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

Percentage Accurate: 97.6% → 99.0%

Time: 8.9s

Alternatives: 13

Speedup: 1.0×

• 32.9% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-+l- 97.3%

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

   2. associate--l+ 97.3%

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

   3. fma-def 98.1%

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

   4. associate-*l/ 98.1%

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

   5. fma-neg 98.5%

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

   6. sub-neg 98.5%

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

   7. distribute-neg-in 98.5%

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

   8. remove-double-neg 98.5%

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

   9. associate-/l* 98.8%

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

   10. distribute-frac-neg 98.8%

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

   11. associate-/r/ 98.8%

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

   12. fma-def 98.8%

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

   13. neg-mul-1 98.8%

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

   14. *-commutative 98.8%

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

   15. associate-/l* 98.8%

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

   16. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ c + \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \left(b \cdot -0.25\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (+ (* x y) (fma t (* z 0.0625) (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((x * y) + fma(t, (z * 0.0625), (a * (b * -0.25))));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(x * y) + fma(t, Float64(z * 0.0625), Float64(a * Float64(b * -0.25)))))
end

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate--l+ 97.3%

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

   2. associate-*l/ 97.3%

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

   3. *-commutative 97.3%

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

   4. fma-neg 97.3%

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

   5. div-inv 97.3%

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

   6. metadata-eval 97.3%

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

   7. associate-/l* 97.6%

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

   8. distribute-frac-neg 97.6%

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

   9. metadata-eval 97.6%

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

   10. distribute-neg-frac 97.6%

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

   11. frac-2neg 97.6%

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

   12. div-inv 97.6%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{a \cdot \frac{1}{\frac{-4}{b}}}\right)\right) + c \]

   13. clear-num 97.7%

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

   14. div-inv 97.7%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \color{blue}{\left(b \cdot \frac{1}{-4}\right)}\right)\right) + c \]

   15. metadata-eval 97.7%

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

3. Applied egg-rr 97.7%

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

4. Final simplification 97.7%

   \[\leadsto c + \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \left(b \cdot -0.25\right)\right)\right) \]

Alternative 3: 98.1% accurate, 0.1× speedup

Math

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

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(Float64(z / 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[(N[(z / 16.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(c + N[(a / N[(-4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.3%

