Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.6% → 98.8%

Time: 11.5s

Alternatives: 17

Speedup: 1.0×

• 32.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma x y (fma b (* -0.25 a) (fma z (/ t 16.0) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, fma(b, (-0.25 * a), fma(z, (t / 16.0), c)));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(x, y, fma(b, Float64(-0.25 * a), fma(z, Float64(t / 16.0), c)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * y + N[(b * N[(-0.25 * a), $MachinePrecision] + N[(z * N[(t / 16.0), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. +-commutative 98.4%

      \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a \cdot b}{4} - c\right) \]

   3. associate--l+ 98.4%

      \[\leadsto \color{blue}{\frac{z \cdot t}{16} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   4. +-commutative 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) + \frac{z \cdot t}{16}} \]

   5. associate-+l- 98.4%

      \[\leadsto \color{blue}{x \cdot y - \left(\left(\frac{a \cdot b}{4} - c\right) - \frac{z \cdot t}{16}\right)} \]

   6. fma-neg 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -\left(\left(\frac{a \cdot b}{4} - c\right) - \frac{z \cdot t}{16}\right)\right)} \]

   7. neg-sub0 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{0 - \left(\left(\frac{a \cdot b}{4} - c\right) - \frac{z \cdot t}{16}\right)}\right) \]

   8. associate--l- 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, 0 - \color{blue}{\left(\frac{a \cdot b}{4} - \left(c + \frac{z \cdot t}{16}\right)\right)}\right) \]

   9. associate-+l- 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(0 - \frac{a \cdot b}{4}\right) + \left(c + \frac{z \cdot t}{16}\right)}\right) \]

   10. neg-sub0 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-\frac{a \cdot b}{4}\right)} + \left(c + \frac{z \cdot t}{16}\right)\right) \]

   11. *-commutative 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \left(-\frac{\color{blue}{b \cdot a}}{4}\right) + \left(c + \frac{z \cdot t}{16}\right)\right) \]

   12. associate-*r/ 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \left(-\color{blue}{b \cdot \frac{a}{4}}\right) + \left(c + \frac{z \cdot t}{16}\right)\right) \]

   13. distribute-rgt-neg-in 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{b \cdot \left(-\frac{a}{4}\right)} + \left(c + \frac{z \cdot t}{16}\right)\right) \]

   14. fma-def 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(b, -\frac{a}{4}, c + \frac{z \cdot t}{16}\right)}\right) \]

   15. distribute-frac-neg 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{\frac{-a}{4}}, c + \frac{z \cdot t}{16}\right)\right) \]

   16. neg-mul-1 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \frac{\color{blue}{-1 \cdot a}}{4}, c + \frac{z \cdot t}{16}\right)\right) \]

   17. associate-/l* 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{\frac{4}{a}}}, c + \frac{z \cdot t}{16}\right)\right) \]

   18. associate-/r/ 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{4} \cdot a}, c + \frac{z \cdot t}{16}\right)\right) \]

   19. metadata-eval 99.2%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

4. Final simplification 99.2%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right) \]

Alternative 2: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - b \cdot \frac{a}{4}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma t (/ z 16.0) (fma x y (- c (* b (/ a 4.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(t, (z / 16.0), fma(x, y, (c - (b * (a / 4.0)))));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(t, Float64(z / 16.0), fma(x, y, Float64(c - Float64(b * Float64(a / 4.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(t * N[(z / 16.0), $MachinePrecision] + N[(x * y + N[(c - N[(b * N[(a / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. +-commutative 98.4%

      \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a \cdot b}{4} - c\right) \]

   3. associate--l+ 98.4%

      \[\leadsto \color{blue}{\frac{z \cdot t}{16} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   4. associate-*l/ 98.4%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   5. *-commutative 98.4%

      \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   6. fma-def 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{16}, x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   7. fma-neg 99.2%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \color{blue}{\mathsf{fma}\left(x, y, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

   8. neg-sub0 99.2%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

   9. associate-+l- 99.2%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{\left(0 - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

   10. neg-sub0 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{\left(-\frac{a \cdot b}{4}\right)} + c\right)\right) \]

   11. +-commutative 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{c + \left(-\frac{a \cdot b}{4}\right)}\right)\right) \]

   12. unsub-neg 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{c - \frac{a \cdot b}{4}}\right)\right) \]

   13. *-commutative 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - \frac{\color{blue}{b \cdot a}}{4}\right)\right) \]

   14. associate-*r/ 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - \color{blue}{b \cdot \frac{a}{4}}\right)\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - b \cdot \frac{a}{4}\right)\right)} \]

4. Final simplification 99.2%

   \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - b \cdot \frac{a}{4}\right)\right) \]

Alternative 3: 97.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) + \left(c - \frac{a}{\frac{4}{b}}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (fma x y (/ z (/ 16.0 t))) (- c (/ a (/ 4.0 b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, (z / (16.0 / t))) + (c - (a / (4.0 / b)));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(fma(x, y, Float64(z / Float64(16.0 / t))) + Float64(c - Float64(a / Float64(4.0 / b))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y + N[(z / N[(16.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c - N[(a / N[(4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. sub-neg 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\left(\frac{a \cdot b}{4} - c\right)\right)} \]

