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

Percentage Accurate: 99.8% → 99.8%

Time: 18.6s

Alternatives: 23

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate-+l+ 99.5%

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

   2. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. +-commutative 99.5%

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

   5. associate-+r+ 99.5%

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

   6. associate-+l+ 99.5%

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

   7. +-commutative 99.5%

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

   8. associate-+l+ 99.5%

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

   9. +-commutative 99.5%

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

   10. fma-def 99.5%

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

   11. +-commutative 99.5%

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

   12. fma-def 99.5%

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

   13. sub-neg 99.5%

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

   14. metadata-eval 99.5%

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

   15. +-commutative 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate-+l+ 99.5%

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

   2. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. +-commutative 99.5%

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

   5. associate-+r+ 99.5%

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

   6. associate-+l+ 99.5%

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

   7. +-commutative 99.5%

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

   8. associate-+l+ 99.5%

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

   9. +-commutative 99.5%

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

   10. fma-def 99.5%

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

   11. +-commutative 99.5%

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

   12. fma-def 99.5%

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

   13. sub-neg 99.5%

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

   14. metadata-eval 99.5%

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

   15. +-commutative 99.5%

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

3. Simplified 99.5%

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

   1. fma-udef 99.5%

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

   2. metadata-eval 99.5%

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

   3. sub-neg 99.5%

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

   4. fma-udef 99.5%

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

   5. associate-+r+ 99.5%

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

   6. +-commutative 99.5%

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

   7. associate-+l+ 99.5%

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

   8. +-commutative 99.5%

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

   9. associate-+l+ 99.5%

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

   10. associate-+l+ 99.5%

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

   11. associate-+l+ 99.5%

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

   12. sub-neg 99.5%

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

   13. metadata-eval 99.5%

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

   14. *-commutative 99.5%

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

6. Applied egg-rr 99.5%

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

7. Final simplification 99.5%

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

Alternative 3: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(i, y, t_1\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(b + -0.5\right) \cdot \log c + \left(z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(t_1 + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.1e+127)
     (+ a (+ z (fma i y t_1)))
     (if (<= x 1.9e+65)
       (fma y i (+ (* (+ b -0.5) (log c)) (+ z (+ t a))))
       (+ a (+ t (+ z (+ t_1 (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.1e+127) {
		tmp = a + (z + fma(i, y, t_1));
	} else if (x <= 1.9e+65) {
		tmp = fma(y, i, (((b + -0.5) * log(c)) + (z + (t + a))));
	} else {
		tmp = a + (t + (z + (t_1 + (y * i))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.1e+127)
		tmp = Float64(a + Float64(z + fma(i, y, t_1)));
	elseif (x <= 1.9e+65)
		tmp = fma(y, i, Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(z + Float64(t + a))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + Float64(y * i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+127], N[(a + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+65], N[(y * i + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999992e127

   1. Initial program 97.5%

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

      1. add-cube-cbrt 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 97.4%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.0%

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

      1. fma-def 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in t around 0 84.4%

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

      1. fma-def 84.4%

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

      2. *-commutative 84.4%

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

   10. Simplified 84.4%

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

   if -2.09999999999999992e127 < x < 1.90000000000000006e65

   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 98.3%

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

      1. fma-udef 98.3%

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

      2. *-commutative 98.3%

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

      3. +-commutative 98.3%

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

   7. Applied egg-rr 98.3%

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

   if 1.90000000000000006e65 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.2%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(b + -0.5\right) \cdot \log c + \left(z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;a \leq 3.2 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(t_1 + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, t_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= a 3.2e+136)
     (+ (* y i) (+ t (+ z (+ t_1 (* (log c) (- b 0.5))))))
     (+ a (+ t (+ z (fma i y t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (a <= 3.2e+136) {
		tmp = (y * i) + (t + (z + (t_1 + (log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + (z + fma(i, y, t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (a <= 3.2e+136)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(t_1 + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3.2e+136], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 3.19999999999999988e136

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 86.0%

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

   if 3.19999999999999988e136 < a

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.4%

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

      1. fma-def 92.4%

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

   7. Simplified 92.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((log(c) * (b - 0.5)) + (a + (t + (z + (x * log(y)))))) + (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 = ((log(c) * (b - 0.5d0)) + (a + (t + (z + (x * log(y)))))) + (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 ((Math.log(c) * (b - 0.5)) + (a + (t + (z + (x * Math.log(y)))))) + (y * i);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Final simplification 99.5%

