) + Float64(a + Float64(t + Float64(x * log(y))))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.2e+118], N[Not[LessEqual[x, 8.5e+236]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e118 or 8.5000000000000008e236 < x

   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. Add Preprocessing

   3. Taylor expanded in b around 0 90.9%

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

   4. Taylor expanded in z around 0 87.9%

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

      1. +-commutative 87.9%

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

   6. Simplified 87.9%

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

   if -1.2e118 < x < 8.5000000000000008e236

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 97.2%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+118} \lor \neg \left(x \leq 8.5 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot i + \left(-0.5 \cdot \log c + \left(a + \left(t + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+145} \lor \neg \left(x \leq 2.4 \cdot 10^{+239}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= x -7.5e+145) (not (<= x 2.4e+239)))
     (+ a (+ t (+ (* x (log y)) t_1)))
     (+ a (+ t (+ z (+ (* y i) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((x <= -7.5e+145) || !(x <= 2.4e+239)) {
		tmp = a + (t + ((x * log(y)) + t_1));
	} else {
		tmp = a + (t + (z + ((y * i) + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if ((x <= (-7.5d+145)) .or. (.not. (x <= 2.4d+239))) then
        tmp = a + (t + ((x * log(y)) + t_1))
    else
        tmp = a + (t + (z + ((y * i) + t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((x <= -7.5e+145) || !(x <= 2.4e+239)) {
		tmp = a + (t + ((x * Math.log(y)) + t_1));
	} else {
		tmp = a + (t + (z + ((y * i) + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (x <= -7.5e+145) or not (x <= 2.4e+239):
		tmp = a + (t + ((x * math.log(y)) + t_1))
	else:
		tmp = a + (t + (z + ((y * i) + t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((x <= -7.5e+145) || !(x <= 2.4e+239))
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + t_1)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((x <= -7.5e+145) || ~((x <= 2.4e+239)))
		tmp = a + (t + ((x * log(y)) + t_1));
	else
		tmp = a + (t + (z + ((y * i) + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -7.5e+145], N[Not[LessEqual[x, 2.4e+239]], $MachinePrecision]], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000006e145 or 2.4e239 < x

   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. Add Preprocessing

   3. Taylor expanded in y around 0 77.4%

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

   4. Taylor expanded in z around 0 71.6%

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

   if -7.50000000000000006e145 < x < 2.4e239

   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. Add Preprocessing

   3. Taylor expanded in x around 0 96.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145} \lor \neg \left(x \leq 2.4 \cdot 10^{+239}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+145} \lor \neg \left(x \leq 1.1 \cdot 10^{+240}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= x -7.5e+145) (not (<= x 1.1e+240)))
     (+ a (+ t (+ (* x (log y)) t_1)))
     (fma y i (+ a (+ t (+ z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((x <= -7.5e+145) || !(x <= 1.1e+240)) {
		tmp = a + (t + ((x * log(y)) + t_1));
	} else {
		tmp = fma(y, i, (a + (t + (z + t_1))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((x <= -7.5e+145) || !(x <= 1.1e+240))
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + t_1)));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -7.5e+145], N[Not[LessEqual[x, 1.1e+240]], $MachinePrecision]], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000006e145 or 1.1000000000000001e240 < x

   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. Add Preprocessing

   3. Taylor expanded in y around 0 77.4%

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

   4. Taylor expanded in z around 0 71.6%

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

   if -7.50000000000000006e145 < x < 1.1000000000000001e240

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 96.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145} \lor \neg \left(x \leq 1.1 \cdot 10^{+240}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 8: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;a \leq 8.5 \cdot 10^{+120}:\\ \;\;\;\;t + \left(z + t\_1\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+226}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* (log c) (- b 0.5)))))
   (if (<= a 8.5e+120)
     (+ t (+ z t_1))
     (if (<= a 2.6e+226) (+ a (+ t (fma y i z))) (+ a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (log(c) * (b - 0.5));
	double tmp;
	if (a <= 8.5e+120) {
		tmp = t + (z + t_1);
	} else if (a <= 2.6e+226) {
		tmp = a + (t + fma(y, i, z));
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))
	tmp = 0.0
	if (a <= 8.5e+120)
		tmp = Float64(t + Float64(z + t_1));
	elseif (a <= 2.6e+226)
		tmp = Float64(a + Float64(t + fma(y, i, z)));
	else
		tmp = Float64(a + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 8.5e+120], N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+226], N[(a + N[(t + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 8.50000000000000026e120