   3. neg-mul-1 98.4%

      \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{-1 \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

   4. metadata-eval 98.4%

      \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{\left(-1\right)} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

   5. metadata-eval 98.4%

      \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

   6. cancel-sign-sub-inv 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

   7. fma-def 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

   8. associate-/l* 98.7%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{\frac{16}{t}}}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

   9. metadata-eval 98.7%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{1} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

   10. *-lft-identity 98.7%

       \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{\left(\frac{a \cdot b}{4} - c\right)} \]

   11. associate-/l* 98.7%

       \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\color{blue}{\frac{a}{\frac{4}{b}}} - c\right) \]

3. Simplified 98.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right)} \]

4. Final simplification 98.7%

   \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) + \left(c - \frac{a}{\frac{4}{b}}\right) \]

Alternative 4: 44.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -9 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -2.15 \cdot 10^{-41}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -1.8 \cdot 10^{-70}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 8.6 \cdot 10^{-290}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-156}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 1.32 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -0.25 (* b a))))
   (if (<= (* b a) -9e+133)
     t_1
     (if (<= (* b a) -2.15e-41)
       (* x y)
       (if (<= (* b a) -1.8e-70)
         c
         (if (<= (* b a) 8.6e-290)
           (* (* z t) 0.0625)
           (if (<= (* b a) 5e-156)
             c
             (if (<= (* b a) 1.32e+109) (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -9e+133) {
		tmp = t_1;
	} else if ((b * a) <= -2.15e-41) {
		tmp = x * y;
	} else if ((b * a) <= -1.8e-70) {
		tmp = c;
	} else if ((b * a) <= 8.6e-290) {
		tmp = (z * t) * 0.0625;
	} else if ((b * a) <= 5e-156) {
		tmp = c;
	} else if ((b * a) <= 1.32e+109) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (-0.25d0) * (b * a)
    if ((b * a) <= (-9d+133)) then
        tmp = t_1
    else if ((b * a) <= (-2.15d-41)) then
        tmp = x * y
    else if ((b * a) <= (-1.8d-70)) then
        tmp = c
    else if ((b * a) <= 8.6d-290) then
        tmp = (z * t) * 0.0625d0
    else if ((b * a) <= 5d-156) then
        tmp = c
    else if ((b * a) <= 1.32d+109) then
        tmp = x * y
    else
        tmp = 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 t_1 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -9e+133) {
		tmp = t_1;
	} else if ((b * a) <= -2.15e-41) {
		tmp = x * y;
	} else if ((b * a) <= -1.8e-70) {
		tmp = c;
	} else if ((b * a) <= 8.6e-290) {
		tmp = (z * t) * 0.0625;
	} else if ((b * a) <= 5e-156) {
		tmp = c;
	} else if ((b * a) <= 1.32e+109) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -0.25 * (b * a)
	tmp = 0
	if (b * a) <= -9e+133:
		tmp = t_1
	elif (b * a) <= -2.15e-41:
		tmp = x * y
	elif (b * a) <= -1.8e-70:
		tmp = c
	elif (b * a) <= 8.6e-290:
		tmp = (z * t) * 0.0625
	elif (b * a) <= 5e-156:
		tmp = c
	elif (b * a) <= 1.32e+109:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (Float64(b * a) <= -9e+133)
		tmp = t_1;
	elseif (Float64(b * a) <= -2.15e-41)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= -1.8e-70)
		tmp = c;
	elseif (Float64(b * a) <= 8.6e-290)
		tmp = Float64(Float64(z * t) * 0.0625);
	elseif (Float64(b * a) <= 5e-156)
		tmp = c;
	elseif (Float64(b * a) <= 1.32e+109)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -0.25 * (b * a);
	tmp = 0.0;
	if ((b * a) <= -9e+133)
		tmp = t_1;
	elseif ((b * a) <= -2.15e-41)
		tmp = x * y;
	elseif ((b * a) <= -1.8e-70)
		tmp = c;
	elseif ((b * a) <= 8.6e-290)
		tmp = (z * t) * 0.0625;
	elseif ((b * a) <= 5e-156)
		tmp = c;
	elseif ((b * a) <= 1.32e+109)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -9e+133], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -2.15e-41], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -1.8e-70], c, If[LessEqual[N[(b * a), $MachinePrecision], 8.6e-290], N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e-156], c, If[LessEqual[N[(b * a), $MachinePrecision], 1.32e+109], N[(x * y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -8.9999999999999997e133 or 1.32000000000000008e109 < (*.f64 a b)

   1. Initial program 96.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 96.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. sub-neg 96.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. neg-mul-1 96.1%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{-1 \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      4. metadata-eval 96.1%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{\left(-1\right)} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      5. metadata-eval 96.1%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      6. cancel-sign-sub-inv 96.1%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      7. fma-def 96.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      8. associate-/l* 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{\frac{16}{t}}}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      9. metadata-eval 96.1%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{1} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      10. *-lft-identity 96.1%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{\left(\frac{a \cdot b}{4} - c\right)} \]