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

Alternative 6: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(i, y, t_1\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(t_1 + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -5.8e+124)
     (+ a (+ z (fma i y t_1)))
     (if (<= x 2e+65)
       (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
       (+ a (+ t (+ z (+ t_1 (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -5.8e+124) {
		tmp = a + (z + fma(i, y, t_1));
	} else if (x <= 2e+65) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + (z + (t_1 + (y * i))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -5.8e+124)
		tmp = Float64(a + Float64(z + fma(i, y, t_1)));
	elseif (x <= 2e+65)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + Float64(y * i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+124], N[(a + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+65], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.80000000000000043e124

   1. Initial program 97.5%

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

      1. add-cube-cbrt 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 97.4%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.0%

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

      1. fma-def 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in t around 0 84.4%

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

      1. fma-def 84.4%

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

      2. *-commutative 84.4%

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

   10. Simplified 84.4%

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

   if -5.80000000000000043e124 < x < 2e65

   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 98.3%

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

   if 2e65 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.2%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+163} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -4e+163) (not (<= (- b 0.5) 5e+215)))
   (+ a (+ z (* (log c) (- b 0.5))))
   (+ a (+ t (+ z (+ (* x (log y)) (* 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 - 0.5) <= -4e+163) || !((b - 0.5) <= 5e+215)) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = a + (t + (z + ((x * log(y)) + (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 - 0.5d0) <= (-4d+163)) .or. (.not. ((b - 0.5d0) <= 5d+215))) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = a + (t + (z + ((x * log(y)) + (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 - 0.5) <= -4e+163) || !((b - 0.5) <= 5e+215)) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = a + (t + (z + ((x * Math.log(y)) + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -4e+163) or not ((b - 0.5) <= 5e+215):
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = a + (t + (z + ((x * math.log(y)) + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -4e+163) || !(Float64(b - 0.5) <= 5e+215))
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + 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 - 0.5) <= -4e+163) || ~(((b - 0.5) <= 5e+215)))
		tmp = a + (z + (log(c) * (b - 0.5)));
	else
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -4e+163], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+215]], $MachinePrecision]], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -3.9999999999999998e163 or 5.0000000000000001e215 < (-.f64 b 1/2)

   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 0 90.5%

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

   4. Taylor expanded in t around 0 88.5%

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

   5. Taylor expanded in y around 0 74.2%

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

   if -3.9999999999999998e163 < (-.f64 b 1/2) < 5.0000000000000001e215

   1. Initial program 99.4%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+163} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+163} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -4e+163) (not (<= (- b 0.5) 5e+215)))
   (+ a (+ z (* (log c) (- b 0.5))))
   (+ a (+ z (+ (* x (log y)) (* 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 - 0.5) <= -4e+163) || !((b - 0.5) <= 5e+215)) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = a + (z + ((x * log(y)) + (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 - 0.5d0) <= (-4d+163)) .or. (.not. ((b - 0.5d0) <= 5d+215))) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = a + (z + ((x * log(y)) + (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 - 0.5) <= -4e+163) || !((b - 0.5) <= 5e+215)) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = a + (z + ((x * Math.log(y)) + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -4e+163) or not ((b - 0.5) <= 5e+215):
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = a + (z + ((x * math.log(y)) + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -4e+163) || !(Float64(b - 0.5) <= 5e+215))
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(x * log(y)) + 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 - 0.5) <= -4e+163) || ~(((b - 0.5) <= 5e+215)))
		tmp = a + (z + (log(c) * (b - 0.5)));
	else
		tmp = a + (z + ((x * log(y)) + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -4e+163], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+215]], $MachinePrecision]], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -3.9999999999999998e163 or 5.0000000000000001e215 < (-.f64 b 1/2)