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

   1. sub-neg 97.3%

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

   2. associate-+l+ 97.3%

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

   3. fma-def 97.7%

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

   4. associate-*l/ 97.7%

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

   5. distribute-frac-neg 97.7%

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

   6. distribute-rgt-neg-out 97.7%

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

   7. associate-/l* 98.0%

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

   8. neg-mul-1 98.0%

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

   9. associate-/r* 98.0%

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

   10. metadata-eval 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 4: 42.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -9 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.92 \cdot 10^{+96}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* -0.25 (* a b))))
   (if (<= (* a b) -9e+159)
     t_2
     (if (<= (* a b) -3.5e+46)
       t_1
       (if (<= (* a b) -2.1e+35)
         t_2
         (if (<= (* a b) -1e-316)
           c
           (if (<= (* a b) 3.8e-130)
             t_1
             (if (<= (* a b) 1.92e+96) c t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -9e+159) {
		tmp = t_2;
	} else if ((a * b) <= -3.5e+46) {
		tmp = t_1;
	} else if ((a * b) <= -2.1e+35) {
		tmp = t_2;
	} else if ((a * b) <= -1e-316) {
		tmp = c;
	} else if ((a * b) <= 3.8e-130) {
		tmp = t_1;
	} else if ((a * b) <= 1.92e+96) {
		tmp = c;
	} 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 = 0.0625d0 * (z * t)
    t_2 = (-0.25d0) * (a * b)
    if ((a * b) <= (-9d+159)) then
        tmp = t_2
    else if ((a * b) <= (-3.5d+46)) then
        tmp = t_1
    else if ((a * b) <= (-2.1d+35)) then
        tmp = t_2
    else if ((a * b) <= (-1d-316)) then
        tmp = c
    else if ((a * b) <= 3.8d-130) then
        tmp = t_1
    else if ((a * b) <= 1.92d+96) then
        tmp = c
    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 = 0.0625 * (z * t);
	double t_2 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -9e+159) {
		tmp = t_2;
	} else if ((a * b) <= -3.5e+46) {
		tmp = t_1;
	} else if ((a * b) <= -2.1e+35) {
		tmp = t_2;
	} else if ((a * b) <= -1e-316) {
		tmp = c;
	} else if ((a * b) <= 3.8e-130) {
		tmp = t_1;
	} else if ((a * b) <= 1.92e+96) {
		tmp = c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = -0.25 * (a * b)
	tmp = 0
	if (a * b) <= -9e+159:
		tmp = t_2
	elif (a * b) <= -3.5e+46:
		tmp = t_1
	elif (a * b) <= -2.1e+35:
		tmp = t_2
	elif (a * b) <= -1e-316:
		tmp = c
	elif (a * b) <= 3.8e-130:
		tmp = t_1
	elif (a * b) <= 1.92e+96:
		tmp = c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -9e+159)
		tmp = t_2;
	elseif (Float64(a * b) <= -3.5e+46)
		tmp = t_1;
	elseif (Float64(a * b) <= -2.1e+35)
		tmp = t_2;
	elseif (Float64(a * b) <= -1e-316)
		tmp = c;
	elseif (Float64(a * b) <= 3.8e-130)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.92e+96)
		tmp = c;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = -0.25 * (a * b);
	tmp = 0.0;
	if ((a * b) <= -9e+159)
		tmp = t_2;
	elseif ((a * b) <= -3.5e+46)
		tmp = t_1;
	elseif ((a * b) <= -2.1e+35)
		tmp = t_2;
	elseif ((a * b) <= -1e-316)
		tmp = c;
	elseif ((a * b) <= 3.8e-130)
		tmp = t_1;
	elseif ((a * b) <= 1.92e+96)
		tmp = c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -9e+159], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -3.5e+46], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2.1e+35], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1e-316], c, If[LessEqual[N[(a * b), $MachinePrecision], 3.8e-130], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.92e+96], c, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.00000000000000053e159 or -3.49999999999999985e46 < (*.f64 a b) < -2.0999999999999999e35 or 1.92e96 < (*.f64 a b)

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0 87.0%

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

   3. Taylor expanded in c around 0 80.7%

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

   4. Taylor expanded in t around 0 74.2%

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

   if -9.00000000000000053e159 < (*.f64 a b) < -3.49999999999999985e46 or -9.999999837e-317 < (*.f64 a b) < 3.7999999999999998e-130

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-neg 100.0%

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

      5. div-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. associate-/l* 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. distribute-neg-frac 100.0%

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

      11. frac-2neg 100.0%

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

      12. div-inv 100.0%

          \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{a \cdot \frac{1}{\frac{-4}{b}}}\right)\right) + c \]

      13. clear-num 100.0%

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

      14. div-inv 100.0%

          \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \color{blue}{\left(b \cdot \frac{1}{-4}\right)}\right)\right) + c \]

      15. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*r* 59.3%

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

      3. *-commutative 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in t around inf 38.4%

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

   if -2.0999999999999999e35 < (*.f64 a b) < -9.999999837e-317 or 3.7999999999999998e-130 < (*.f64 a b) < 1.92e96

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. associate-+l+ 97.9%

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

      3. fma-def 99.0%

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

      4. associate-*l/ 99.0%

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

      5. distribute-frac-neg 99.0%

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

      6. distribute-rgt-neg-out 99.0%

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

      7. associate-/l* 99.0%

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

      8. neg-mul-1 99.0%

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

      9. associate-/r* 99.0%

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

      10. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in c around inf 41.4%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9 \cdot 10^{+159}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 1.92 \cdot 10^{+96}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 5: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -4.2 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* 0.0625 (* z t))) (t_3 (* -0.25 (* a b))))
   (if (<= (* a b) -8e+159)
     t_3
     (if (<= (* a b) -1.05e-17)
       t_1
       (if (<= (* a b) -4.2e-46)
         t_2
         (if (<= (* a b) 1e-251)
           t_1
           (if (<= (* a b) 1.2e-185)
             t_2
             (if (<= (* a b) 3.8e+98) t_1 t_3))))))))