      11. associate-/l* 95.9%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\color{blue}{\frac{a}{\frac{4}{b}}} - c\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 95.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{\frac{16}{t}}\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      2. associate-/l* 96.0%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. +-commutative 96.0%

         \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      4. associate-/l* 95.9%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. div-inv 96.0%

         \[\leadsto \left(\color{blue}{z \cdot \frac{1}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      6. clear-num 96.0%

         \[\leadsto \left(z \cdot \color{blue}{\frac{t}{16}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      7. div-inv 96.0%

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot \frac{1}{16}\right)} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      8. metadata-eval 96.0%

         \[\leadsto \left(z \cdot \left(t \cdot \color{blue}{0.0625}\right) + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 96.0%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 0.0625\right) + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in a around inf 67.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]

   8. Simplified 67.0%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]

   if -8.9999999999999997e133 < (*.f64 a b) < -2.1499999999999999e-41 or 5.00000000000000007e-156 < (*.f64 a b) < 1.32000000000000008e109

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 89.6%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   3. Taylor expanded in c around 0 67.5%

      \[\leadsto \color{blue}{y \cdot x + 0.0625 \cdot \left(t \cdot z\right)} \]

   4. Taylor expanded in y around inf 46.6%

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

   if -2.1499999999999999e-41 < (*.f64 a b) < -1.8000000000000001e-70 or 8.6000000000000004e-290 < (*.f64 a b) < 5.00000000000000007e-156

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 67.5%

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

   if -1.8000000000000001e-70 < (*.f64 a b) < 8.6000000000000004e-290

   1. Initial program 98.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 72.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in t around inf 45.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -9 \cdot 10^{+133}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -2.15 \cdot 10^{-41}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -1.8 \cdot 10^{-70}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 8.6 \cdot 10^{-290}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-156}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 1.32 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 5: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -1.45 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1.1 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 7.8 \cdot 10^{-144}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 1.22 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* -0.25 (* b a)))))
   (if (<= (* b a) -1.45e+133)
     t_2
     (if (<= (* b a) -1.1e-43)
       t_1
       (if (<= (* b a) 7.8e-144)
         (+ c (* t (* z 0.0625)))
         (if (<= (* b a) 1.22e+103) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (-0.25 * (b * a));
	double tmp;
	if ((b * a) <= -1.45e+133) {
		tmp = t_2;
	} else if ((b * a) <= -1.1e-43) {
		tmp = t_1;
	} else if ((b * a) <= 7.8e-144) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 1.22e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + ((-0.25d0) * (b * a))
    if ((b * a) <= (-1.45d+133)) then
        tmp = t_2
    else if ((b * a) <= (-1.1d-43)) then
        tmp = t_1
    else if ((b * a) <= 7.8d-144) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((b * a) <= 1.22d+103) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = c + (x * y);
	double t_2 = c + (-0.25 * (b * a));
	double tmp;
	if ((b * a) <= -1.45e+133) {
		tmp = t_2;
	} else if ((b * a) <= -1.1e-43) {
		tmp = t_1;
	} else if ((b * a) <= 7.8e-144) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 1.22e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (-0.25 * (b * a))
	tmp = 0
	if (b * a) <= -1.45e+133:
		tmp = t_2
	elif (b * a) <= -1.1e-43:
		tmp = t_1
	elif (b * a) <= 7.8e-144:
		tmp = c + (t * (z * 0.0625))
	elif (b * a) <= 1.22e+103:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(-0.25 * Float64(b * a)))
	tmp = 0.0
	if (Float64(b * a) <= -1.45e+133)
		tmp = t_2;
	elseif (Float64(b * a) <= -1.1e-43)
		tmp = t_1;
	elseif (Float64(b * a) <= 7.8e-144)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(b * a) <= 1.22e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (-0.25 * (b * a));
	tmp = 0.0;
	if ((b * a) <= -1.45e+133)
		tmp = t_2;
	elseif ((b * a) <= -1.1e-43)
		tmp = t_1;
	elseif ((b * a) <= 7.8e-144)
		tmp = c + (t * (z * 0.0625));
	elseif ((b * a) <= 1.22e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1.45e+133], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1.1e-43], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 7.8e-144], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1.22e+103], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.4500000000000001e133 or 1.22e103 < (*.f64 a b)

   1. Initial program 96.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 76.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

   4. Simplified 76.9%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

   if -1.4500000000000001e133 < (*.f64 a b) < -1.09999999999999999e-43 or 7.8000000000000003e-144 < (*.f64 a b) < 1.22e103

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 69.6%

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

   if -1.09999999999999999e-43 < (*.f64 a b) < 7.8000000000000003e-144

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 76.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

      2. associate-*r* 76.9%

         \[\leadsto \color{blue}{t \cdot \left(z \cdot 0.0625\right)} + c \]

      3. *-commutative 76.9%

         \[\leadsto t \cdot \color{blue}{\left(0.0625 \cdot z\right)} + c \]