   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. Add Preprocessing

   3. Taylor expanded in x around 0 85.4%

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

   4. Taylor expanded in a around 0 76.7%

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

   if 8.50000000000000026e120 < a < 2.6000000000000002e226

   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. Add Preprocessing

   3. Taylor expanded in x around 0 91.1%

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

   4. Taylor expanded in i around inf 81.6%

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

      1. *-commutative 81.6%

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

   6. Simplified 81.6%

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

      1. +-commutative 81.6%

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

      2. fma-def 81.6%

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

   8. Applied egg-rr 81.6%

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

   if 2.6000000000000002e226 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in t around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around 0 98.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+120}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+226}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -7.5e+145)
   (+ a (+ t (+ z (* x (log y)))))
   (+ a (+ t (+ z (+ (* y i) (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.5e+145) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-7.5d+145)) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.5e+145) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = a + (t + (z + ((y * i) + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -7.5e+145:
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = a + (t + (z + ((y * i) + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -7.5e+145)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -7.5e+145)
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -7.5e+145], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000006e145

   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. Add Preprocessing

   3. Taylor expanded in y around 0 81.4%

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

   4. Taylor expanded in x around inf 70.7%

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

   if -7.50000000000000006e145 < x

   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. Add Preprocessing

   3. Taylor expanded in x around 0 92.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+228} \lor \neg \left(b \leq 7.5 \cdot 10^{+206}\right):\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.8e+228) (not (<= b 7.5e+206)))
   (+ a (* b (log c)))
   (+ a (+ t (fma y i z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.8e+228) || !(b <= 7.5e+206)) {
		tmp = a + (b * log(c));
	} else {
		tmp = a + (t + fma(y, i, z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.8e+228) || !(b <= 7.5e+206))
		tmp = Float64(a + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(t + fma(y, i, z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.8e+228], N[Not[LessEqual[b, 7.5e+206]], $MachinePrecision]], N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8e228 or 7.49999999999999958e206 < 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. Add Preprocessing

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in t around 0 89.9%

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

      1. associate-+r+ 89.9%

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

      2. *-commutative 89.9%

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

      3. sub-neg 89.9%

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

      4. metadata-eval 89.9%

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

      5. +-commutative 89.9%

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

      6. +-commutative 89.9%

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

      7. fma-def 89.9%

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

   6. Simplified 89.9%

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

   7. Taylor expanded in y around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. sub-neg 73.0%

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

      3. metadata-eval 73.0%

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

      4. fma-def 73.0%

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

   9. Simplified 73.0%

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

   10. Taylor expanded in b around inf 66.7%

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

       1. *-commutative 66.7%

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

   12. Simplified 66.7%

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

   if -1.8e228 < b < 7.49999999999999958e206

   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. Add Preprocessing

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in i around inf 77.9%

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

      1. *-commutative 77.9%

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

   6. Simplified 77.9%

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

      1. +-commutative 77.9%

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

      2. fma-def 77.9%

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

   8. Applied egg-rr 77.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+228} \lor \neg \left(b \leq 7.5 \cdot 10^{+206}\right):\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8.6e+69)
   (+ a (+ t (fma y i z)))
   (+ a (+ (* y i) (* (log c) (- b 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8.6e+69) {
		tmp = a + (t + fma(y, i, z));
	} else {
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8.6e+69)
		tmp = Float64(a + Float64(t + fma(y, i, z)));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8.6e+69], N[(a + N[(t + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999986e69