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 = 0.0625 * (z * t);
	double t_3 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -8e+159) {
		tmp = t_3;
	} else if ((a * b) <= -1.05e-17) {
		tmp = t_1;
	} else if ((a * b) <= -4.2e-46) {
		tmp = t_2;
	} else if ((a * b) <= 1e-251) {
		tmp = t_1;
	} else if ((a * b) <= 1.2e-185) {
		tmp = t_2;
	} else if ((a * b) <= 3.8e+98) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = 0.0625d0 * (z * t)
    t_3 = (-0.25d0) * (a * b)
    if ((a * b) <= (-8d+159)) then
        tmp = t_3
    else if ((a * b) <= (-1.05d-17)) then
        tmp = t_1
    else if ((a * b) <= (-4.2d-46)) then
        tmp = t_2
    else if ((a * b) <= 1d-251) then
        tmp = t_1
    else if ((a * b) <= 1.2d-185) then
        tmp = t_2
    else if ((a * b) <= 3.8d+98) then
        tmp = t_1
    else
        tmp = t_3
    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 = 0.0625 * (z * t);
	double t_3 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -8e+159) {
		tmp = t_3;
	} else if ((a * b) <= -1.05e-17) {
		tmp = t_1;
	} else if ((a * b) <= -4.2e-46) {
		tmp = t_2;
	} else if ((a * b) <= 1e-251) {
		tmp = t_1;
	} else if ((a * b) <= 1.2e-185) {
		tmp = t_2;
	} else if ((a * b) <= 3.8e+98) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = 0.0625 * (z * t)
	t_3 = -0.25 * (a * b)
	tmp = 0
	if (a * b) <= -8e+159:
		tmp = t_3
	elif (a * b) <= -1.05e-17:
		tmp = t_1
	elif (a * b) <= -4.2e-46:
		tmp = t_2
	elif (a * b) <= 1e-251:
		tmp = t_1
	elif (a * b) <= 1.2e-185:
		tmp = t_2
	elif (a * b) <= 3.8e+98:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -8e+159)
		tmp = t_3;
	elseif (Float64(a * b) <= -1.05e-17)
		tmp = t_1;
	elseif (Float64(a * b) <= -4.2e-46)
		tmp = t_2;
	elseif (Float64(a * b) <= 1e-251)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.2e-185)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.8e+98)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = 0.0625 * (z * t);
	t_3 = -0.25 * (a * b);
	tmp = 0.0;
	if ((a * b) <= -8e+159)
		tmp = t_3;
	elseif ((a * b) <= -1.05e-17)
		tmp = t_1;
	elseif ((a * b) <= -4.2e-46)
		tmp = t_2;
	elseif ((a * b) <= 1e-251)
		tmp = t_1;
	elseif ((a * b) <= 1.2e-185)
		tmp = t_2;
	elseif ((a * b) <= 3.8e+98)
		tmp = t_1;
	else
		tmp = t_3;
	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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -8e+159], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -1.05e-17], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -4.2e-46], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1e-251], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.2e-185], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+98], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -7.9999999999999994e159 or 3.7999999999999999e98 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 87.8%

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

   3. Taylor expanded in c around 0 81.3%

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

   4. Taylor expanded in t around 0 73.7%

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

   if -7.9999999999999994e159 < (*.f64 a b) < -1.04999999999999996e-17 or -4.19999999999999975e-46 < (*.f64 a b) < 1.00000000000000002e-251 or 1.2000000000000001e-185 < (*.f64 a b) < 3.7999999999999999e98

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 73.4%

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

   if -1.04999999999999996e-17 < (*.f64 a b) < -4.19999999999999975e-46 or 1.00000000000000002e-251 < (*.f64 a b) < 1.2000000000000001e-185