   4. Simplified 76.9%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.45 \cdot 10^{+133}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -1.1 \cdot 10^{-43}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 7.8 \cdot 10^{-144}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 1.22 \cdot 10^{+103}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 6: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -1.45 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5.1 \cdot 10^{-144}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 3.6 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* -0.25 (* b a))))
   (if (<= (* b a) -1.45e+171)
     t_2
     (if (<= (* b a) -1.65e-39)
       t_1
       (if (<= (* b a) 5.1e-144)
         (+ c (* t (* z 0.0625)))
         (if (<= (* b a) 3.6e+183) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -1.45e+171) {
		tmp = t_2;
	} else if ((b * a) <= -1.65e-39) {
		tmp = t_1;
	} else if ((b * a) <= 5.1e-144) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 3.6e+183) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = (-0.25d0) * (b * a)
    if ((b * a) <= (-1.45d+171)) then
        tmp = t_2
    else if ((b * a) <= (-1.65d-39)) then
        tmp = t_1
    else if ((b * a) <= 5.1d-144) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((b * a) <= 3.6d+183) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = c + (x * y);
	double t_2 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -1.45e+171) {
		tmp = t_2;
	} else if ((b * a) <= -1.65e-39) {
		tmp = t_1;
	} else if ((b * a) <= 5.1e-144) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 3.6e+183) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = -0.25 * (b * a)
	tmp = 0
	if (b * a) <= -1.45e+171:
		tmp = t_2
	elif (b * a) <= -1.65e-39:
		tmp = t_1
	elif (b * a) <= 5.1e-144:
		tmp = c + (t * (z * 0.0625))
	elif (b * a) <= 3.6e+183:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (Float64(b * a) <= -1.45e+171)
		tmp = t_2;
	elseif (Float64(b * a) <= -1.65e-39)
		tmp = t_1;
	elseif (Float64(b * a) <= 5.1e-144)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(b * a) <= 3.6e+183)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = -0.25 * (b * a);
	tmp = 0.0;
	if ((b * a) <= -1.45e+171)
		tmp = t_2;
	elseif ((b * a) <= -1.65e-39)
		tmp = t_1;
	elseif ((b * a) <= 5.1e-144)
		tmp = c + (t * (z * 0.0625));
	elseif ((b * a) <= 3.6e+183)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1.45e+171], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1.65e-39], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5.1e-144], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 3.6e+183], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.44999999999999992e171 or 3.60000000000000023e183 < (*.f64 a b)

   1. Initial program 95.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 95.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. sub-neg 95.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. neg-mul-1 95.0%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{-1 \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      4. metadata-eval 95.0%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{\left(-1\right)} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      5. metadata-eval 95.0%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      6. cancel-sign-sub-inv 95.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      7. fma-def 95.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      8. associate-/l* 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{\frac{16}{t}}}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      9. metadata-eval 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{1} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      10. *-lft-identity 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{\left(\frac{a \cdot b}{4} - c\right)} \]

      11. associate-/l* 94.8%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\color{blue}{\frac{a}{\frac{4}{b}}} - c\right) \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 94.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{\frac{16}{t}}\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      2. associate-/l* 94.8%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. +-commutative 94.8%

         \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      4. associate-/l* 94.8%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. div-inv 94.8%

         \[\leadsto \left(\color{blue}{z \cdot \frac{1}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      6. clear-num 94.8%

         \[\leadsto \left(z \cdot \color{blue}{\frac{t}{16}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      7. div-inv 94.8%

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot \frac{1}{16}\right)} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      8. metadata-eval 94.8%

         \[\leadsto \left(z \cdot \left(t \cdot \color{blue}{0.0625}\right) + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 0.0625\right) + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in a around inf 76.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]

   8. Simplified 76.9%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]

   if -1.44999999999999992e171 < (*.f64 a b) < -1.64999999999999992e-39 or 5.1e-144 < (*.f64 a b) < 3.60000000000000023e183

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 64.7%

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

   if -1.64999999999999992e-39 < (*.f64 a b) < 5.1e-144

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 76.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

      2. associate-*r* 76.9%

         \[\leadsto \color{blue}{t \cdot \left(z \cdot 0.0625\right)} + c \]

      3. *-commutative 76.9%

         \[\leadsto t \cdot \color{blue}{\left(0.0625 \cdot z\right)} + c \]

   4. Simplified 76.9%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.45 \cdot 10^{+171}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 5.1 \cdot 10^{-144}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 3.6 \cdot 10^{+183}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 7: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+71}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+96}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t_2\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)) (t_2 (* (* z t) 0.0625)))
   (if (<= (* b a) -2e+71)
     (- (+ c (* x y)) t_1)
     (if (<= (* b a) 5e+96) (+ c (+ (* x y) t_2)) (- (+ c t_2) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if ((b * a) <= -2e+71) {
		tmp = (c + (x * y)) - t_1;
	} else if ((b * a) <= 5e+96) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = (z * t) * 0.0625d0
    if ((b * a) <= (-2d+71)) then
        tmp = (c + (x * y)) - t_1
    else if ((b * a) <= 5d+96) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + t_2) - 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 t_1 = (b * a) * 0.25;
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if ((b * a) <= -2e+71) {
		tmp = (c + (x * y)) - t_1;
	} else if ((b * a) <= 5e+96) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = (z * t) * 0.0625
	tmp = 0
	if (b * a) <= -2e+71:
		tmp = (c + (x * y)) - t_1
	elif (b * a) <= 5e+96:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if (Float64(b * a) <= -2e+71)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(b * a) <= 5e+96)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = (z * t) * 0.0625;
	tmp = 0.0;
	if ((b * a) <= -2e+71)
		tmp = (c + (x * y)) - t_1;
	elseif ((b * a) <= 5e+96)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + t_2) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2e+71], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e+96], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e71