   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 0 90.5%

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

   4. Taylor expanded in t around 0 88.5%

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

   5. Taylor expanded in y around 0 74.2%

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

   if -3.9999999999999998e163 < (-.f64 b 1/2) < 5.0000000000000001e215

   1. Initial program 99.4%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.1%

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

      1. fma-def 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in t around 0 74.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+163} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+126}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (+ (* x (log y)) (* y i)))))
   (if (<= x -3e+126)
     (+ a t_1)
     (if (<= x 2e+65)
       (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
       (+ a (+ t t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + ((x * log(y)) + (y * i));
	double tmp;
	if (x <= -3e+126) {
		tmp = a + t_1;
	} else if (x <= 2e+65) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + ((x * log(y)) + (y * i))
    if (x <= (-3d+126)) then
        tmp = a + t_1
    else if (x <= 2d+65) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = a + (t + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + ((x * Math.log(y)) + (y * i));
	double tmp;
	if (x <= -3e+126) {
		tmp = a + t_1;
	} else if (x <= 2e+65) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + ((x * math.log(y)) + (y * i))
	tmp = 0
	if x <= -3e+126:
		tmp = a + t_1
	elif x <= 2e+65:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = a + (t + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))
	tmp = 0.0
	if (x <= -3e+126)
		tmp = Float64(a + t_1);
	elseif (x <= 2e+65)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(a + Float64(t + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + ((x * log(y)) + (y * i));
	tmp = 0.0;
	if (x <= -3e+126)
		tmp = a + t_1;
	elseif (x <= 2e+65)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = a + (t + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+126], N[(a + t$95$1), $MachinePrecision], If[LessEqual[x, 2e+65], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000002e126

   1. Initial program 97.5%

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

      1. add-cube-cbrt 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 97.4%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.0%

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

      1. fma-def 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in t around 0 84.4%

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

   if -3.0000000000000002e126 < x < 2e65

   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 98.3%

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

   if 2e65 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+126}:\\ \;\;\;\;a + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+126}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (+ (* x (log y)) (* y i)))))
   (if (<= x -8.5e+126)
     (+ a t_1)
     (if (<= x 2e+65)
       (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))
       (+ a (+ t t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + ((x * log(y)) + (y * i));
	double tmp;
	if (x <= -8.5e+126) {
		tmp = a + t_1;
	} else if (x <= 2e+65) {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = a + (t + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + ((x * log(y)) + (y * i))
    if (x <= (-8.5d+126)) then
        tmp = a + t_1
    else if (x <= 2d+65) then
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = a + (t + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + ((x * Math.log(y)) + (y * i));
	double tmp;
	if (x <= -8.5e+126) {
		tmp = a + t_1;
	} else if (x <= 2e+65) {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = a + (t + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + ((x * math.log(y)) + (y * i))
	tmp = 0
	if x <= -8.5e+126:
		tmp = a + t_1
	elif x <= 2e+65:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = a + (t + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))
	tmp = 0.0
	if (x <= -8.5e+126)
		tmp = Float64(a + t_1);
	elseif (x <= 2e+65)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(a + Float64(t + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + ((x * log(y)) + (y * i));
	tmp = 0.0;
	if (x <= -8.5e+126)
		tmp = a + t_1;
	elseif (x <= 2e+65)
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	else
		tmp = a + (t + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+126], N[(a + t$95$1), $MachinePrecision], If[LessEqual[x, 2e+65], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999944e126

   1. Initial program 97.5%

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

      1. add-cube-cbrt 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 97.4%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 97.4%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.0%

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

      1. fma-def 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in t around 0 84.4%

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

   if -8.49999999999999944e126 < x < 2e65

   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 98.3%

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

   4. Taylor expanded in t around 0 81.7%

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

   if 2e65 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+126}:\\ \;\;\;\;a + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-121}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-58}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 2.1e-121)
   (+ a (+ t (+ z (* x (log y)))))
   (if (<= y 6e-58)
     (+ a (+ z (* (log c) (- b 0.5))))
     (+ 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 (y <= 2.1e-121) {
		tmp = a + (t + (z + (x * log(y))));
	} else if (y <= 6e-58) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} 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 (y <= 2.1e-121)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	elseif (y <= 6e-58)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	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[LessEqual[y, 2.1e-121], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-58], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.0999999999999999e-121

   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 98.9%

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

   4. Taylor expanded in x around inf 83.9%

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

   if 2.0999999999999999e-121 < y < 6.00000000000000015e-58

   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 93.4%

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

   4. Taylor expanded in t around 0 78.0%

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

   5. Taylor expanded in y around 0 75.1%

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

   if 6.00000000000000015e-58 < y

   1. Initial program 99.2%

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

      1. add-cube-cbrt 99.0%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.0%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.0%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.0%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.0%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.0%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 86.4%