   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. Add Preprocessing

   3. Taylor expanded in x around 0 88.3%

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

   4. Taylor expanded in i around inf 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

      1. +-commutative 72.1%

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

      2. fma-def 72.1%

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

   8. Applied egg-rr 72.1%

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

   if -8.59999999999999986e69 < z

   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. Add Preprocessing

   3. Taylor expanded in x around 0 86.2%

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

   4. Taylor expanded in t around 0 69.6%

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

      1. associate-+r+ 69.6%

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

      2. *-commutative 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

      5. +-commutative 69.6%

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

      6. +-commutative 69.6%

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

      7. fma-def 69.6%

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

   6. Simplified 69.6%

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

   7. Taylor expanded in z around 0 60.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+226} \lor \neg \left(b \leq 3.1 \cdot 10^{+202}\right):\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.8e+226) (not (<= b 3.1e+202)))
   (+ a (* b (log c)))
   (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.8e+226) || !(b <= 3.1e+202)) {
		tmp = a + (b * log(c));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-1.8d+226)) .or. (.not. (b <= 3.1d+202))) then
        tmp = a + (b * log(c))
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.8e+226) || !(b <= 3.1e+202)) {
		tmp = a + (b * Math.log(c));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.8e+226) or not (b <= 3.1e+202):
		tmp = a + (b * math.log(c))
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.8e+226) || !(b <= 3.1e+202))
		tmp = Float64(a + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -1.8e+226) || ~((b <= 3.1e+202)))
		tmp = a + (b * log(c));
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.8e+226], N[Not[LessEqual[b, 3.1e+202]], $MachinePrecision]], N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7999999999999999e226 or 3.09999999999999991e202 < 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. Add Preprocessing

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in t around 0 89.9%

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

      1. associate-+r+ 89.9%

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

      2. *-commutative 89.9%

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

      3. sub-neg 89.9%

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

      4. metadata-eval 89.9%

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

      5. +-commutative 89.9%

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

      6. +-commutative 89.9%

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

      7. fma-def 89.9%

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

   6. Simplified 89.9%

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

   7. Taylor expanded in y around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. sub-neg 73.0%

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

      3. metadata-eval 73.0%

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

      4. fma-def 73.0%

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

   9. Simplified 73.0%

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

   10. Taylor expanded in b around inf 66.7%

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

       1. *-commutative 66.7%

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

   12. Simplified 66.7%

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

   if -1.7999999999999999e226 < b < 3.09999999999999991e202

   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. Add Preprocessing

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in i around inf 77.9%

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

      1. *-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+226} \lor \neg \left(b \leq 3.1 \cdot 10^{+202}\right):\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+90}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 8e+90) (+ a (+ z (* (log c) (- b 0.5)))) (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8e+90) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 8d+90) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8e+90) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 8e+90:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 8e+90)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 8e+90)
		tmp = a + (z + (log(c) * (b - 0.5)));
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 8e+90], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.99999999999999973e90

   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. Add Preprocessing

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. associate-+r+ 65.2%

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

      2. *-commutative 65.2%

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

      3. sub-neg 65.2%

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

      4. metadata-eval 65.2%

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

      5. +-commutative 65.2%

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

      6. +-commutative 65.2%

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

      7. fma-def 65.2%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in y around 0 57.3%

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

   if 7.99999999999999973e90 < y

   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. Add Preprocessing

   3. Taylor expanded in x around 0 91.0%

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

   4. Taylor expanded in i around inf 81.2%

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

      1. *-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+90}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145} \lor \neg \left(x \leq 2.9 \cdot 10^{+240}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -7.5e+145) (not (<= x 2.9e+240)))
   (* x (log y))
   (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -7.5e+145) || !(x <= 2.9e+240)) {
		tmp = x * log(y);
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-7.5d+145)) .or. (.not. (x <= 2.9d+240))) then
        tmp = x * log(y)
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -7.5e+145) || !(x <= 2.9e+240)) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -7.5e+145) or not (x <= 2.9e+240):
		tmp = x * math.log(y)
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -7.5e+145) || !(x <= 2.9e+240))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -7.5e+145) || ~((x <= 2.9e+240)))
		tmp = x * log(y);
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -7.5e+145], N[Not[LessEqual[x, 2.9e+240]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000006e145 or 2.89999999999999998e240 < x