   1. Initial program 96.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 85.7%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2.0000000000000001e71 < (*.f64 a b) < 5.0000000000000004e96

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 95.4%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   if 5.0000000000000004e96 < (*.f64 a b)

   1. Initial program 97.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 89.9%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+71}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+96}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;b \cdot a \leq -1.75 \cdot 10^{+176} \lor \neg \left(b \cdot a \leq 1.8 \cdot 10^{+179}\right):\\ \;\;\;\;t_1 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625)))
   (if (or (<= (* b a) -1.75e+176) (not (<= (* b a) 1.8e+179)))
     (- t_1 (* (* b a) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double tmp;
	if (((b * a) <= -1.75e+176) || !((b * a) <= 1.8e+179)) {
		tmp = t_1 - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (z * t) * 0.0625d0
    if (((b * a) <= (-1.75d+176)) .or. (.not. ((b * a) <= 1.8d+179))) then
        tmp = t_1 - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double tmp;
	if (((b * a) <= -1.75e+176) || !((b * a) <= 1.8e+179)) {
		tmp = t_1 - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	tmp = 0
	if ((b * a) <= -1.75e+176) or not ((b * a) <= 1.8e+179):
		tmp = t_1 - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if ((Float64(b * a) <= -1.75e+176) || !(Float64(b * a) <= 1.8e+179))
		tmp = Float64(t_1 - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	tmp = 0.0;
	if (((b * a) <= -1.75e+176) || ~(((b * a) <= 1.8e+179)))
		tmp = t_1 - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[Or[LessEqual[N[(b * a), $MachinePrecision], -1.75e+176], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.8e+179]], $MachinePrecision]], N[(t$95$1 - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.75000000000000001e176 or 1.7999999999999999e179 < (*.f64 a b)

   1. Initial program 95.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 89.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 85.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.75000000000000001e176 < (*.f64 a b) < 1.7999999999999999e179

   1. Initial program 99.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 91.3%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.75 \cdot 10^{+176} \lor \neg \left(b \cdot a \leq 1.8 \cdot 10^{+179}\right):\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 9: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+71} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot y + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -2e+71) (not (<= (* b a) 2e+111)))
   (+ (* x y) (- c (/ a (/ 4.0 b))))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -2e+71) || !((b * a) <= 2e+111)) {
		tmp = (x * y) + (c - (a / (4.0 / b)));
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((b * a) <= (-2d+71)) .or. (.not. ((b * a) <= 2d+111))) then
        tmp = (x * y) + (c - (a / (4.0d0 / b)))
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    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 tmp;
	if (((b * a) <= -2e+71) || !((b * a) <= 2e+111)) {
		tmp = (x * y) + (c - (a / (4.0 / b)));
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -2e+71) or not ((b * a) <= 2e+111):
		tmp = (x * y) + (c - (a / (4.0 / b)))
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -2e+71) || !(Float64(b * a) <= 2e+111))
		tmp = Float64(Float64(x * y) + Float64(c - Float64(a / Float64(4.0 / b))));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -2e+71) || ~(((b * a) <= 2e+111)))
		tmp = (x * y) + (c - (a / (4.0 / b)));
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -2e+71], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+111]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c - N[(a / N[(4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.0000000000000001e71 or 1.99999999999999991e111 < (*.f64 a b)

   1. Initial program 96.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 96.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. sub-neg 96.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. neg-mul-1 96.6%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{-1 \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      4. metadata-eval 96.6%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{\left(-1\right)} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      5. metadata-eval 96.6%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      6. cancel-sign-sub-inv 96.6%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      7. fma-def 96.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      8. associate-/l* 96.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{\frac{16}{t}}}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      9. metadata-eval 96.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{1} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      10. *-lft-identity 96.6%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{\left(\frac{a \cdot b}{4} - c\right)} \]

      11. associate-/l* 96.5%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\color{blue}{\frac{a}{\frac{4}{b}}} - c\right) \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 96.5%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{\frac{16}{t}}\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      2. associate-/l* 96.5%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. +-commutative 96.5%

         \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      4. associate-/l* 96.5%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. div-inv 96.5%

         \[\leadsto \left(\color{blue}{z \cdot \frac{1}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      6. clear-num 96.5%

         \[\leadsto \left(z \cdot \color{blue}{\frac{t}{16}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      7. div-inv 96.5%