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

      1. fma-def 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in x around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. fma-def 73.6%

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

   10. Simplified 73.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-121}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-58}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+173} \lor \neg \left(x \leq 1.12 \cdot 10^{+220}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.9e+173) (not (<= x 1.12e+220)))
   (+ a (* x (log y)))
   (+ 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 ((x <= -1.9e+173) || !(x <= 1.12e+220)) {
		tmp = a + (x * log(y));
	} 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 ((x <= -1.9e+173) || !(x <= 1.12e+220))
		tmp = Float64(a + Float64(x * log(y)));
	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[x, -1.9e+173], N[Not[LessEqual[x, 1.12e+220]], $MachinePrecision]], N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000005e173 or 1.12000000000000006e220 < x

   1. Initial program 97.5%

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

      1. add-cube-cbrt 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 97.5%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.9%

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

      1. fma-def 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in x around inf 67.6%

      \[\leadsto a + \color{blue}{x \cdot \log y} \]
   9. Step-by-step derivation

      1. *-commutative 67.6%

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

   10. Simplified 67.6%

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

   if -1.90000000000000005e173 < x < 1.12000000000000006e220

   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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 80.1%

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

      1. fma-def 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in x around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. fma-def 72.4%

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

   10. Simplified 72.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+173} \lor \neg \left(x \leq 1.12 \cdot 10^{+220}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+174} \lor \neg \left(x \leq 4.6 \cdot 10^{+220}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -7.2e+174) (not (<= x 4.6e+220)))
   (+ a (* x (log y)))
   (+ a (+ (+ z t) (* 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 <= -7.2e+174) || !(x <= 4.6e+220)) {
		tmp = a + (x * log(y));
	} else {
		tmp = a + ((z + t) + (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 <= (-7.2d+174)) .or. (.not. (x <= 4.6d+220))) then
        tmp = a + (x * log(y))
    else
        tmp = a + ((z + t) + (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 <= -7.2e+174) || !(x <= 4.6e+220)) {
		tmp = a + (x * Math.log(y));
	} else {
		tmp = a + ((z + t) + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -7.2e+174) or not (x <= 4.6e+220):
		tmp = a + (x * math.log(y))
	else:
		tmp = a + ((z + t) + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -7.2e+174) || !(x <= 4.6e+220))
		tmp = Float64(a + Float64(x * log(y)));
	else
		tmp = Float64(a + Float64(Float64(z + t) + 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 <= -7.2e+174) || ~((x <= 4.6e+220)))
		tmp = a + (x * log(y));
	else
		tmp = a + ((z + t) + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -7.2e+174], N[Not[LessEqual[x, 4.6e+220]], $MachinePrecision]], N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z + t), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000003e174 or 4.59999999999999993e220 < x

   1. Initial program 97.5%

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

      1. add-cube-cbrt 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 97.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 97.5%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.9%

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

      1. fma-def 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in x around inf 67.6%

      \[\leadsto a + \color{blue}{x \cdot \log y} \]
   9. Step-by-step derivation

      1. *-commutative 67.6%

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

   10. Simplified 67.6%

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

   if -7.2000000000000003e174 < x < 4.59999999999999993e220

   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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 80.1%

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

      1. fma-def 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in x around 0 72.4%

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

      1. associate-+r+ 72.4%

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

      2. +-commutative 72.4%

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

      3. *-commutative 72.4%

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

   10. Simplified 72.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+174} \lor \neg \left(x \leq 4.6 \cdot 10^{+220}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+25}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.12e+25) (+ a (+ t (+ z (* x (log y))))) (+ 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 (y <= 1.12e+25) {
		tmp = a + (t + (z + (x * log(y))));
	} 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 (y <= 1.12e+25)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	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[LessEqual[y, 1.12e+25], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(y * i + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.1200000000000001e25

   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 95.1%

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

   4. Taylor expanded in x around inf 74.5%

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

   if 1.1200000000000001e25 < y

   1. Initial program 99.0%

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

      1. add-cube-cbrt 98.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 98.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 98.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 98.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 98.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 98.9%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 85.8%

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

      1. fma-def 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in x around 0 74.9%