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-neg 100.0%

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

      5. div-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. associate-/l* 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. distribute-neg-frac 100.0%

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

      11. frac-2neg 100.0%

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

      12. div-inv 100.0%

          \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{a \cdot \frac{1}{\frac{-4}{b}}}\right)\right) + c \]

      13. clear-num 100.0%

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

      14. div-inv 100.0%

          \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \color{blue}{\left(b \cdot \frac{1}{-4}\right)}\right)\right) + c \]

      15. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-*r* 93.7%

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

      3. *-commutative 93.7%

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

   6. Simplified 93.7%

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

   7. Taylor expanded in t around inf 85.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+159}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -4.2 \cdot 10^{-46}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{-251}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{-185}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 6: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.75 \cdot 10^{-203}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -9.5e+83)
     t_2
     (if (<= (* x y) -2.6e-92)
       t_1
       (if (<= (* x y) -3.75e-203)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 5.4e+75) 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 + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -9.5e+83) {
		tmp = t_2;
	} else if ((x * y) <= -2.6e-92) {
		tmp = t_1;
	} else if ((x * y) <= -3.75e-203) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 5.4e+75) {
		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 + (a * (b * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-9.5d+83)) then
        tmp = t_2
    else if ((x * y) <= (-2.6d-92)) then
        tmp = t_1
    else if ((x * y) <= (-3.75d-203)) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 5.4d+75) 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 + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -9.5e+83) {
		tmp = t_2;
	} else if ((x * y) <= -2.6e-92) {
		tmp = t_1;
	} else if ((x * y) <= -3.75e-203) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 5.4e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -9.5e+83:
		tmp = t_2
	elif (x * y) <= -2.6e-92:
		tmp = t_1
	elif (x * y) <= -3.75e-203:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 5.4e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -9.5e+83)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.6e-92)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.75e-203)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 5.4e+75)
		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 + (a * (b * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -9.5e+83)
		tmp = t_2;
	elseif ((x * y) <= -2.6e-92)
		tmp = t_1;
	elseif ((x * y) <= -3.75e-203)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 5.4e+75)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9.5e+83], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e-92], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.75e-203], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.4e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.5000000000000002e83 or 5.39999999999999996e75 < (*.f64 x y)

   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 inf 75.0%

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

   if -9.5000000000000002e83 < (*.f64 x y) < -2.6e-92 or -3.75000000000000014e-203 < (*.f64 x y) < 5.39999999999999996e75

   1. Initial program 99.2%

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

   2. Taylor expanded in a around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*r* 75.5%

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

   4. Simplified 75.5%

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

   if -2.6e-92 < (*.f64 x y) < -3.75000000000000014e-203

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 84.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -3.75 \cdot 10^{-203}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 7: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{-185}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* -0.25 (* a b))))
   (if (<= (* a b) -3.5e+159)
     t_2
     (if (<= (* a b) 2.5e-296)
       t_1
       (if (<= (* a b) 2.8e-185)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* a b) 3.8e+98) 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 * (a * b);
	double tmp;
	if ((a * b) <= -3.5e+159) {
		tmp = t_2;
	} else if ((a * b) <= 2.5e-296) {
		tmp = t_1;
	} else if ((a * b) <= 2.8e-185) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 3.8e+98) {
		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) * (a * b)
    if ((a * b) <= (-3.5d+159)) then
        tmp = t_2
    else if ((a * b) <= 2.5d-296) then
        tmp = t_1
    else if ((a * b) <= 2.8d-185) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((a * b) <= 3.8d+98) 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 * (a * b);
	double tmp;
	if ((a * b) <= -3.5e+159) {
		tmp = t_2;
	} else if ((a * b) <= 2.5e-296) {
		tmp = t_1;
	} else if ((a * b) <= 2.8e-185) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 3.8e+98) {
		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 * (a * b)
	tmp = 0
	if (a * b) <= -3.5e+159:
		tmp = t_2
	elif (a * b) <= 2.5e-296:
		tmp = t_1
	elif (a * b) <= 2.8e-185:
		tmp = c + (0.0625 * (z * t))
	elif (a * b) <= 3.8e+98:
		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(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -3.5e+159)
		tmp = t_2;
	elseif (Float64(a * b) <= 2.5e-296)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.8e-185)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 3.8e+98)
		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 * (a * b);
	tmp = 0.0;
	if ((a * b) <= -3.5e+159)
		tmp = t_2;
	elseif ((a * b) <= 2.5e-296)
		tmp = t_1;
	elseif ((a * b) <= 2.8e-185)
		tmp = c + (0.0625 * (z * t));
	elseif ((a * b) <= 3.8e+98)
		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[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.5e+159], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2.5e-296], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.8e-185], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+98], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.4999999999999999e159 or 3.7999999999999999e98 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 87.8%