   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. Add Preprocessing

   3. Taylor expanded in x around inf 56.0%

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

   if -7.50000000000000006e145 < x < 2.89999999999999998e240

   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. Add Preprocessing

   3. Taylor expanded in x around 0 96.8%

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

   4. Taylor expanded in i around inf 76.4%

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

      1. *-commutative 76.4%

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

   6. Simplified 76.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145} \lor \neg \left(x \leq 2.9 \cdot 10^{+240}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.8% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-208}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-136}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 3e-208) z (if (<= y 4.4e-136) a (if (<= y 1.55e+83) z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 3e-208) {
		tmp = z;
	} else if (y <= 4.4e-136) {
		tmp = a;
	} else if (y <= 1.55e+83) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 3d-208) then
        tmp = z
    else if (y <= 4.4d-136) then
        tmp = a
    else if (y <= 1.55d+83) then
        tmp = z
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 3e-208) {
		tmp = z;
	} else if (y <= 4.4e-136) {
		tmp = a;
	} else if (y <= 1.55e+83) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 3e-208:
		tmp = z
	elif y <= 4.4e-136:
		tmp = a
	elif y <= 1.55e+83:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 3e-208)
		tmp = z;
	elseif (y <= 4.4e-136)
		tmp = a;
	elseif (y <= 1.55e+83)
		tmp = z;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 3e-208)
		tmp = z;
	elseif (y <= 4.4e-136)
		tmp = a;
	elseif (y <= 1.55e+83)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 3e-208], z, If[LessEqual[y, 4.4e-136], a, If[LessEqual[y, 1.55e+83], z, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.99999999999999986e-208 or 4.4000000000000002e-136 < y < 1.54999999999999996e83

   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. Add Preprocessing

   3. Taylor expanded in z around inf 20.9%

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

   if 2.99999999999999986e-208 < y < 4.4000000000000002e-136

   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. Add Preprocessing

   3. Taylor expanded in a around inf 23.8%

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

   if 1.54999999999999996e83 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-208}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-136}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.1% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-209}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-136}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;y \leq 10^{+78}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 5.2e-209) z (if (<= y 7e-136) (+ t a) (if (<= y 1e+78) z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.2e-209) {
		tmp = z;
	} else if (y <= 7e-136) {
		tmp = t + a;
	} else if (y <= 1e+78) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 5.2d-209) then
        tmp = z
    else if (y <= 7d-136) then
        tmp = t + a
    else if (y <= 1d+78) then
        tmp = z
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.2e-209) {
		tmp = z;
	} else if (y <= 7e-136) {
		tmp = t + a;
	} else if (y <= 1e+78) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 5.2e-209:
		tmp = z
	elif y <= 7e-136:
		tmp = t + a
	elif y <= 1e+78:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 5.2e-209)
		tmp = z;
	elseif (y <= 7e-136)
		tmp = Float64(t + a);
	elseif (y <= 1e+78)
		tmp = z;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 5.2e-209)
		tmp = z;
	elseif (y <= 7e-136)
		tmp = t + a;
	elseif (y <= 1e+78)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 5.2e-209], z, If[LessEqual[y, 7e-136], N[(t + a), $MachinePrecision], If[LessEqual[y, 1e+78], z, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.19999999999999969e-209 or 7.00000000000000058e-136 < y < 1.00000000000000001e78