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

      1. +-commutative 74.9%

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

      2. *-commutative 74.9%

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

      3. fma-def 74.9%

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

   10. Simplified 74.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+25}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(y, i, z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+191} \lor \neg \left(b \leq 3.7 \cdot 10^{+215}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -4.2e+191) (not (<= b 3.7e+215)))
   (* b (log c))
   (+ a (+ (+ z t) (* 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 <= -4.2e+191) || !(b <= 3.7e+215)) {
		tmp = b * log(c);
	} else {
		tmp = a + ((z + t) + (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 <= (-4.2d+191)) .or. (.not. (b <= 3.7d+215))) then
        tmp = b * log(c)
    else
        tmp = a + ((z + t) + (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 <= -4.2e+191) || !(b <= 3.7e+215)) {
		tmp = b * Math.log(c);
	} else {
		tmp = a + ((z + t) + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -4.2e+191) or not (b <= 3.7e+215):
		tmp = b * math.log(c)
	else:
		tmp = a + ((z + t) + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -4.2e+191) || !(b <= 3.7e+215))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(a + Float64(Float64(z + t) + 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 <= -4.2e+191) || ~((b <= 3.7e+215)))
		tmp = b * log(c);
	else
		tmp = a + ((z + t) + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -4.2e+191], N[Not[LessEqual[b, 3.7e+215]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z + t), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2000000000000001e191 or 3.69999999999999971e215 < 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 b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if -4.2000000000000001e191 < b < 3.69999999999999971e215

   1. Initial program 99.4%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.2%

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

      1. fma-def 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in x around 0 72.8%

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

      1. associate-+r+ 72.8%

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

      2. +-commutative 72.8%

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

      3. *-commutative 72.8%

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

   10. Simplified 72.8%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+191} \lor \neg \left(b \leq 3.7 \cdot 10^{+215}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -7.2e+174) (* x (log y)) (+ a (+ (+ z t) (* 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 <= -7.2e+174) {
		tmp = x * log(y);
	} else {
		tmp = a + ((z + t) + (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 <= (-7.2d+174)) then
        tmp = x * log(y)
    else
        tmp = a + ((z + t) + (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 <= -7.2e+174) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + ((z + t) + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -7.2e+174:
		tmp = x * math.log(y)
	else:
		tmp = a + ((z + t) + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -7.2e+174)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(Float64(z + t) + 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 <= -7.2e+174)
		tmp = x * log(y);
	else
		tmp = a + ((z + t) + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -7.2e+174], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z + t), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000003e174

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 63.5%

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

   if -7.2000000000000003e174 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 81.3%

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

      1. fma-def 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in x around 0 70.0%

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

      1. associate-+r+ 70.0%

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

      2. +-commutative 70.0%

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

      3. *-commutative 70.0%

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

   10. Simplified 70.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-163}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.6e-219) z (if (<= y 8.6e-163) a (if (<= y 2.9e+49) 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 <= 1.6e-219) {
		tmp = z;
	} else if (y <= 8.6e-163) {
		tmp = a;
	} else if (y <= 2.9e+49) {
		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 <= 1.6d-219) then
        tmp = z
    else if (y <= 8.6d-163) then
        tmp = a
    else if (y <= 2.9d+49) 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 <= 1.6e-219) {
		tmp = z;
	} else if (y <= 8.6e-163) {
		tmp = a;
	} else if (y <= 2.9e+49) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.6e-219:
		tmp = z
	elif y <= 8.6e-163:
		tmp = a
	elif y <= 2.9e+49:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.6e-219)
		tmp = z;
	elseif (y <= 8.6e-163)
		tmp = a;
	elseif (y <= 2.9e+49)
		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 <= 1.6e-219)
		tmp = z;
	elseif (y <= 8.6e-163)
		tmp = a;
	elseif (y <= 2.9e+49)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.6e-219], z, If[LessEqual[y, 8.6e-163], a, If[LessEqual[y, 2.9e+49], z, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.59999999999999999e-219 or 8.60000000000000017e-163 < y < 2.9e49