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot \frac{1}{16}\right)} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      8. metadata-eval 96.5%

         \[\leadsto \left(z \cdot \left(t \cdot \color{blue}{0.0625}\right) + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 0.0625\right) + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in z around 0 85.8%

      \[\leadsto \color{blue}{y \cdot x} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   if -2.0000000000000001e71 < (*.f64 a b) < 1.99999999999999991e111

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 94.9%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+71} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot y + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 10: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+71} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -2e+71) (not (<= (* b a) 2e+111)))
   (- (+ c (* x y)) (* (* b a) 0.25))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -2e+71) || !((b * a) <= 2e+111)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((b * a) <= (-2d+71)) .or. (.not. ((b * a) <= 2d+111))) then
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    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 tmp;
	if (((b * a) <= -2e+71) || !((b * a) <= 2e+111)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -2e+71) or not ((b * a) <= 2e+111):
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -2e+71) || !(Float64(b * a) <= 2e+111))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -2e+71) || ~(((b * a) <= 2e+111)))
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -2e+71], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+111]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.0000000000000001e71 or 1.99999999999999991e111 < (*.f64 a b)

   1. Initial program 96.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 85.9%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2.0000000000000001e71 < (*.f64 a b) < 1.99999999999999991e111

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 94.9%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+71} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 11: 86.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.35 \cdot 10^{+148}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq 4.3 \cdot 10^{+172}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* b a) -1.35e+148)
   (+ c (* -0.25 (* b a)))
   (if (<= (* b a) 4.3e+172)
     (+ c (+ (* x y) (* (* z t) 0.0625)))
     (- (* x y) (* (* b a) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b * a) <= -1.35e+148) {
		tmp = c + (-0.25 * (b * a));
	} else if ((b * a) <= 4.3e+172) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (x * y) - ((b * a) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if ((b * a) <= (-1.35d+148)) then
        tmp = c + ((-0.25d0) * (b * a))
    else if ((b * a) <= 4.3d+172) then
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    else
        tmp = (x * y) - ((b * a) * 0.25d0)
    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 tmp;
	if ((b * a) <= -1.35e+148) {
		tmp = c + (-0.25 * (b * a));
	} else if ((b * a) <= 4.3e+172) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (x * y) - ((b * a) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b * a) <= -1.35e+148:
		tmp = c + (-0.25 * (b * a))
	elif (b * a) <= 4.3e+172:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	else:
		tmp = (x * y) - ((b * a) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b * a) <= -1.35e+148)
		tmp = Float64(c + Float64(-0.25 * Float64(b * a)));
	elseif (Float64(b * a) <= 4.3e+172)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b * a) <= -1.35e+148)
		tmp = c + (-0.25 * (b * a));
	elseif ((b * a) <= 4.3e+172)
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	else
		tmp = (x * y) - ((b * a) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b * a), $MachinePrecision], -1.35e+148], N[(c + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 4.3e+172], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.35000000000000009e148

   1. Initial program 93.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 84.2%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 84.2%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

   4. Simplified 84.2%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

   if -1.35000000000000009e148 < (*.f64 a b) < 4.3000000000000003e172

   1. Initial program 99.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 91.7%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   if 4.3000000000000003e172 < (*.f64 a b)

   1. Initial program 96.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 86.7%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 80.9%

      \[\leadsto \color{blue}{y \cdot x - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.35 \cdot 10^{+148}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq 4.3 \cdot 10^{+172}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-275}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-112}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625)))
   (if (<= t -6.6e-6)
     t_1
     (if (<= t -4.4e-226)
       (* x y)
       (if (<= t -1.85e-275)
         c
         (if (<= t 9.2e-236)
           (* x y)
           (if (<= t 2.4e-112) c (if (<= t 5e+78) (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double tmp;
	if (t <= -6.6e-6) {
		tmp = t_1;
	} else if (t <= -4.4e-226) {
		tmp = x * y;
	} else if (t <= -1.85e-275) {
		tmp = c;
	} else if (t <= 9.2e-236) {
		tmp = x * y;
	} else if (t <= 2.4e-112) {
		tmp = c;
	} else if (t <= 5e+78) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (z * t) * 0.0625d0
    if (t <= (-6.6d-6)) then
        tmp = t_1
    else if (t <= (-4.4d-226)) then
        tmp = x * y
    else if (t <= (-1.85d-275)) then
        tmp = c
    else if (t <= 9.2d-236) then
        tmp = x * y
    else if (t <= 2.4d-112) then
        tmp = c
    else if (t <= 5d+78) then
        tmp = x * y
    else
        tmp = 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 t_1 = (z * t) * 0.0625;
	double tmp;
	if (t <= -6.6e-6) {
		tmp = t_1;
	} else if (t <= -4.4e-226) {
		tmp = x * y;
	} else if (t <= -1.85e-275) {
		tmp = c;
	} else if (t <= 9.2e-236) {
		tmp = x * y;
	} else if (t <= 2.4e-112) {
		tmp = c;
	} else if (t <= 5e+78) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	tmp = 0
	if t <= -6.6e-6:
		tmp = t_1
	elif t <= -4.4e-226:
		tmp = x * y
	elif t <= -1.85e-275:
		tmp = c
	elif t <= 9.2e-236:
		tmp = x * y
	elif t <= 2.4e-112:
		tmp = c
	elif t <= 5e+78:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if (t <= -6.6e-6)
		tmp = t_1;
	elseif (t <= -4.4e-226)
		tmp = Float64(x * y);
	elseif (t <= -1.85e-275)
		tmp = c;
	elseif (t <= 9.2e-236)
		tmp = Float64(x * y);
	elseif (t <= 2.4e-112)
		tmp = c;
	elseif (t <= 5e+78)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	tmp = 0.0;
	if (t <= -6.6e-6)
		tmp = t_1;
	elseif (t <= -4.4e-226)
		tmp = x * y;
	elseif (t <= -1.85e-275)
		tmp = c;
	elseif (t <= 9.2e-236)
		tmp = x * y;
	elseif (t <= 2.4e-112)
		tmp = c;
	elseif (t <= 5e+78)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[t, -6.6e-6], t$95$1, If[LessEqual[t, -4.4e-226], N[(x * y), $MachinePrecision], If[LessEqual[t, -1.85e-275], c, If[LessEqual[t, 9.2e-236], N[(x * y), $MachinePrecision], If[LessEqual[t, 2.4e-112], c, If[LessEqual[t, 5e+78], N[(x * y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.60000000000000034e-6 or 4.99999999999999984e78 < t