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

   3. Taylor expanded in c around 0 81.3%

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

   4. Taylor expanded in t around 0 73.7%

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

   if -3.4999999999999999e159 < (*.f64 a b) < 2.50000000000000015e-296 or 2.79999999999999991e-185 < (*.f64 a b) < 3.7999999999999999e98

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 71.8%

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

   if 2.50000000000000015e-296 < (*.f64 a b) < 2.79999999999999991e-185

   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 z around inf 86.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+159}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{-296}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{-185}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-29}:\\ \;\;\;\;c + \left(t_1 - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* x y) -1.2e+86)
     (+ c (+ (* x y) t_1))
     (if (<= (* x y) 6e-29) (+ c (- t_1 t_2)) (+ c (- (* x y) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((x * y) <= -1.2e+86) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 6e-29) {
		tmp = c + (t_1 - t_2);
	} else {
		tmp = c + ((x * y) - 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 = 0.0625d0 * (z * t)
    t_2 = (a * b) * 0.25d0
    if ((x * y) <= (-1.2d+86)) then
        tmp = c + ((x * y) + t_1)
    else if ((x * y) <= 6d-29) then
        tmp = c + (t_1 - t_2)
    else
        tmp = c + ((x * y) - 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 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((x * y) <= -1.2e+86) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 6e-29) {
		tmp = c + (t_1 - t_2);
	} else {
		tmp = c + ((x * y) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	tmp = 0
	if (x * y) <= -1.2e+86:
		tmp = c + ((x * y) + t_1)
	elif (x * y) <= 6e-29:
		tmp = c + (t_1 - t_2)
	else:
		tmp = c + ((x * y) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(x * y) <= -1.2e+86)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	elseif (Float64(x * y) <= 6e-29)
		tmp = Float64(c + Float64(t_1 - t_2));
	else
		tmp = Float64(c + Float64(Float64(x * y) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((x * y) <= -1.2e+86)
		tmp = c + ((x * y) + t_1);
	elseif ((x * y) <= 6e-29)
		tmp = c + (t_1 - t_2);
	else
		tmp = c + ((x * y) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.2e+86], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e-29], N[(c + N[(t$95$1 - t$95$2), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.2e86

   1. Initial program 95.2%

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

   2. Taylor expanded in a around 0 88.3%

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

   if -1.2e86 < (*.f64 x y) < 6.0000000000000005e-29

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0 94.8%

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

   if 6.0000000000000005e-29 < (*.f64 x y)

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 91.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-29}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \end{array} \]

Alternative 9: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+171} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+160}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+171) (not (<= (* a b) 2e+160)))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+171) || !((a * b) <= 2e+160)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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 (((a * b) <= (-5d+171)) .or. (.not. ((a * b) <= 2d+160))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+171) || !((a * b) <= 2e+160)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+171) or not ((a * b) <= 2e+160):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+171) || !(Float64(a * b) <= 2e+160))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+171) || ~(((a * b) <= 2e+160)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+171], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+160]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000004e171 or 2.00000000000000001e160 < (*.f64 a b)