   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 13.3%

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

   if 1.59999999999999999e-219 < y < 8.60000000000000017e-163

   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 a around inf 20.2%

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

   if 2.9e49 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 46.7%

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

      1. *-commutative 46.7%

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

   5. Simplified 46.7%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-163}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-162}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 6.8e-219) z (if (<= y 5e-162) (+ t a) (if (<= y 2e+49) 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 <= 6.8e-219) {
		tmp = z;
	} else if (y <= 5e-162) {
		tmp = t + a;
	} else if (y <= 2e+49) {
		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 <= 6.8d-219) then
        tmp = z
    else if (y <= 5d-162) then
        tmp = t + a
    else if (y <= 2d+49) 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 <= 6.8e-219) {
		tmp = z;
	} else if (y <= 5e-162) {
		tmp = t + a;
	} else if (y <= 2e+49) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 6.8e-219:
		tmp = z
	elif y <= 5e-162:
		tmp = t + a
	elif y <= 2e+49:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 6.8e-219)
		tmp = z;
	elseif (y <= 5e-162)
		tmp = Float64(t + a);
	elseif (y <= 2e+49)
		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 <= 6.8e-219)
		tmp = z;
	elseif (y <= 5e-162)
		tmp = t + a;
	elseif (y <= 2e+49)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 6.8e-219], z, If[LessEqual[y, 5e-162], N[(t + a), $MachinePrecision], If[LessEqual[y, 2e+49], z, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.7999999999999997e-219 or 5.00000000000000014e-162 < y < 1.99999999999999989e49

   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 13.3%

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

   if 6.7999999999999997e-219 < y < 5.00000000000000014e-162

   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. Step-by-step derivation

      1. add-cube-cbrt 99.2%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.2%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.2%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.2%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.2%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 78.7%

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

      1. fma-def 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around inf 35.2%

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

   if 1.99999999999999989e49 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 46.7%

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

      1. *-commutative 46.7%

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

   5. Simplified 46.7%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-219}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-162}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 44.9% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+42}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 3.8e+42) (+ 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 (y <= 3.8e+42) {
		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 (y <= 3.8d+42) 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 (y <= 3.8e+42) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 3.8e+42:
		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 (y <= 3.8e+42)
		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 (y <= 3.8e+42)
		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[y, 3.8e+42], N[(z + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.7999999999999998e42

   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. Step-by-step derivation

      1. add-cube-cbrt 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.5%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 79.7%

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

      1. fma-def 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in z around inf 32.6%

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

   if 3.7999999999999998e42 < y

   1. Initial program 99.0%

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

      1. add-cube-cbrt 98.8%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 98.8%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 98.8%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 98.8%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 98.8%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 98.8%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 85.6%

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

      1. fma-def 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in i around inf 56.6%

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

      1. *-commutative 56.6%

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

   10. Simplified 56.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+42}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 67.8% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. add-cube-cbrt 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

   2. pow3 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

   3. sub-neg 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

   4. metadata-eval 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

   5. *-commutative 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

4. Applied egg-rr 99.2%

   \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

5. Taylor expanded in b around inf 82.5%

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

   1. fma-def 82.5%

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

7. Simplified 82.5%

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

8. Taylor expanded in x around 0 65.1%

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

   1. associate-+r+ 65.1%

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

   2. +-commutative 65.1%

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

   3. *-commutative 65.1%

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

10. Simplified 65.1%

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

11. Final simplification 65.1%

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

Alternative 21: 40.5% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.6e+112) (+ 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 <= 1.6e+112) {
		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 <= 1.6d+112) 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 <= 1.6e+112) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.6e+112:
		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 <= 1.6e+112)
		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 <= 1.6e+112)
		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, 1.6e+112], N[(z + a), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.59999999999999993e112

   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. Step-by-step derivation

      1. add-cube-cbrt 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c} \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right) \cdot \sqrt[3]{\left(b - 0.5\right) \cdot \log c}}\right) + y \cdot i \]

      2. pow3 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. sub-neg 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-commutative 99.5%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 99.5%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 82.2%

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

      1. fma-def 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in z around inf 33.1%

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

   if 1.59999999999999993e112 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 50.8%

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

      1. *-commutative 50.8%

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

   5. Simplified 50.8%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.0% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -4e+83) 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 <= -4e+83) {
		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 <= (-4d+83)) 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 <= -4e+83) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4e+83:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4e+83)
		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 <= -4e+83)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4e+83], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000012e83

   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 z around inf 21.2%

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

   if -4.00000000000000012e83 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around inf 17.5%

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

4. Final simplification 18.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 16.9% 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 99.5%

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

3. Taylor expanded in a around inf 17.7%

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

4. Final simplification 17.7%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(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)))