   1. Initial program 97.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 78.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in t around inf 50.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]

   if -6.60000000000000034e-6 < t < -4.4e-226 or -1.84999999999999985e-275 < t < 9.20000000000000024e-236 or 2.4000000000000001e-112 < t < 4.99999999999999984e78

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 71.3%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   3. Taylor expanded in c around 0 46.9%

      \[\leadsto \color{blue}{y \cdot x + 0.0625 \cdot \left(t \cdot z\right)} \]

   4. Taylor expanded in y around inf 36.7%

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

   if -4.4e-226 < t < -1.84999999999999985e-275 or 9.20000000000000024e-236 < t < 2.4000000000000001e-112

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 56.0%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-6}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-275}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-112}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 13: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + -0.25 \cdot \left(b \cdot a\right)\\ t_2 := x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;z \leq -4 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -57000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-274}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* -0.25 (* b a)))) (t_2 (+ (* x y) (* (* z t) 0.0625))))
   (if (<= z -4e+89)
     t_2
     (if (<= z -57000.0)
       t_1
       (if (<= z -2.3e-274) (+ c (* x y)) (if (<= z 8e-108) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (-0.25 * (b * a));
	double t_2 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if (z <= -4e+89) {
		tmp = t_2;
	} else if (z <= -57000.0) {
		tmp = t_1;
	} else if (z <= -2.3e-274) {
		tmp = c + (x * y);
	} else if (z <= 8e-108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + ((-0.25d0) * (b * a))
    t_2 = (x * y) + ((z * t) * 0.0625d0)
    if (z <= (-4d+89)) then
        tmp = t_2
    else if (z <= (-57000.0d0)) then
        tmp = t_1
    else if (z <= (-2.3d-274)) then
        tmp = c + (x * y)
    else if (z <= 8d-108) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = c + (-0.25 * (b * a));
	double t_2 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if (z <= -4e+89) {
		tmp = t_2;
	} else if (z <= -57000.0) {
		tmp = t_1;
	} else if (z <= -2.3e-274) {
		tmp = c + (x * y);
	} else if (z <= 8e-108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (-0.25 * (b * a))
	t_2 = (x * y) + ((z * t) * 0.0625)
	tmp = 0
	if z <= -4e+89:
		tmp = t_2
	elif z <= -57000.0:
		tmp = t_1
	elif z <= -2.3e-274:
		tmp = c + (x * y)
	elif z <= 8e-108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(-0.25 * Float64(b * a)))
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625))
	tmp = 0.0
	if (z <= -4e+89)
		tmp = t_2;
	elseif (z <= -57000.0)
		tmp = t_1;
	elseif (z <= -2.3e-274)
		tmp = Float64(c + Float64(x * y));
	elseif (z <= 8e-108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (-0.25 * (b * a));
	t_2 = (x * y) + ((z * t) * 0.0625);
	tmp = 0.0;
	if (z <= -4e+89)
		tmp = t_2;
	elseif (z <= -57000.0)
		tmp = t_1;
	elseif (z <= -2.3e-274)
		tmp = c + (x * y);
	elseif (z <= 8e-108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+89], t$95$2, If[LessEqual[z, -57000.0], t$95$1, If[LessEqual[z, -2.3e-274], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999998e89 or 8.00000000000000032e-108 < z

   1. Initial program 97.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 82.7%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   3. Taylor expanded in c around 0 69.1%

      \[\leadsto \color{blue}{y \cdot x + 0.0625 \cdot \left(t \cdot z\right)} \]

   if -3.99999999999999998e89 < z < -57000 or -2.29999999999999996e-274 < z < 8.00000000000000032e-108

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 74.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 74.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