   1. Initial program 93.6%

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

   2. Taylor expanded in a around inf 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*r* 86.9%

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

   4. Simplified 86.9%

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

   if -5.0000000000000004e171 < (*.f64 a b) < 2.00000000000000001e160

   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 a around 0 89.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+171} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+160}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 10: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-8} \lor \neg \left(a \cdot b \leq 10^{+77}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e-8) (not (<= (* a b) 1e+77)))
   (+ c (- (* x y) (* (* a b) 0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e-8) || !((a * b) <= 1e+77)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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 (((a * b) <= (-1d-8)) .or. (.not. ((a * b) <= 1d+77))) then
        tmp = c + ((x * y) - ((a * b) * 0.25d0))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e-8) || !((a * b) <= 1e+77)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1e-8) or not ((a * b) <= 1e+77):
		tmp = c + ((x * y) - ((a * b) * 0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1e-8) || !(Float64(a * b) <= 1e+77))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1e-8) || ~(((a * b) <= 1e+77)))
		tmp = c + ((x * y) - ((a * b) * 0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e-8], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+77]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1e-8 or 9.99999999999999983e76 < (*.f64 a b)

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 84.9%

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

   if -1e-8 < (*.f64 a b) < 9.99999999999999983e76

   1. Initial program 98.6%

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

   2. Taylor expanded in a around 0 96.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-8} \lor \neg \left(a \cdot b \leq 10^{+77}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (((x * y) + ((z * t) / 16.0)) - ((a * b) / 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 + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 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 + (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Final simplification 97.3%

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

Alternative 12: 41.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.2 \cdot 10^{+31} \lor \neg \left(a \cdot b \leq 9.5 \cdot 10^{+95}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2.2e+31) (not (<= (* a b) 9.5e+95)))
   (* -0.25 (* a b))
   c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2.2e+31) || !((a * b) <= 9.5e+95)) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = c;
	}
	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 (((a * b) <= (-2.2d+31)) .or. (.not. ((a * b) <= 9.5d+95))) then
        tmp = (-0.25d0) * (a * b)
    else
        tmp = c
    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 (((a * b) <= -2.2e+31) || !((a * b) <= 9.5e+95)) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2.2e+31) or not ((a * b) <= 9.5e+95):
		tmp = -0.25 * (a * b)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2.2e+31) || !(Float64(a * b) <= 9.5e+95))
		tmp = Float64(-0.25 * Float64(a * b));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2.2e+31) || ~(((a * b) <= 9.5e+95)))
		tmp = -0.25 * (a * b);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2.2e+31], N[Not[LessEqual[N[(a * b), $MachinePrecision], 9.5e+95]], $MachinePrecision]], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.2000000000000001e31 or 9.5000000000000004e95 < (*.f64 a b)

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in c around 0 77.8%

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

   4. Taylor expanded in t around 0 65.9%

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

   if -2.2000000000000001e31 < (*.f64 a b) < 9.5000000000000004e95

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. fma-def 99.3%

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

      4. associate-*l/ 99.3%

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

      5. distribute-frac-neg 99.3%

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

      6. distribute-rgt-neg-out 99.3%

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

      7. associate-/l* 99.3%

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

      8. neg-mul-1 99.3%

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

      9. associate-/r* 99.3%

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

      10. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in c around inf 34.5%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.2 \cdot 10^{+31} \lor \neg \left(a \cdot b \leq 9.5 \cdot 10^{+95}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 13: 22.2% 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 97.3%

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

   1. sub-neg 97.3%

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

   2. associate-+l+ 97.3%

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

   3. fma-def 97.7%

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

   4. associate-*l/ 97.7%

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

   5. distribute-frac-neg 97.7%

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

   6. distribute-rgt-neg-out 97.7%

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

   7. associate-/l* 98.0%

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

   8. neg-mul-1 98.0%

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

   9. associate-/r* 98.0%

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

   10. metadata-eval 98.0%

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

3. Simplified 98.0%

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

4. Taylor expanded in c around inf 24.6%

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

5. Final simplification 24.6%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023322 
(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))