   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. Add Preprocessing

   3. Taylor expanded in z around inf 20.9%

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

   if 5.19999999999999969e-209 < y < 7.00000000000000058e-136

   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. Add Preprocessing

   3. Taylor expanded in x around 0 83.7%

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

   4. Taylor expanded in i around inf 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in t around inf 43.1%

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

   if 1.00000000000000001e78 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-209}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-136}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;y \leq 10^{+78}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.0% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.5e+120) (+ z a) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.5e+120) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-6.5d+120)) then
        tmp = z + a
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.5e+120) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.5e+120:
		tmp = z + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.5e+120)
		tmp = Float64(z + a);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -6.5e+120)
		tmp = z + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.5e+120], N[(z + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999997e120

   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. Add Preprocessing

   3. Taylor expanded in x around 0 93.7%

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

   4. Taylor expanded in t around 0 85.6%

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

      1. associate-+r+ 85.6%

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

      2. *-commutative 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

      5. +-commutative 85.6%

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

      6. +-commutative 85.6%

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

      7. fma-def 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in z around inf 49.2%

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

   if -6.4999999999999997e120 < z

   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. Add Preprocessing

   3. Taylor expanded in x around 0 85.2%

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

   4. Taylor expanded in t around 0 69.2%

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

      1. associate-+r+ 69.2%

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

      2. *-commutative 69.2%

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

      3. sub-neg 69.2%

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

      4. metadata-eval 69.2%

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

      5. +-commutative 69.2%

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

      6. +-commutative 69.2%

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

      7. fma-def 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around inf 43.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.4% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+121}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2e+121) (+ a (+ z t)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+121) {
		tmp = a + (z + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2d+121)) then
        tmp = a + (z + t)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+121) {
		tmp = a + (z + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2e+121:
		tmp = a + (z + t)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2e+121)
		tmp = Float64(a + Float64(z + t));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2e+121)
		tmp = a + (z + t);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2e+121], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000007e121

   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. Add Preprocessing

   3. Taylor expanded in x around 0 93.7%

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

   4. Taylor expanded in z around inf 56.2%

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

   if -2.00000000000000007e121 < z

   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. Add Preprocessing

   3. Taylor expanded in x around 0 85.2%

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

   4. Taylor expanded in t around 0 69.2%

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

      1. associate-+r+ 69.2%

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

      2. *-commutative 69.2%

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

      3. sub-neg 69.2%

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

      4. metadata-eval 69.2%

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

      5. +-commutative 69.2%

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

      6. +-commutative 69.2%

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

      7. fma-def 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around inf 43.2%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+121}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.0% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0 86.6%

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

4. Taylor expanded in i around inf 68.1%

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

   1. *-commutative 68.1%

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

6. Simplified 68.1%

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

7. Final simplification 68.1%

   \[\leadsto a + \left(t + \left(z + y \cdot i\right)\right) \]
8. Add Preprocessing

Alternative 20: 39.8% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+105}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.7e+105) (+ z a) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.7e+105) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.7d+105) then
        tmp = z + a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.7e+105) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.7e+105:
		tmp = z + a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.7e+105)
		tmp = Float64(z + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.7e+105)
		tmp = z + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.7e+105], N[(z + a), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7e105

   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. Add Preprocessing

   3. Taylor expanded in x around 0 84.0%

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

   4. Taylor expanded in t around 0 66.1%

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

      1. associate-+r+ 66.1%

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

      2. *-commutative 66.1%

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

      3. sub-neg 66.1%

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

      4. metadata-eval 66.1%

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

      5. +-commutative 66.1%

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

      6. +-commutative 66.1%

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

      7. fma-def 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in z around inf 36.1%

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

   if 1.7e105 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+105}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.5% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -1.95e+86) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.95e+86) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.95d+86)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.95e+86) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.95e+86:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.95e+86)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.95e+86)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.95e+86], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e86

   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. Add Preprocessing

   3. Taylor expanded in z around inf 35.3%

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

   if -1.9500000000000001e86 < z

   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. Add Preprocessing

   3. Taylor expanded in a around inf 15.2%

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

4. Final simplification 19.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 15.7% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf 14.1%

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

4. Final simplification 14.1%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))