   4. Simplified 74.9%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

   if -57000 < z < -2.29999999999999996e-274

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 67.8%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+89}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;z \leq -57000:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-274}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-108}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 14: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c + \left(\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (+ (/ (* z t) 16.0) (* x y)) (/ (* b a) 4.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = c + ((((z * t) / 16.0d0) + (x * y)) - ((b * a) / 4.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0));
}

Python

def code(x, y, z, t, a, b, c):
	return c + ((((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(Float64(Float64(z * t) / 16.0) + Float64(x * y)) - Float64(Float64(b * a) / 4.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + ((((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Final simplification 98.4%

   \[\leadsto c + \left(\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\right) \]

Alternative 15: 63.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5.1 \cdot 10^{+174} \lor \neg \left(b \cdot a \leq 1.35 \cdot 10^{+182}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -5.1e+174) (not (<= (* b a) 1.35e+182)))
   (* -0.25 (* b a))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -5.1e+174) || !((b * a) <= 1.35e+182)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((b * a) <= (-5.1d+174)) .or. (.not. ((b * a) <= 1.35d+182))) then
        tmp = (-0.25d0) * (b * a)
    else
        tmp = c + (x * y)
    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 tmp;
	if (((b * a) <= -5.1e+174) || !((b * a) <= 1.35e+182)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -5.1e+174) or not ((b * a) <= 1.35e+182):
		tmp = -0.25 * (b * a)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -5.1e+174) || !(Float64(b * a) <= 1.35e+182))
		tmp = Float64(-0.25 * Float64(b * a));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -5.1e+174) || ~(((b * a) <= 1.35e+182)))
		tmp = -0.25 * (b * a);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -5.1e+174], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.35e+182]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0999999999999997e174 or 1.3500000000000001e182 < (*.f64 a b)

   1. Initial program 95.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 95.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. sub-neg 95.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\left(\frac{a \cdot b}{4} - c\right)\right)} \]

      3. neg-mul-1 95.0%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{-1 \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      4. metadata-eval 95.0%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \color{blue}{\left(-1\right)} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      5. metadata-eval 95.0%

         \[\leadsto \left(x \cdot y + \frac{z \cdot t}{16}\right) + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      6. cancel-sign-sub-inv 95.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right)} \]

      7. fma-def 95.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16}\right)} - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      8. associate-/l* 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{\frac{16}{t}}}\right) - \left(--1\right) \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      9. metadata-eval 94.9%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{1} \cdot \left(\frac{a \cdot b}{4} - c\right) \]

      10. *-lft-identity 94.9%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{\left(\frac{a \cdot b}{4} - c\right)} \]

      11. associate-/l* 94.8%

          \[\leadsto \mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\color{blue}{\frac{a}{\frac{4}{b}}} - c\right) \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right)} \]
   4. Step-by-step derivation

      1. fma-udef 94.8%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z}{\frac{16}{t}}\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      2. associate-/l* 94.8%

         \[\leadsto \left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. +-commutative 94.8%

         \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      4. associate-/l* 94.8%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. div-inv 94.8%

         \[\leadsto \left(\color{blue}{z \cdot \frac{1}{\frac{16}{t}}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      6. clear-num 94.8%

         \[\leadsto \left(z \cdot \color{blue}{\frac{t}{16}} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      7. div-inv 94.8%

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot \frac{1}{16}\right)} + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      8. metadata-eval 94.8%

         \[\leadsto \left(z \cdot \left(t \cdot \color{blue}{0.0625}\right) + x \cdot y\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 0.0625\right) + x \cdot y\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in a around inf 76.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]

   8. Simplified 76.9%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]

   if -5.0999999999999997e174 < (*.f64 a b) < 1.3500000000000001e182

   1. Initial program 99.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 63.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5.1 \cdot 10^{+174} \lor \neg \left(b \cdot a \leq 1.35 \cdot 10^{+182}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 16: 36.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9500000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+83}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -9500000.0) (* x y) (if (<= y 5.5e+83) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -9500000.0) {
		tmp = x * y;
	} else if (y <= 5.5e+83) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (y <= (-9500000.0d0)) then
        tmp = x * y
    else if (y <= 5.5d+83) then
        tmp = c
    else
        tmp = x * y
    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 tmp;
	if (y <= -9500000.0) {
		tmp = x * y;
	} else if (y <= 5.5e+83) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -9500000.0:
		tmp = x * y
	elif y <= 5.5e+83:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -9500000.0)
		tmp = Float64(x * y);
	elseif (y <= 5.5e+83)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -9500000.0)
		tmp = x * y;
	elseif (y <= 5.5e+83)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -9500000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 5.5e+83], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e6 or 5.4999999999999996e83 < y

   1. Initial program 96.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 86.7%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   3. Taylor expanded in c around 0 66.3%

      \[\leadsto \color{blue}{y \cdot x + 0.0625 \cdot \left(t \cdot z\right)} \]

   4. Taylor expanded in y around inf 52.1%

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

   if -9.5e6 < y < 5.4999999999999996e83

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 28.2%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9500000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+83}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 17: 22.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Taylor expanded in c around inf 25.7%

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

3. Final simplification 25.7%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))